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The Saddest Thing Is That I Have Had to Use Words: A Madeline Gins Reader
Madeline Gins, edited by Lucy Ives. Siglio, $28 (328p) ISBN 978-1-938221-24-8
ARCHITECTURAL BODY
This wide-ranging, energetic anthology of poetry and experimental fiction, with an authoritative introduction by Ives (Loudermilk) shows how Gins (1941–2014) explored the possibilities of literary form and its relationship to content. Gins published more than a dozen books, and also worked extensively as an architect and visual artist. These disciplines are exhilaratingly expressed in her poetry, formed by unusual typefaces and lists. Some poems look handwritten and smudged and/or crossed out, as Gins works with the look and sounds of words. Also included are two early essays, lengthy excerpts from two other books, and her experimental novel cum artist's book, Word Rain (1969), which employs a sensual approach to language and the confines of the page ("I massage geometry with a scented oil. The maintenance of lips. The battles of containers. I speak in the midst of a sifted silence"). Gins's playfulness emerges in unattributed quotes from modernist literature (Beckett, Woolf) along with graphic design elements, such as a thumb protruding from the side of a page. At one point, Gins writes, "Words are moving over me." A long section of imperatives—by turns ominous, hilarious, trivial—appears in all caps separated by white space. Stimulating and consistently surprising, this is a treat for those interested in interdisciplinary artists such as John Cage. (Apr.)
Reviewed on : 02/26/2020


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Charlie Lyons is an American media executive and a producer of motion pictures, television, and stage. He is the managing partner of Holding Pictures and a partner in Beacon Communications. Lyons' film and stage enterprises have generated over two billion dollars in revenue and worldwide critical acclaim. He is a business partner and advisor to Kevin Costner and TIG Productions. He is also a frequent collaborator with Harrison Ford Productions.

Lyons and his companies have produced dozens of films, including Air Force One, The Water Horse, Open Range, The Guardian, Spy Game, The Family Man, Firewall, Raising Helen, A Lot Like Love, The Hurricane and Thirteen Days. Lyons executive produces and guides the multi-platform Bring It On Franchise. He was producer and presenter of Bring It On The Musical, which toured throughout the United States and overseas. Bring It On had a Broadway engagement at the Historic St. James Theater and was nominated for two Tony Awards, including Best Musical, and five Drama Desk Awards.

Lyons is the founder and past chairman / CEO of Ascent Entertainment Group Inc., a global media company. In 1990, Lyons was hired to lead the turnaround of a division of Comsat Corporation. He built the division into a public company to include On Command Corporation (the largest worldwide hotel VOD cable, satellite and Internet network), Ascent Network Services (the broadcast provider for NBC), the NBA's Denver Nuggets, the NHL's Colorado Avalanche, Colorado Studios (later known as HDNet) and Beacon Communications.

Ascent developed and financed the Pepsi Center, home to over 200 live events annually. In May of 1995, Ascent acquired the Quebec Nordiques and relocated the team to Denver.  The franchise was renamed the Colorado Avalanche. In 1996, they won the Stanley Cup, bringing the city its first world championship. The Avalanche won eight division titles, an NHL record, and qualified for the playoffs 10 years in a row. They hold an all-time NHL record for consecutive sellouts at home (487).

In the 1980s Lyons held numerous executive positions for the Marriott Corporation.

Lyons began his career as an aide to Vice President of the United States Nelson A. Rockefeller. He worked with the Hon. William D. Rogers to finalize the Panama Canal Treaties. He has served on corporate and charitable boards, including the National Basketball Association, the Women's National Basketball Association, National Hockey League, National Jewish Hospital and Gallaudet University. Lyons is a graduate of Washington University in St. Louis, and completed the SMM Executive Program at Harvard Business School. He is an instrument-rated pilot.

References

Colorado Avalanche executives
National Hockey League executives
Stanley Cup champions
Year of birth missing (living people)
Living people
Washington University in St. Louis alumni
Harvard Business School alumni

redpajama_set_name: RedPajamaWikipedia


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Actonel EC 35mg tablet - oval yellow tablet, with EC 35 marked on one side.


Fashion tackles football helmets for Super Bowl XLVIII.
If the fashion industry started playing football this is what their helmets would look like. Forty-eight design houses have created one-of-a-kind helmets in partnership with the CFDA and the NFL. The creations from brands like Rag and Bone, Public School (shown above) and Marchesa range from black matte leather with simple detailing to 3D-all over lace prints. The helmets will be auctioned off to benefit the NFL Foundation, a nonprofit organization which supports educational football programs, health and safety measures in sports, and community health initiatives.
Bidding on the helmets will take place from January 15 to February 4.
See more of the customized helmets for Super Bowl XLVIII below.


But don't take our word for it: Sri Panwa Resort has won the Award for Best Thailand Property Developer (2012 by Thailand Property Award), the Award for Best World 3 Beach Bars (2011 by CNN), the Award for Hotel with the Best View in the World (2011 by Best Beach Property UK), voted in the Hot 100 Coolest Place (2010 by Australian Gourmet Traveller), awarded Excellence for 2010-2012 (by TripAdvisor), awarded Best Luxury Hotel (2008 by Anywhere Magazine). There are many more awards the Sri Panwa Hotel Resort has managed to win over time, but we think you got the idea.
Sri Panwa Hotel is the best place for relaxation and nature integration in style. The villas offer a grandiose view over the Panwa Bay. All these are now available at discounted prices as TripEconomy.com gets you up to 30% discount from the direct hotel price list, so book your holiday today and enjoy an amazing travel experience – visit Sri Panwa on TripEconomy to choose travel dates and get discounted prices.


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5.5 Raising Multi-Racial Children
Growing up as a mult-racial child, I often felt my racial identity shifting and developing — heck, even as an adult I do!
Navigating what it means to be mult-racial continues to be a journey for me, which is why I was so excited to be able to interview Dr. Jennifer Noble.
Dr. Jenn, as she's known online, is a...
5.4 Black Lives Matter: How Will You Respond?
In the summer of 2020, author Veronica Chambers had what she calls an "aha moment."
Born in Panama and raised in Brooklyn, New York, Veronica's Afro-Latina heritage has always been very important to her, and she worked hard to make sure her then-12-year-old daughter felt the power of her "Black...
5.3 Stop Using MLK to Justify Racism
Martin Luther King Jr. Day is less than a week away, and I couldn't let this important day pass without another episode.
It's actually my THIRD episode about Martin Luther King Jr., and I feel like this episode shows our journey as a community and my journey as an anti-racist (both personally and as an educator).
5.2 Rich People Commit Crimes Too
This past week we've had some deep and meaningful conversations about responding to the myth of "Black on Black crime." As our conversations unfolded I realized that I left out one key detail, rich people commit crimes too! I made this clarification on our "Ask Jasmine" segment this week and wanted to make...
5.1: What About Black On Black Crime?
When a white person murders a Black person and we try to call it like it is — RACISM — there's a response that, without fail, will crop up.
The heartbreaking circumstances of the killing can differ — whether it's police violence like in the cases of Breonna Taylor and George Floyd or racist white vigilantes...

redpajama_set_name: RedPajamaCommonCrawl


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Генарий Осипович Корганов (, , Грузия — , ) — российский композитор и пианист.

Семья
Сын генерал-майора Осипа Ивановича Корганова (1811—1870). Пятеро братьев и сестёр Генария Корганова стали вокалистами: певицы Елена Терьян-Корганова, Нина Корганова (Дариали), Мария Корганова (Светадзе), певцы Иван (Ованес) и Константин Коргановы.

Биография
Начал заниматься музыкой в Тифлисе под руководством Эдуарда Эпштейна. Затем учился в Лейпцигской консерватории (1874—1877) у Карла Райнеке, Саломона Ядассона и Э. Ф. Венцеля, в 1877—1879 гг. совершенствовался как пианист в Санкт-Петербургской консерватории у Луи Брассена и Густава Кросса. Вернувшись в 1880 г. в Грузию и обосновавшись в Тифлисе, поступил на государственную службу, продолжая заниматься композицией в свободное время. Концертировал в городе как солист, принадлежал к ближайшему окружению Михаила Ипполитова-Иванова. Выступал в тифлисских газетах как музыкальный критик. Участвовал в работе тифлисского отделения Императорского Русского музыкального общества, от которого в 1889 году был делегирован в Санкт-Петербург на празднование юбилея Антона Рубинштейна. Умер по пути из Петербурга домой.

Творчество
Корганову принадлежит ряд фортепианных пьес (фантазия «Баяти», «Арабески», «Миниатюры», «Акварели» и др.) и романсов («Серенада Дон-Жуана», «Острой секирой» — на слова А. К. Толстого, «О чём в тиши ночей» — на слова А. Н. Майкова, и др.), некоторые из них пользовались при жизни автора определённой популярностью (в частности, Артур Хартман опубликовал в США скрипичные переложения). Стиль Корганова связан как с влиянием Н. А. Римского-Корсакова, так и с использованием местных закавказских мелодий: по мнению армянского музыковеда Ш. Апояна, «большую ценность для формирования армянской фортепианной музыки представляют произведения Корганова, связанные с армянской тематикой».

Примечания

Ссылки

Композиторы России
Академические музыканты России
Композиторы по алфавиту
Музыканты по алфавиту


This weekend we are finally the height of cool. Not in a style way or anything like that, obviously, but we just got central air conditioning installed in our house. It's quite remarkable – makes such a huge huge difference to our comfort. Especially as we are in the 9th day in a row of highs being over 90F with high humidity. It's been a bit crazy, but it's much better inside now.
Anyway, the point of this post: lots of new photos of Toby. Enjoy.
This entry was posted on Sunday, July 17th, 2005 at 19:31	and is filed under personal, toby. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.


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Governor's push for reopening creates rift with health experts
As the governor moves to reopen 77 counties across the state, some public health officials are raising alarms that the actions will result in a resurgence in infections and deaths.
Katina Zentz
Gov. Kim Reynolds speaks during the Condition of the State address at the Iowa State Capitol on Tuesday, January 14, 2020.
Caleb McCullough, Assistant Politics Editor
Though public health experts are warning against reopening the state too early, Gov. Kim Reynolds is pushing for a quick return to business across the state, backed by a swath of Republican legislators.
Though she said her decisions aren't political, response to Reynolds' actions has fallen fairly evenly along party lines. On April 24, nine Republican state legislators signed on to a letter commending Reynolds' efforts to open up the state and pushing for businesses to be able to open again quickly.
Reynolds' decision to reopen parts of the state went against a report given to the Iowa Department of Public Health by University of Iowa researchers, saying a second wave of infection is likely if the state lifts social distancing guidelines too early.
Republicans supporting reopening echoed the governor's own sentiment that the economic and mental health implications of the shutdown need to be taken into the calculus of when and how to reopen.
Friday, businesses and retail stores in 77 counties were allowed to resume operations at 50 percent capacity while observing social distancing guidelines. Religious services across the state are allowed to resume, though many churches are still continuing online and drive-in services. Elective surgeries and farmers markets were also allowed to resume April 24.
Rep. Steven Holt, R-Denison, who wrote the letter, mentioned that people aren't going to hospitals for routine screenings, and so heart disease, diabetes and other conditions may not be getting caught as early as they would otherwise.
"We have to understand the ramifications," he said. "When we're looking at this situation, we have to look at not only the coronavirus, we can't look at that in a vacuum … remaining closed is doing a lot of damage to our hospital system."
Rural hospitals are increasingly strapped for cash as elective procedures have dried up. As of May 3, 357 COVID-19 patients were hospitalized in the state. Iowa has 247 ICU beds available and more than 4,000 standard hospital beds, according to the Institute for Health Metrics and Evaluation updated May 4.
One major justification for aggressive containment measures in March was to prevent overwhelming the hospital system, but advocates for reopening say that has not happened.
However, Megan Srinivas, an infectious disease doctor at the Fort Dodge Community Clinic, said the hospitalization rates don't adequately communicate the capacity of the state's health-care system.
Srinivas said a lot of COVID-19 patients end up needing intensive care, and so the ICU bed capacity is an important factor. Additionally, personal protective equipment and special equipment are needed to care for patients, and many hospitals in Iowa are still facing shortages.
Reynolds' decision has drawn fire from Democrats and public health experts who say the restrictions are being lifted too early, and that the state is not in a position to test at the volume it should be to contain the coronavirus.
On the same day our governor is "reopening" 77 counties, we have a new one-day high of 740 new #COVID19 infections. What is going on here? https://t.co/GfqtXd8B5R
— Zach Wahls | Social Distancing Saves Lives (@ZachWahls) May 1, 2020
During Reynolds' daily press conferences, she said the report from the UI researchers was not based on Iowa-specific modeling, even though the researchers used Iowa-specific data.
Aaron Miller, an assistant professor of epidemiology at the UI who worked on the report, said any easing of social distancing will increase the reproductive number of the virus, which determines how many secondary infections will result from a typical case.
When it comes to Reynolds' current orders, Miller said that the results will largely depend on how Iowans behave, which can be difficult to project on a model.
"It could be the case that as we open things back up, people don't change their behavior at all. Businesses don't actually open up, people don't go back out. And then you might not see as much of a second wave or a continuation of an increase in cases," he said.
But if activity in counties that are opening back up returns to the same levels as before the virus, Miller said cases are likely to shoot back up.
The push to open Iowa comes as more than a dozen other states are lifting shelter-in-place orders and reopening, trying to strike a delicate balance between public health and economic viability.
In Georgia, gyms, restaurants, and movie theaters have been allowed to reopen. In South Dakota, Gov. Kristi Noem, a Republican, is allowing employers and local governments to make the decision on reopening.
Despite official White House guidelines requiring two weeks of decreasing cases and robust testing, President Trump has been encouraging states reopening, sometimes against his own administration's guidance.
Srinivas and Miller both said Iowa has likely not seen a peak in cases. Positive tests as a proportion of total tests increased throughout April and early May, and Srinivas said with three fourths of the state easing social distancing, cases are likely to continue increasing.
"It's really going to be in about three to five weeks that we see that drain on our hospital resources and or health-care resources," Srinivas said. "And that's the time when we're going to see the impact of the decisions we make today."
Testing is another area that experts say should be improved in order to properly handle the virus.
Christine Petersen, director of the Center for Emerging Infectious Diseases at the University of Iowa, said the goals set forth by Test Iowa — the public-private partnership expected to increase testing in the state by 3,000 tests a day for three months — were on track with where testing should be, but that the state hasn't been able to implement the program fully yet.
As of May 1, the State Hygienic Lab was still working to validate the Test Iowa equipment, which involves running several negative and positive tests through an accredited lab.
In addition, testing volume for SHL has grown significantly over the past month, as initial clinical testing of individual patients has expanded to include testing at long-term care facilities and meat-packing plants, serology testing and work related to the Test Iowa program, Communications Director at the Office of the Vice President for Research wrote in an email to the DI May 1.
Petersen said health officials face bottlenecks in supplies for testing which make it difficult to test as many people as planned.
"I hope that our ambition can be met by the ability to do the testing, and then we should be fine," Petersen said.
On May 1, the state reported 2,925 total tests. Higher single-day totals have been reported in days since, but those numbers include a backlog of tests from the previous week at Test Iowa sites.
Srinivas said testing is still inefficient in the state. She pointed to a study recently done by the Harvard Global Health Institute, which estimates that 152 tests should be administered per 100,000 people to properly understand the extent of the virus and identify pockets of high infections.
In Iowa, that would mean testing 4,788 people a day.
"Without any data, we're just making assumptions based on, really nothing," she said. "And that's the dangerous part. Some of the assumptions might end up being correct based on when we get data but some of them are likely not."
Caleb McCullough, Managing Editor
Caleb McCullough is a Managing Editor at The Daily Iowan. In his freshman year, Caleb worked as a news...
Katina Zentz, Creative Director
Katina Zentz is the Creative Director of The Daily Iowan. She is a senior at the University of Iowa and transferred from...
University of Iowa will supply PPE to students beginning Wednesday
Over 9,000 doses of the COVD-19 vaccine given in Johnson County
UI athletics department reports 14 positive COVID-19 PCR tests out of 411 tests conducted
COVID-19 vaccine, CARES Act funding soon to be available for University of Iowa campus
University of Iowa reports 13 new cases of COVID-19
University of Iowa reports 16 new COVID-19 cases


"There are so many ways that human beings are the same, and yet people feel very alone in their own stories. When you are able to tell a story, whether it be photographically or in film, that touches a core story in people, they and you react. They feel recognized and understood and you feel so much less alone in the world."
"The work often goes through weeks of labor, with many layers of paint, because I like the idea of work to carry weight and substance. Scratches, scrapes, dark colors, soft edges, muted light, energy, quiet. Life contains all of it, why not a painting?"
"There's something irreverent about getting muddy. Plus, its related to play and recreation. My mother was OCD about keeping the floors clean, her hair in place. This is all counter to my mud series, which by the way is not appreciated by my parents. They have a visceral reaction to my mud paintings. That's one advantage to being a mature artist, though, there's no time to waste and I do what I want, but they remain scandalized."
"I've always believed that the painting is there if you're willing to do the work and put in the time. It's there if you believe."


COLUMBUS, Ohio— The Ohio State women's golf team is enjoying spring break in sunny Florida and are set to compete in the 2014 SunTrust Gator Women's Invitational, March 14-16. The three-day, 54-hole tournament will take place on the par 70, 6,002-yard Mark Bostick Golf Course in Gainesville.
A field of 14 teams will compete in the weekend's tournament, including nine teams ranked in the Top 50.
The Ohio State lineup will feature three freshmen, one senior and one junior competing for team score and one junior playing as an individual.
Leading the way are freshmen Jessica Porvasnik, Katja Pogacar and Zoe-Beth Brake, ranking in the top three on the team in stroke average. Brake, who began competing in February, has a team-best 72.5 average over six rounds played. Porvasnik and Pogacar have averages of 73.22 and 74.78, respectively.
Senior Allison Harper and junior Claudia Lim will also compete for team score, while junior Jan Chanpalangsri will don the Scarlet and Gray as an individual.
Porvasnik, Pogacar, Lim and Chanpalangsri have represented Ohio State in all six tournaments this season and will competing in their seventh of the year.
With a program record of 838, the Ohio State women's golf team captured the Westbrook Spring Invitational title in Peoria, Ariz., Feb. 23-24. The Buckeyes tallied a third round score of 279 on the par 72, 6,269-yard Westbrook Village Golf Club Vistas Course to secure their win by a 10-stroke margin over second-place Oregon.
The Buckeyes' win was the first since the team captured the 2012 Lady Buckeye Spring Invite. The team's three-round total of 26-under 838 broke the program's 54-hole record previously set in May 2005 by 18 strokes. Ohio State totaled an 856 at the 2005 NCAA East Regional and that mark held for nine years.
Clinching the first individual win of her career was freshman Jessica Porvasnik. Leading after scores of 65 and 67 on day one, the Hinckley, Ohio, product carded a final round of 1-under 71 to take medalist honors by four strokes.
Also finding spots in the top 10 were freshmen Zoe-Beth Brake and Katja Pogacar and senior Allison Harper. Brake finished tied for second overall with a 9-under 207. Harper came in fifth with a 5-under 211, while Pogacar concluded the tournament in 10th with a 2-under 214.
Jessica Porvasnik was named Big Ten Women's Golfer of the Week, Feb. 26. The honor was the first of her career.
Porvasnik clinched the first individual win of her career as she captured medalist honors at the Westbrook Spring Invitational by four strokes with a tournament-record 203 (-13). The Hinckley, Ohio, product finished with 14 birdies over three rounds and recorded the first hole-in-one of her career in round two on the par 3, 163-yard second hole using an 8-iron.
Porvasnik kicked off her record-breaking tournament with a 7-under 65 in round one, breaking the 11-year single round program record of 66. That mark was first set by Kristen White in 2003 and again by White in 2004. Porvasnik followed with rounds of 67 and 71 on her way to a 13-under 203 for the tournament.
The 2014 installment of the SunTrust Gator Women's Invitational is the tournament's 42nd-annual event. Since it started in 1973, the tournament has featured many quality teams and players, including Nancy Lopez, Pat Bradley and Betsy King. Alabama captured the 2013 team title, while Oklahoma's Chriapat Jao-Javanil took individual accolades.
Ohio State last competed in the tournament in 2011, finishing third overall.
The three-day tournament will be played on the par 70, 6,002-yard Mark Bostick Golf Course in Gainesville, Fla. The course has been home to the University of Florida for over 80 years and was originally designed by renowned architect Donald Ross.
The weather for the first round calls for 70 degree temperatures with sunny skies. Saturday looks to be partly cloudy with a high of 74, while Sunday's final round is looking wet with a 70 percent chance for thunderstorms.


Before you start to think about the perfect diamond for your girlfriend's engagement ring you will have to get the ring itself just right. The ring comes in two distinct parts, the metal band and the setting, and you will need to choose a type of metal and a style of setting.
Choosing the metal for an engagement ring involves a little research into your girlfriend's jewellery collection. Does she wear mainly gold jewellery or silver jewellery? Most women have a strong preference for one or the other, usually depending on their skin tone, so once you know which one she wears you can start from there.
If your girlfriend wears mainly gold jewellery, your best option is an 18k yellow gold ring. However if she prefers silver jewellery you have a choice between platinum and white gold. Here is a quick comparison of platinum and white gold.
This is the most common setting for an engagement ring and is used in the popular solitaire ring. With a prong or claw setting the diamond is raised up from the metal band and is held in place by a number of metal prongs or claws. This type of setting allows light under the diamond adding to its sparkle. A four prong setting, as shown in this illustration, is popular as it shows off more of the diamond, whereas a six prong setting is slightly more secure.
The prong or claw setting can be used for a solitaire ring with a single diamond, or with multiple diamonds. A three stone ring is often used as an engagement ring with a large central diamond and a smaller diamond on each side, or a different central gemstone flanked by diamonds. The three diamonds of this type of ring symbolise the past the present and the future.
A bezel setting can also be used for an engagement ring with a single diamond, but it is seen as a more practical choice. The diamond is totally encircled by a metal collar that holds it in place, and the stone is usually set closer to the ring than with a prong or claw setting. A bezel setting is a contemporary choice and a good option for women that lead very active lives or have physical jobs. A doctor may prefer a bezel setting, for example, to avoid the possibility of scratching her patients.
A channel set engagement ring features a number of diamonds lined up in a row. As the name suggests, the diamonds are set in a metal channel, and they are flush with the band of the ring.
An engagement ring that features purely channel set diamonds is a modern design, and again is quite practical. However, rows of channel set diamonds can also be used either side of a claw set solitaire to give the central diamond more sparkle, as seen in this illustration.


#OnlyatGW is more than a hashtag, it is a simple fact of life on campus. Whether you want to take advantage of the hustle and bustle of Washington, D.C., find your niche among classmates who share your interests or seek guidance for the years ahead, we are committed to making your college experience worthwhile and memorable.
During Commencement Weekend, Columbian College holds separate Celebration ceremonies to honor our undergraduate and graduate students.
Political communication major Steven Kelly co-founded a No Labels chapter to create something constructive for GW's politically active student body.
Communication major Alexa Dectis, BA '15, made the most of her time at GW by staying active in the student community and taking advantage of university resources.


Magandang buhay sa inyong lahat! Let me begin by saying congratulations to everyone. Congratulations to us September 2016 LET passers. YES, we did it!
To our PRC Board for Professional Teachers Chairperson Hon. Rosita L. Navarro, Board Vice-Chairperson Hon. Paz Lucido, BOPT Member Hon. Paraluman Giron and our PRC OIC Mam Evangeline Marilyn Vergara, good morning!
To our parents, families and friends and to all mentors present, give yourselves a pat on the shoulders for you did good. You paved the way for us to be here celebrating today.
Each of us has individual LET stories to tell. Some struggles were real. Some sacrificed other things like quitting their jobs to attend the review, selling some stuff for financial support, being away from their families for weeks or during family day on weekends… for some, this could be their second time, third time, nth time… Ilan ba sa inyo dito ang nagmahal, nasaktan, tapos nag-LET?… at pumasa!
But no matter how our LET stories started, it all ended beautifully and successfully. We are all topnotchers in our own right. We are all winners! Your bright smiles and the glow in your eyes today can attest to that. God has a very beautiful and unique plan for each one of us. We are motivated because our hearts are so ever hungry to learn. That kind of hunger is a gift to our country.
Yes, our success today is the result of our inspirations, perspirations and hard work. But may the inspirations we feel today be translated into emulation tomorrow. Wherever God brings us, let us be a model of resilience, courage and hard work.
Our fight does not end here. Our victory today is just a prologue to the real battlefield of education. After this event, we will all go back to our hometowns with our licenses as proof of being professional teachers. Some of you will start applying for a teaching position either in private or public schools. Some of you maybe already a teacher… But the moment we all step inside the classroom, let us put on our suit of armour so that we may be able to stand firm and defend our students against ignorance and illiteracy. Let us be dead serious to produce students who are most creative, most passionate, most courageous and most excellence-driven. We need to give our students that kind of fighting spirit. They have to win in life in this country.
My fellow professional teachers, we have a country to fix. And fixing should start from the quality of education we give to our students. Let us shape them into good citizens. May we have the perseverance, creativity, and brilliance to create our own paradigm for various academic disciplines.
We must consistently be sensitive and responsive to our students' needs. Let us be the source of understanding and grace for the most difficult and hurting students in the class. Let us be the good character models the students would want to look up to. Let us be the breather of hope and dispenser of love in a faculty room of tired and frustrated teachers.
We are lifelong-learners. We are the catalyst of change and our influence never stop. Tayo'y mga gurong hindi basta-basta. Tayo'y mga gurong pinanday hindi lamang sa LET kundi para tuklasin ang ating kontribusyon sa edukasyon. Tayo ay mga gurong progresibo. Gurong nagsasaliksik at tumutuklas, gurong nagbabasa, gurong nakikinig at umuunawa, gurong out-of-the box, gurong fit and healthy, gurong hi-tech at millennial, gurong may itsura, gurong person of authority, gurong in-love, gurong para sa kapwa-Pilipino.
Posing with MindGym coach Anna Casiding in the middle.
Now, I would like to take this opportunity to convey my gratitude and honour the schools where I came from – first the Mondriaan Aura College in Subic Bay where I graduated Bachelor of Science in Accountancy and the Gordon College in Olongapo City where I earned my Professional Education units. For now, I am serving as a college instructor and a Senior High school teacher in Aura College as my way of giving back to my Alma Mater.
Also, I would like to thank the Mindgym Philippines in Quezon City for training and mentoring me and believing in my capacities. They inspired me for triple hard work, value for lifelong-learning and dreaming big for myself so I can dream big for my students.
Also, thank you to my very supportive and loving husband, Jonathan Tugade and my life-saver and constant runner Kristanya. Btw, Happy 15th wedding anniversary sa iyo honey ko.
To my classmates and friends who are here as passers, too, thank you for joining me in my LET journey… Hats off to you guys!
But all praises and glory be to our Almighty Jehovah God who took care of me in my LET journey. He guided me all the time. I couldn't thank him enough for all these blessings.
Again, CONGRATULATIONS, mga ma'am, sir ng bayan… Magandang buhay para sa ating lahat!
Christine Almiñe Tugade is the Top 9 in the 2016 September Licensure Examination for Teachers (LET), Secondary Education division, Social Studies major. She finished BS-Accountancy at the Mondrigan Aura College, and is currently residing at Baguio. She reviewed in MindGym's 18-day LET coaching during her preparation for the LET.


text:
Een  w-kromme is een meetkundige kromme in een projectieve ruimte die invariant is onder een groep van projectieve transformaties met één parameter.
W-krommen werden voor het eerst in 1871 onderzocht door Felix Klein en Sophus Lie, die ze ook hun naam gaven. W-krommen kunnen met enkel een liniaal geconstrueerd worden. Vele bekende krommen zijn w-krommen, bijvoorbeeld kegelsneden, logaritmische spiralen, (grafieken van) machten (zoals ), logaritmen en de schroeflijn (helix); echter, goniometrische functies zijn bijvoorbeeld geen w-krommen. W-krommen komen veelvuldig voor in het plantenrijk.

Naam
De letter 'W' komt van het Duitse 'Wurf', dat een rij van vier punten op een lijn betekent. Een eendimensionale w-kromme (dat wil zeggen: de beweging van een punt op een projectieve lijn) is door zo'n rij bepaald.

Het Duitse "W-Kurve" klinkt bijna hetzelfde als "Weg-Kurve", en dat kan in Engels vertaald worden met "path curve". Daarom vindt men in de Engelse literatuur vaak "path curve" of "pathcurve".

Literatuur
 Felix Klein en Sophus Lie: Ueber diejenigen ebenen Curven... in Mathematische Annalen, Band 4, 1871; online beschikbaar bij de Universiteit van Goettingen
 Voor een inleiding in de w-krommen en hoe ze te tekenen, zie Lawrence Edwards Projective Geometry, Floris Books 2003, ISBN 0-86315-393-3
 Over w-krommen in de natuur, zie Lawrence Edwards The vortex of life, Floris Books 1993, ISBN 0-86315-148-5
 Voor een algebraïsche classificatie van de 2- en 3-dimensionale w-krommen, zie Classification of pathcurves

Wiskundige kromme
Projectieve meetkunde


This formulation is a multi-beneficial corrective serum that amplify's the skin's hyaluronic acid levels.
This unique formulation contains a high concentration of pure hyaluronic acid and botanical extracts to support skin's hyaluronic acid levels and deliver surface hydration, helping improve the visible appearance of firmness, smoothness, and facial plumpness.
Highly viscous solution with outstanding spreading and lubricating properties.
Hyaluronic is regarded as one of the best moisturizing ingredients available due to its moisture retention properties.
This pure product is assayed by the manufacturer (Texas Natural Supply) to contain at least 43% of one of the active components, glucuronic acid.
Source: Biotechnologically produced from glucose, soy peptone & yeast extract (does not contain any animal products).
Hyaluronic acid is a natural polysaccharide.
Storage: Keep container tightly closed and in a cool, well ventilated area.
Microbial contamination of thisproduct will cause it to degrade and lose its thickness (viscosity).
If over time the solution becomes thin or loses its thickness and viscosity it should be discarded.


Devyn Denton is a 2019 Candidate for Edmond City Council Ward 1, a nonpartisan race. She is seeking the endorsement of Our Revolution Oklahoma. She previously ran in 2018 for HD 39, and she was endorsed in that race.
Devyn's roots are deep in Oklahoma, with a rich family background extending back to the Civil War of proud Oklahomans including farmers, veterans, teachers, and nurses. She was born in Oklahoma City and grew up in the rural, sacred lands of the Cherokee Nation. First female Cherokee Chief Wilma Mankiller was her godmother, and tribal spiritual leader Crosslin Smith was a close advisor and mentor to the Denton family. As a result of these guiding influences, she was instilled from a young age with an overpowering desire to help others and achieve excellence, which manifested as a calling to join the world of medicine.
A proud resident of Edmond, Devyn has two children, one of them a junior at Edmond North High School and the other pursuing college. As a trauma nurse, first responder, volunteer firefighter, and 5th generation teacher, she has a long history of going above and beyond to serve her community.
Devyn Denton is a 2018 Democratic Party Candidate for House District 39. She has been endorsed by Our Revolution Oklahoma.


text:
« EMELD | Main | Ethnography, journalism and interview rituals »
The elephant fights back
A few weeks ago, I posted a few comments about Derek Bickerton's new theory that our ancestors developed language so they could cut up dead elephants better. In more dignified and scientific terms, he suggests that language emerged because of the need to recruit and coordinate crews to scavenge the carcasses of naturally-deceased megafauna. Yesterday, Derek posted a reply, in which he starts off with a wink
Thanks, Mark, for spreading the word, even if I don't altogether agree with your conclusions. Maybe you're the reason my site visits doubled last month. So if I say anything personal--it's not personal! Get it?
and then throws a few hard shots behind a snappy jab:
Of course you can compare apples and oranges (or, perhaps more relevant here, shit and Shinola) and come to the conclusion that they're both round, or both brown, so hey, what's the difference, let's move on. Sure saves thinking too hard.
Since it's time for me to head out to today's EMELD sessions, I'll have to get through this round with a rope-a-dope strategy. But just wait till I'm back in Philly!
More importantly, Derek also posted a preprint entitled "Language Evolution: a Brief Guide for Linguists", a version of a paper that will appear in Journal of Linguistics at some point in the future. It's full of interesting ideas, and fun to read. For example:
Into the middle of this confused and confusing situation there appeared in the journal Science a paper (Hauser, Chomsky & Fitch 2002) aimed at setting the scientific community straight with regard to language evolution. Its magisterial tone was surprising, considering how little work any of its authors had previously produced in the field, but no more surprising than the collaborators themselves: since Hauser was known as a strong continuist and Chomsky as a strong discontinuist, it was almost as if Ariel Sharon and Yasser Arafat had coauthored a position paper on the Middle East.
I think you can tell that this isn't a balanced and dispassionate survey, but a strong presentation of an interesting individual perspective. More on it later.
Posted by Mark Liberman at July 2, 2005 07:35 AM


Object reference not set to an instance object.
Clicking OK to the error will close ESC entirely.
This error can happen if MapPoint has been enabled on an ESC workstation, but there is an issue with the MapPoint program. This commonly occurs if Microsoft MapPoint has been recently installed but the program was not opened on the machine first. The first time MapPoint is opened, the user will be asked to accept the license terms and register the software. These pop-up boxes will prevent ESC from being able to access the MapPoint program and therefore will cause the Run-time error.
This problem may also occur if there is a trial of the software installed instead of a full version, corruption within the program itself or if the version of MapPoint installed on this machine is not compatible with the version of Windows or ESC installed.
Close out of ESC and then within Windows, open up the MapPoint software directly. When it first starts you will have to accept the agreement and then clear the software registration screen. After that, you will be able to get right into the Microsoft MapPoint program. Close out of MapPoint and then start ESC and now the dispatch board will load correctly without the error.
Refer to the Microsoft MapPoint System Requirements in order to ensure that the version of MapPoint you have installed is compatible with your Windows operating system.
You may also refer to our System Requirements to ensure that the version of MapPoint you have installed is compatible with the version of ESC you have installed.


A new original musical premieres in Johannesburg in August.
Johannesburg audiences are in for a treat when the world premiere of the new and original musical, Calling Me Home takes place on 17 August on The Mandela Stage at Joburg Theatre, running until 3 September 2017.
Cape Town audiences get their chance next year with negotations currently taking place to tour the show internationally thereafter.
Calling me Home is a powerful love story of hope, courage, longing and compassion that will resonate with people everywhere. As the audience follows the story of Grace, a young woman, who flees her homeland due to the outbreak of a brutal civil war, it is taken on an exciting journey that stretches from the splendours of the African continent, across the ocean to a great foreign city.
In this new, hugely diverse and colourful community, Grace experiences both joy and great danger. She also falls deeply in love and most importantly, learns the true meaning of 'home'.
Premiering in Women's Month, Calling Me Home is a collaboration between two highly creative and powerful women in the South African music and theatre industry.
The book, score and libretto were written by composer and producer Alice Gillham, who is signed with EMI Music Publishing / Sony/ATV and who lives and works in South Africa. She effortlessly fuses the genres of classical music, African hybrid, jazz and traditional folksong to create bewitching and evocative music that brings the story to life, providing her audience with a deeply human and emotional experience.
Joining Gillham in bringing this musical to the stage, is director Magdalene Minnaar. According to Minnaar this production has the potential to have a profound impact on the world.
Calling Me Home depicts the journeys of three women who each find their own personal power.
Grace (Lynelle Kenned) a young African woman flees her war-torn homeland to try to survive in a country of concrete cityscapes, crime and danger.
With her is her new friend Lindiwe (Zolani Mahola), who too has fled her home, but in Lindiwe's case it is a flight from abuse and pain. Finally, there is the beautiful but deeply troubled Isabella (Samantha Peo), who finds the strength and courage to conquer almost insurmountable challenges when she overcomes addiction, both chemical and emotional, to take the moral lead in her community. The work is a global story with far-reaching current relevance.
Each cast member of this large ensemble piece will play a vital part in the story.
According to Minnaar, choosing the right artists was critical as they will have the opportunity to bring their characters to life for the very first time. "We have carefully chosen hugely talented singers who bring storytelling energy, creativity and a spirit of adventure to this journey. Their energy is amazing and their talent world-class," Minnaar stated.
With a stong emphasis on the music being new and original, composed specifically for the production, Calling Me Home will be releasing a selection of the songs to the public throughout the season.
Calling Me Home runs at Joburg Theatre from 17 August – 3 September 2017.
Performances are Tuesdays to Fridays at 20h00; Saturdays at 15h00 and 20h00 and Sundays at 14h00.
Ticket prices range from R180 – R420. And can be booked online at www.joburgtheatre.com or by calling the Box Office on 0861 670 670 or through Webtickets.
For group bookings of 10 or more tickets, contact Joburg Theatre's ticketing office on (011) 877 6853/4.
The duration of the show is 2 hours 20 minutes excluding interval.


text:
Bătălia de la Canton (28 decembrie 1857 - 1 ianuarie 1858) a fost o bătălie din timpul celui de-al Doilea Război al Opiului. Franța și Anglia au atacat orașul chinez Canton. Orașul a căzut la 1 ianuarie 1858 și europenii au preluat controlul.

Note

Legături externe

Istoria Chinei
Al Doilea Război al Opiului
1857


Use the link to access pay-per-view options for the article published in Library Hi Tech News available from Emerlad. The abstract reads as follows: "Purpose – The paper aims to describe the characteristics and purposes of Pakistan Research Repository (PRR). A quantitative analysis of this repository is carried out by analyzing the content of the repository. A critical analysis of the entire growth strategy, population and web interface is also included in this paper. This study also proposes certain measures to make it more effective and efficient for archiving the research output of a nation. The study was designed to investigate issues relating to PRR and outline steps to develop a strategy to overcome these challenges. Design/methodology/approach – This article focuses on quantitative aspects and critical analysis of PRR. A multi-tier research design was used to meet the objectives of the study. A web search was conducted, and information was drawn from documents available on the Web site of Higher Education Commission (HEC) of Pakistan, PRR and directories of open-access repositories; data were complemented by quantitative and critical analysis of the content of the repository. Information was also gathered by literature-based review of project documents which were created for the implementation of this project. Findings – The paper has highlighted how far this repository has succeeded in bringing the research output from universities across Pakistan to the researcher community by analyzing the available content by institution, type, subject and year. This study has provided a valuable insight about the current status of PRR by identifying gaps in the content of the repository. The quantitative analysis of the repository shows that the creation of this repository was a landmark achievement, as it provided the opportunity to researchers, faculty and students for preserving, disseminating and furthering their existing knowledge at a national-level platform. Research limitations/implications – This research article is a case study and focuses on PRR only. Therefore, researchers are encouraged to throw light on other repositories in Pakistan and sharing of resources among institutional repositories in Pakistan. Practical implications – This study will be helpful for the administrative authorities of HEC and university faculty to plan for effective collection of content from the institutions and digitization of this content. The paper includes implications for the development of repositories at an institutional level in Pakistan. Social implications – This paper will help in managing PRR, and it will ultimately lead to enhance and better manage research output in Pakistan. Originality/value – This paper has identified the characteristics and purposes for creating a research repository at the national level and provided a critical view of policies and statistical view of the content of the repository."


There arise situations when you simply run out of USB ports and it is really irritating. How about having your wish fulfilled and 4 additional USB ports springing out of your computer speakers! Sounds to be too much of a fantasy but that's exactly what Cubite provide. Yes, a 4 USB 1.1 hub and speaker all bundled into one unit. The speaker also has a 3.5mm stereo jack. And its 3 watt output is quite impressive.
The multipurpose market is booming. And something like the Cubite is very welcome and ingenious. £24.95 sounds like a fair enough price.


When you buy from Bike Tech, you get everything you need for safe, fun, affordable cycling. The truth is, you get so much more than just a bike if you choose to shop with us. We strive to be YOUR local bike shop. We're here for every type of cyclist, whether you're a roadie, a mountain bike junkie, a casual cruiser, or a parent shopping for your child's first bike. Our friendly, expert staff is available to help with all of your cycling needs. Learn more about what you can expect when you visit us.
We stock more Specialized, Cannondale, Scott and Salsa bikes than anyone else in Florida. With nearly 2000 bicycles in stock, we're bound to have something for you. Stop by or browse our inventory online.
You want your new bike running perfectly, and so do we! New bikes sometimes need adjustments, we're here for you. Bring your new bike to any of our stores and well go over all the major systems of your bicycle to insure they are working as intended. This service generally takes less than 30 minutes and can often be done while you wait.
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We partner with local event companies, riders and parks to help support our cycling community.


Static caravans for sale in Cornwall could help you to escape from your own home to a home right by the seaside. Getting away for a few days without having to pre book could be closer than you thought when you have a property just the way you left it to escape to. Without your own holiday home you would have to hope for good weather months in advance, but this doesn't have to be the case. The sun comes out and you just have to pack up and go for as short or long time as you wish.
There are different sited static caravans for sale in Cornwall to suit all budgets and family sizes making it an ideal home from home. You can decorate the property just how you want it and be just a short distance from all conveniences. Most people that own their holiday home let it out to others when they are not there, which creates an extra income. There are lots of people that want a getaway but rent rather than buy, so you can be sure that the property will not be empty for long if at all.
If you like the great outdoors you will be spoiled for choice as to whether to go to a beach to relax, build sandcastles with the children or even try your hand at surfing and other water sports. There are many amenities close by to entertain the whole family from museums to find out about the town's history, the ST Austell brewery, arcades, theme parks and much more.
The Oasis fun pools and waterslides are excellent for rainy days where they cater for the youngest toddlers in the splash pools to the biggest kids with the different sized pools from the toe dippers to the thrill seekers. The extreme academy is a great place to visit for anyone that wants to learn or improve their waveski, land board and many other activities whether on land or water.
For those that are looking for a quieter time away there is the beautiful scenery to explore including the Kestle Barton gallery and garden which is a ancient farmstead that has been restored on beautiful fields with woods for long country walks and the Frenchman's Creek and Helford River to look down on. The Victorian Gardens are laid out just like a maze with lots of features to enjoy on your way around and stretching out to nearly 4 acres there is a lot of exploring to undertake. Photographers will delight in being able to take panoramic pictures of Port Isaac and Quin Bays.
Looking at the static caravans in Cornwall will show you just how much there is to be gained from purchasing rather than renting and how easy it is to just drop everything and get away from the busier way of modern life.


text:
Aerospace Expansion Brings Up to 100 New Jobs to Georgia
Firth Rixson Forgings LLC, a subsidiary of U.K.-based Firth Rixson Limited, has announced it will expand its forged metal operation in Midway, GA, which manufactures aerospace industry components. The company expects to add 75 to 100 jobs--bringing its total employees to at about 304--when the plant is in full production mode. Groundbreaking for the expansion is set for January 2012.
"We are delighted to increase our presence among the other aero industry leaders doing business in Georgia," said Firth Rixson CEO David Mortimer. "The addition of isothermal forging capability once again affirms Firth Rixson's commitment to provide the aerospace industry with technological solutions to cost, capability, and capacity constraints. This expansion facilitates the development of unique technological partnerships, guaranteeing supply chain security for the aero industry customer base."
Headquartered in Sheffield, UK, Firth Rixson serves customers worldwide in the Aerospace market sector, and provides forgings and metal products to industries requiring highly engineered material applications. Firth Rixson owns 12 operating facilities in North America, Europe and Asia. The company provides forged and other engineered metal products used to build aircraft engines, structural components, and other applications in more than 40 countries.
During the expansion project Firth Rixson will install a new isothermal forging press, along with a fully automated manufacturing line. The installation will increase the 200,000-sq.-ft. manufacturing floor space at the Georgia facility by around 20 percent, and integrate additional dedicated manufacturing process equipment.
The Midway operation (opened January 2011) is the company's fourth closed die forging operation and largest greenfield investment. It requires a workforce with a high degree of technical expertise and problem-solving capacity.
Governor Nathn Deal noted that not every state or location provide the workforce to handle these highly technical jobs, many of which require engineering expertise. "Georgia can," he said, "and I give great credit to our academic facilities, especially those on the coast, for providing the quality of training companies such as Firth Rixson require."
"As a growth industry in Georgia, aerospace is an area we focus on for business recruitment and expansion," said Chris Cummiskey, commissioner of the Georgia Department of Economic Development. "Our resources for the aerospace industry on the coast have now helped Firth Rixson and Gulfstream make major expansions this year."
Controlling Conditions in Aerospace Manufacturing Facilities
Designing the Aircraft Manufacturing Facility
Personal VTOL Aircraft Take Off: What It Means for U.S. Manufacturing
Where Should Aerospace Companies Invest? Evaluating Aerospace Manufacturing Hubs
U.S. Governors' Strategies to Attract FDI
Practical Considerations for Expanding into the U.S.
Location USA 2019: A Letter from Ian Steff, Deputy Assistant Secretary for Manufacturing, U.S. Department of Commerce
Workforce Strategies for Projects Generated by FDI
FDI in the USA Remains Unrivaled


text:
United States Naval Academy (USNA)
United States Naval Academy
United States Naval Academy Student Essentials
Bill the Goat
Annapolis, Navy
www.usna.edu
Most Selective
About USNA
As one of five service academies, the United States Naval Academy serves as a crucial institution of the American military. Its campus, which is located in Annapolis, Maryland, was established in 1845 and named a National Historic Landmark in 1961.
Of course, the Naval Academy is not your average undergraduate college. While other institutions focus exclusively on academics or career training, the Naval Academy strives to develop its students' moral, academic, professional and physical education.
The admissions process is also quite different. A preliminary application makes you an official candidate, but you must also apply for nomination from a government official (typically a U.S. Representative, Senator, or the President or Vice President).
USNA's academics consist of three main subject areas: Engineering & Weapons, Mathematics & Science, and Humanities & Social Science. There are over 20 majors available in practical fields like Computer Engineering, Quantitative Economics, and Arabic. Grades are based not just on academics, but also on leadership and athletic performance.
Like the other service academies, USNA provides full-tuition financial aid. Once you graduate, you'll be commissioned as an officer in the Navy or Marine Corps. This is certainly no small commitment and obviously not for everyone, but the Naval Academy offers a top-notch, free education to those with the talent and drive to succeed.
USNA Map & Location
View campus map for United States Naval Academy
Getting Around USNA
Seasonal average temperatures for Annapolis, MD
USNA Students
Latino: 12%
Native Hawaiian or Other Pacific Islander: 1%
Undergraduate 100%
Graduate %
Full-Time 97%
Similar to United States Naval Academy
United States Merchant Marine Academy
United States Military Academy at West Point
United States Coast Guard Academy
Georgia Military College, Augusta Campus
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This web site and associated pages are not associated with, endorsed by, or sponsored by United States Naval Academy (USNA). CampusExplorer.com has no official or unofficial affiliation with United States Naval Academy (USNA).


text:
\section{Introduction}

The Jaynes--Cummings--Hubbard (JCH) model \cite{1,2} has been proposed to describe many-body physics in arrays of coupled optical cavities. Each cavity contains a two-level atom interacting with a photon, described by the Jaynes--Cummings (JC) model \cite{3}. In the JCH model, the atom in the cavity is dressed with photons, forming a polariton. The nonlinearity of the JC interaction introduces a polariton--polariton interaction, which leads to the advent of distinctive quantum phases of the polaritons.

Trapped ions are a promising candidate to physically implement the JCH model \cite{4,5}. In the JCH model with trapped ions, local phonons along a radial direction \cite{6,7,8,9,10} are used as bosonic particles instead of photons. The distance between the ions can be increased by weakening the confinement along the axial direction. In this situation, a picture of phonons localized to each ion site can be a good approximation for a short time period, and such `local phonons' exhibit hopping among different sites over a longer period. In addition to phonon hopping, illumination of an ion with a laser resonant with the motional sideband transition induces JC or anti-JC interactions \cite{11}. By driving every ion in a chain at a motional sideband transition, the JCH or anti-JCH model can be realized with trapped ions \cite{4,5}.

The concept of polaritons is important for understanding the quantum dynamics in the JCH model. In the JCH model with trapped ions, a polariton is expressed as the superposition of an internal excitation and a phonon. By tuning the power or frequency of the illuminating laser, it is possible to tune the strength of the polariton--polariton interactions. In this work, we have observed the dynamics of a single polariton and two polaritons in a two-ion chain. A single polariton freely hops between the two ion sites. However, in the presence of multiple polaritons, the polariton--polariton interaction induces a polariton blockade \cite{12,13}, where the hopping of the polaritons is suppressed.

The polariton blockade demonstrated in the present work can be considered as a phenomenon corresponding to the `photon blockade' in a cavity-QED system \cite{14}. In the photon-blockade experiment, the presence of an atom and the first photon in the cavity prevents the transmission of the second photon because of the anharmonicity in the eigenenergies of the coupled atom--cavity system. Similarly, in our experiment, the anharmonic energy levels at each ion site prevent the movement of polaritons. This can be recognized as the emergence of inter-particle interactions between the wave quanta (phonons or polaritons).

The polariton blockade presented in this work and the phonon blockade demonstrated in a previous work \cite{8} have a similarity in that the perturbed energy levels of local phonons at ion sites illuminated with sideband optical pulses play important roles. However, the mechanism of each blockade is different. In the phonon blockade experiment, a particular ion site is illuminated with a laser resonant with the sideband transition, preventing the local phonon from hopping into the illuminated site. This can be explained by a mismatch of energy levels between harmonic and anharmonic oscillators. On the other hand, in our experiment, two anharmonic oscillators with identical energy levels, which are coupled to each other, are realized. Nonetheless, the nonlinearity of the JC interactions introduces an effective polariton--polariton interaction, resulting in blocking of the excitation of the second polariton.

To precisely evaluate the polariton dynamics, we need to measure the quantum state in the polariton basis, which consists of both internal ($\ket{\downarrow}$ or $\ket{\uparrow}$) and phonon ($\ket{n=0, 1, 2\cdots}$) states. However, conventional state-dependent fluorescence detection does not allow the simultaneous evaluation of quantum states in both basis states. Despite this limitation, we can characterize the temporal dynamics of the ions by utilizing appropriate mapping sequences. Thereby, we have confirmed the presence of a polariton blockade by analyzing the experimental data along with numerical simulations.

\section{Theory}

\subsection{Anti-Jaynes--Cummings model}

Driving an ion at the red-sideband motional transition induces the JC interaction \cite{11}. The JC model can be described by the following Hamiltonian (with $\hbar$ set to 1, where $\hbar$ is Planck's constant $h$ divided by $2\pi$):
\begin{equation}
H_{\rm{JC}} = \omega\hat{a}^{\dagger}\hat{a}+(\omega+\Delta_{\rm JC})\hat{\sigma}^{+}\hat{\sigma}^{-}+g_{r}(\hat{a}\hat{\sigma}^{+}+\hat{a}^{\dagger}\hat{\sigma}^{-}),
\end{equation}
where $\hat{a}^{\dagger}$ and $\hat{a}$ are the creation and annihilation operators for phonons with energy $\omega$. The raising and lowering operators for the internal states are defined as $\hat{\sigma}^{+}=\ket{\uparrow}\bra{\downarrow}$ and $\hat{\sigma}^{-}=\ket{\downarrow}\bra{\uparrow}$. The transition frequency between $\ket{\downarrow}$ and $\ket{\uparrow}$ is $\omega_{0}$. $\Delta_{\rm JC}\equiv(\omega_{0}-\omega)-\omega_{\rm L},$ where $\omega_{\rm L}$ is the driving laser frequency. The last term corresponds to the red-sideband transition, where ${\it g_{r}}$ represents the JC coupling strength.

In the present experiment, we use the anti-JC interaction instead of the JC interaction, where the ions are illuminated with lasers resonant with a blue-sideband transition.\footnote{The blue-sideband transition is used in our experiment because the decay time of the contrast in blue-sideband Rabi oscillations is longer than that of the red-sideband Rabi oscillations.} The Hamiltonian for the anti-JC interaction is written as
\begin{equation}
H_{\rm{aJC}} = \omega\hat{a}^{\dagger}\hat{a}+(\omega+\Delta_{\rm aJC})\hat{\sigma}^{-}\hat{\sigma}^{+}+g_{b}(\hat{a}\hat{\sigma}^{-}+\hat{a}^{\dagger}\hat{\sigma}^{+}),
\end{equation}
where $\Delta_{\rm aJC}\equiv\omega_{\rm L}-(\omega_{0}+\omega)$. The last term corresponds to the blue-sideband transition, and ${\it g_{b}}$ represents the anti-JC coupling strength. Note that this anti-JC Hamiltonian is formally equivalent to the JC Hamiltonian given in equation\,(1) as they can be brought to the same form by interchanging the labeling of $\ket{\downarrow}$ and $\ket{\uparrow}$.

Then, at resonance, i.e. $\Delta_{\rm aJC}=0$, the eigenstates of $H_{\rm{aJC}}$ are
\begin{eqnarray}
\left\{
\begin{array}{l}
\ket{l=0}=\ket{\uparrow,0},\\
\ket{l^\pm} = \frac{1}{\sqrt{2}}(\ket{\uparrow,l}\pm\ket{\downarrow,l-1})\quad(l>0).
\end{array}
\right.
\end{eqnarray}
Here, $l$ represents the the number of polaritons. $\ket{\uparrow,l}\equiv\ket{\uparrow}\otimes\ket{n=l}$ and $\ket{\downarrow,l-1}\equiv\ket{\downarrow}\otimes\ket{n=l-1}$. The corresponding eigenenergies are given by
\begin{eqnarray}
\left\{
\begin{array}{l}
E_{0}=0\quad(l=0),\\
E_{\pm,l} = l\omega\pm\sqrt{l}g_{b}\quad(l>0).
\end{array}
\right.
\end{eqnarray}
The energy levels for the anti-JC eigenstates are shown in figure\,1(b).

\subsection{Anti-Jaynes--Cummings--Hubbard model with trapped ions}

The Hamiltonian for the anti-JCH model with $N$ ions with mass $m$ and charge $e$, in a frame rotating with frequency $\omega_r$ for harmonic confinement along a radial direction with the rotating wave approximation, is described as follows:
\begin{equation}
H_{\rm aJCH} = \sum_{i=\rm 1}^{N}\omega_{i}\hat{a}_{i}^{\dagger}\hat{a}_{i}+\sum_{i=\rm 1}^{N}\delta_{i}\hat{\sigma}_{i}^{-}\hat{\sigma}_{i}^{+}+g_{b}\sum_{i=\rm1}^{N}(\hat{a}_{i}\hat{\sigma_{i}}^{-}+\hat{a}_{i}^{\dagger}\hat{\sigma_{i}}^{+})+\sum_{i<j}^{N}\frac{\kappa_{ij}}{2}(\hat{a}_{i}\hat{a}_{j}^{\dagger}+\hat{a}_{j}^{\dagger}\hat{a}_{i}),
\end{equation}
where $\kappa_{ij}=e^{2}/4\pi\varepsilon_{0}\it{m}\it{d_{ij}}^{\rm 3}\omega_{r}$ and $\omega_{i}=-\sum_{i\neq j}^{N}\kappa_{ij}/{\rm 2}$ are the hopping rate and the position-dependent secular frequency shift of the $\it{i}$th ion, respectively. The first term represents the harmonic oscillator, where $\hat{a}_{i}^{\dagger}$ and $\hat{a}_{i}$ are the creation and annihilation operators for local phonons along the radial direction of the $\it{i}$th ion. The second term represents the energy of the $\it{i}$th ion, where the raising and lowering operators for the ${\it i}$th ion are defined as $\hat{\sigma}_{i}^{+}=\ket{\uparrow_{i}}\bra{\downarrow_{i}}$ and $\hat{\sigma}_{i}^{-}=\ket{\downarrow_{i}}\bra{\uparrow_{i}}$. $\delta_{i}$ is the detuning from the resonance of the blue-sideband transition for the $\it{i}$th ion. In the present work, we perform every experiment in the resonant condition, i.e., $\delta_{i}=0$. The third term represents the anti-JC interactions induced by a laser tuned to the blue-sideband transition. ${\it g_{b}}$ can be denoted as $\eta\Omega_{0}/{2}$, where $\eta$ is the Lamb--Dicke parameter and $\Omega_{0}$ is a value close to the Rabi frequency for the carrier transition. The last term describes hopping of phonons between different ion sites. $\kappa_{ij}$ is the hopping rate of local phonons between the $i$th and $j$th ion sites.

\subsection{Polaritons in trapped ions}

In the anti-JCH model with trapped ions, polaritons arise when the ions are illuminated with blue-sideband optical pulses. The energy levels for an ion incorporating both the internal and phonon states are shown in figure\,1(a).

The anti-JCH model is characterized by the polariton number at each ion site. The polariton-number operator for the anti-JCH model at $i$th ion site is defined as $N_{i} = \hat{a}_{i}^{\dagger}\hat{a}_{i}+\hat{\sigma}_{i}^{-}\hat{\sigma}_{i}^{+}$. \footnote{Note that the definition of the internal-state excitation is different from the ordinary convention because of the anti-JC coupling: it gives an expectation value of 1 for the state $\ket{\downarrow_i}$.} In the present experiment, a polariton number of up to two is considered. Since the anti-JCH Hamiltonian commutes with the total polariton-number operator $N_{\rm{t}}$, i.e. $[H_{\rm{aJCH}}, N_{\rm{t}}] = [H_{\rm{aJCH}}, \sum_{i=\rm 1}^{N}N_{i}] = 0$, $N_{\rm{t}}$ is conserved in the anti-JCH system.

\begin{figure}[h]
\centering
  \includegraphics[width=14.0cm]{Fig1_rev.pdf}
\caption{\label{fig1} (a) Basis states relevant to polaritons in the anti-JC model with trapped ions. The unperturbed energy levels for an ion incorporating both the internal and phonon states are depicted. (b) Energy levels for the anti-JC eigenstates when $\Delta_{\rm aJC}=0$. Here the energy of $\ket{\downarrow,n}$ is identified with that of $\ket{\uparrow,n+1}$ by going into the frame rotating with their difference energy.}
\end{figure}

\section{Experimental results}

\subsection{Single-polariton hopping}

We first present single-polariton dynamics in a two-ion chain. The experimental setup is shown in figure\,2(a). Two $^{40}{\rm Ca}^{+}$ ions are trapped in a linear Paul trap. The frequencies for the harmonic confinement along the radial ($\it{x}$ and $\it{y}$) and axial ($\it{z}$) directions for the two ions are $(\omega_{x}, \omega_{y}, \omega_{z})/{\rm 2}\pi=$ (3.00, 2.81, 0.11) MHz. To encode a two-level system, we use the internal states $\ket{S_{1/2},m_{j}=-1/2}\equiv\ket{\downarrow}$ and $\ket{D_{5/2},m_{j}=-1/2}\equiv\ket{\uparrow}$ (see figure\,2(b)). The lifetime of the metastable state $D_{5/2}$ is $\sim1.2$ s. In addition, we use another Zeeman sublevel in the metastable state, $\ket{D_{5/2},m_{j}=-5/2}\equiv\ket{e_{0}}$, as an auxiliary state for shelving probability amplitudes in the detection sequence.

\begin{figure}[h]
\centering
  \includegraphics[width=14.0cm]{Fig2_rev.pdf}
\caption{\label{fig2} (a) Experimental setup: two $^{40}{\rm Ca}^{+}$ ions are trapped in a linear Paul trap. Two 729 nm beams are focused on each ion to manipulate their local phonon states. (b) Relevant energy diagram of $^{40}{\rm Ca}^{+}$ ion. Internal states $\ket{S_{1/2},m_{j}=-1/2}$ and $\ket{D_{5/2},m_{j}=-1/2}$ are used as $\ket{\downarrow}$ and $\ket{\uparrow}$, respectively. We also use the metastable state $\ket{D_{5/2},m_{j}=-5/2}\equiv\ket{e_{0}}$ in the experiments. (c) Experimental sequences to observe single-polariton hopping. To perform the measurement in three different basis states $\ket{\uparrow_{i},0}$, $\ket{\uparrow_{i},1}$, and $\ket{\downarrow_{i},0}$, one of the three different sequences is chosen and conducted. After sideband cooling (SBC), a carrier $\pi$ pulse ($\pi_{\rm C}$) is applied to Ion 1. Then, both ions are illuminated with lasers tuned to the blue-sideband (BSB) transition. After waiting for a duration $\tau$, a mapping pulse sequence is applied to measure the quantum states in each basis state. A shelving $\pi$ pulse ($\pi_{\rm S}$), which drives the transition $\ket{\downarrow_{i},n}\leftrightarrow\ket{{e_{0}}_{i},n}$, and a blue-sideband $\pi$ pulse ($\pi_{\rm B}$) are applied accordingly depending on the target state. Afterwards, the fluorescence detection is performed.}
\end{figure}

The experimental sequence is shown in figure\,2(c). In the experiments, three different transitions are used: carrier ($\ket{\downarrow_{i},n}\leftrightarrow\ket{\uparrow_{i},n}$), blue-sideband ($\ket{\downarrow_{i},n}\leftrightarrow\ket{\uparrow_{i},n+1}$), and ``shelving'' ($\ket{\downarrow_{i},n}\leftrightarrow\ket{{e_{0}}_{i},n}$). The experiment starts with Doppler cooling with lasers at 397 nm (${\it S_{\rm 1/2}}$--${\it P_{\rm 1/2}}$) and 866 nm (${\it D_{\rm 3/2}}$--${\it P_{\rm 1/2}}$) followed by resolved sideband cooling of the radial motional modes. A narrow quadrupole transition (729 nm, ${\it S_{\rm 1/2}}$--${\it D_{\rm 5/2}}$) is used for motional ground state cooling. In the experiment, we employ local phonons along the {\it y} direction. After the sideband cooling, the average quantum number for local phonons along the {\it y} direction is 0.04.

As shown in figure\,2(a), two individual 729 nm beams are focused on the ions for simultaneous addressing. For this simultaneous addressing, we use an optical system that is based on single-mode optical fibers. We prepare two individual beams at 729 nm with a polarization beam splitter and half waveplates. After passing through an acousto-optic modulator, each beam is coupled to a single-mode fiber for stabilizing the optical path. Then, the two beams are aligned with D-shaped mirrors. Compared with other optics such as half mirrors, D-shaped mirrors mitigate optical power losses so that fast Rabi flopping can be realized. By simply adding similar optical paths, we can address more individual ions simultaneously. The beam is focused to a size of $\sim3$ $\mu$m.

We prepare the ions in $\ket{\psi_{\rm Init}}=\ket{\psi_{1}}\otimes\ket{\psi_{2}}=\ket{\uparrow_{1},0}\otimes\ket{\downarrow_{2},0}=\ket{\uparrow_{1},0}\otimes(\ket{1^+}-\ket{1^-})/\sqrt{2}$ by applying a carrier $\pi$ pulse to Ion 1. Here, the polariton numbers for Ion 1 and Ion 2 in the anti-JCH model are 0 and 1, respectively. After preparing a single polariton, both ions are illuminated with a pulse tuned to the blue-sideband transition.

To experimentally observe the quantum dynamics of a single polariton, we need to measure the quantum states in three basis states, $\ket{\uparrow_{i},0}$, $\ket{\uparrow_{i},1}$, and $\ket{\downarrow_{i},1}$. Therefore, we employ three different sequences for three states, shown in figure\,2(c). By utilizing these mapping sequences, it is possible to map the probability amplitude of each state onto an internal state. For detection, 397 nm and 866 nm lasers are applied to collect the state-dependent fluorescence with a CCD camera.

\begin{figure*}[h]
\centering
  \includegraphics[width=16.0cm]{Fig3_rev.pdf}
\caption{\label{fig3} (a) Numerical simulation of single polariton hopping. Simulated populations in $\ket{\uparrow_{i},0}$ (blue), $\ket{\uparrow_{i},1}$ (black), and $\ket{\downarrow_{i},0}$ (orange), as well as the sum of the populations in $\ket{\uparrow_{i},1}$ and $\ket{\downarrow_{i},0}$ (red) are shown. The blue and red solid curves correspond to populations in 0- and 1-polariton manifolds, respectively. A single polariton hops between Ion 1 and Ion 2. (b) Results of the single-polariton hopping experiments of Ion 1 (top) and Ion 2 (bottom). Measured populations in $\ket{\uparrow_{i},0}$ (blue), $\ket{\uparrow_{i},1}$ (black), and $\ket{\downarrow_{i},0}$ (orange), as well as the sum of the populations in $\ket{\uparrow_{i},1}$ and $\ket{\downarrow_{i},0}$ (red), are shown. The blue and red data correspond to populations in 0- and 1-polariton manifolds, respectively. The dotted curves represent numerical calculations for each state or manifold. Each point is the average of 50 measurements. The gray dotted lines represent a population of 1.}
\end{figure*}

We first provide the results of numerical simulations. We employ the Lindblad master equation for the density matrix with parameters $(\kappa_{12}, 2g_{\rm b})/{\rm 2}\pi$ = (2, 15) kHz. The results are shown in figure\,3(a). As an initial state, the quantum states of the ions are prepared in $\ket{\psi_{\rm Init}}=\ket{\uparrow_{1},0}\otimes\ket{\downarrow_{2},0}$. For simplicity, we do not include any decoherence processes in the results of figure\,3(a). The population in the $l$-polariton manifold at the $i$th ion site ($i=1,2$) can be represented as
\begin{eqnarray}
\left\{
\begin{array}{l}
\bra{\uparrow_{i},0}\rho_{i}\ket{\uparrow_{i},0}\quad(l=0),\\
\bra{\uparrow_{i},l}\rho_{i}\ket{\uparrow_{i},l}+\bra{\downarrow_{i},l-1}\rho_{i}\ket{\downarrow_{i},l-1}\quad(l>0),
\end{array}
\right.
\end{eqnarray}
where $\rho_{i}$ is the reduced density matrix for the {\it i}th ion. Accordingly, the population in the 0-polariton manifold can be identified as that in $\ket{\uparrow_{i},0}$, and the population in the 1-polariton manifold is the sum of those in $\ket{\uparrow_{i},1}$ and $\ket{\downarrow_{i},0}$.

In figure\,3(a), the populations in the 0-polariton and 1-polariton manifolds are shown as blue and red solid curves, respectively. Additionally, the simulated populations in $\ket{\uparrow_{i},1}$ and $\ket{\downarrow_{i},0}$ are represented as black and orange solid curves, respectively. As seen in figure\,3(a), there are slow oscillations with a period of $\sim1$ ms in the blue or red curves, and fast oscillations with a period of $\sim70$ $\mu$s in the black or orange curves. The slow oscillations indicate that a single polariton hops between Ion 1 and Ion 2. The fast oscillations correspond to the blue-sideband transition between $\ket{\uparrow_{i},1}$ and $\ket{\downarrow_{i},0}$.

In figure\,3(b), the measured populations in $\ket{\uparrow_{i},0}$ (blue), $\ket{\uparrow_{i},1}$ (black), and $\ket{\downarrow_{i},0}$ (orange) are shown.\footnote{Note that the three populations shown here are the results of independent measurements and are not normalized with respect to their sum. We avoid normalizing them in order not to introduce additional systematic shifts of the populations. The errors of detecting a 1-polariton state may include systematic ones due to the fluctuation of the blue-sideband Rabi frequency, which are discussed later. Thus, normalizing the overall results may lead to the unwanted propagation of such systematic errors among the populations.} The blue and red data represent the measured populations in the 0-polariton and 1-polariton manifolds, respectively. Each point is the average of 50 measurements and the dotted curves are numerically calculated results incorporating the infidelity of the initial preparation and the dephasing of the Rabi oscillation at the carrier, blue-sideband, and shelving transitions. The blue-sideband Rabi frequency used in the numerical simulations is 15.7 kHz. The hopping rate $\kappa_{12}/{\rm 2}\pi$ is experimentally measured to be 2.12 kHz.

In figure\,3(b), the population in the 1-polariton manifold (red) at some data points exceeds 1. This is due to the fluctuation of the blue-sideband Rabi frequency in the measurements. During the experiment, we observe temporal changes of the ions' positions ($\sim0.6$ $\mu$m), which may lead to variations in the blue-sideband Rabi frequencies. The changes can be attributed to fluctuations in stray electric fields. Considering the beam waist ($\sim3$ $\mu$m), the corresponding reduction of the laser power experienced by the ions is estimated to be about 15\%. The population in the 1-polariton manifold (red) is deduced as being the sum of the populations in $\ket{\uparrow_{i},1}$ (black) and $\ket{\downarrow_{i},0}$ (orange). A fluctuation of the Rabi frequency between the measurements could cause errors in these populations such that the summation of the two becomes unphysical.

\subsection{Polariton blockade}

We next present the results of the polariton blockade experiment. The polariton blockade studied in the present experiment is based on the nonlinearity of the anti-JC interactions.

We consider a two-ion chain and assume that initially a single polariton exists at each ion site. The quantum state of the ions is expressed as $\ket{\psi}=\ket{1^\pm}\otimes\ket{1^\pm}\equiv\ket{1^\pm,1^\pm}$. Here, the $l$-polariton state is experessed as $\ket{l=0}=\ket{\uparrow,0}$ or $\ket{l^\pm} = (\ket{\uparrow,l}\pm\ket{\downarrow,l-1})/\sqrt{2}$ $(l>0)$. The polariton hopping induces the transitions $\ket{1^\pm,1^\pm}\leftrightarrow\ket{2^\pm,0}=\ket{2^\pm}\otimes\ket{l=0}$ and  $\ket{1^\pm,1^\pm}\leftrightarrow\ket{0,2^\pm}=\ket{l=0}\otimes\ket{2^\pm}$. According to equation (4), the energy of $\ket{k^\pm,l^\pm}$ ($k+l=L$) is
\begin{equation}
E_{k^\pm}+E_{l^\pm} = L\omega\pm(\sqrt{k}+\sqrt{l})g_{b}.
\end{equation}
The single-polariton hopping corresponds to the case of $L=1$. In this case, the total energies for the possible basis states ($\ket{1^\pm,0}=\ket{1^\pm}\otimes\ket{l=0}$, $\ket{0,1^\pm}=\ket{l=0}\otimes\ket{1^\pm}$) are equal if one of the eigenenergy  branches (+ or $-$) is selected. This energy is explicitly denoted as $E_{1^\pm}+E_{0}=\omega\pm g_{b}$. Therefore, there is no energy gap between the basis states in each branch, i.e. $\ket{1^+,0}$ and $\ket{0,1^+}$, or $\ket{1^-,0}$ and $\ket{0,1^-}$ (see figure\,4(a)(left) for the energy-level diagram).

\begin{figure}[h]
\centering
  \includegraphics[width=13.0cm]{Fig4_rev.pdf}
\caption{\label{fig4} (a) Energy level diagram for a single-polariton (left) and two polaritons in two ions (right). (b) Experimental sequences for observing single-polariton blockades. One measurement sequence is chosen from the three different sequences, which are optimized for measurements in the basis states $\ket{\uparrow_{i},0}$, $\ket{\uparrow_{i},1}$, and $\ket{\downarrow_{i},0}$, respectively. Both ions are cooled to the motional ground states using sideband cooling (SBC). Then, both ions are illuminated with lasers detuned at the blue-sideband (BSB) transition. The illumination time of the BSB pulse $\tau$ is varied. After waiting for a duration $\tau$, a mapping pulse sequence is applied to measure the quantum states in each basis state. A shelving $\pi$ pulse ($\pi_{\rm S}$) and a blue-sideband $\pi$ pulse ($\pi_{\rm B}$) are employed depending on each state. Afterward, fluorescence detection is performed.}
\end{figure}

On the other hand, in the case of $L = 2$, there is an energy gap between $\ket{2^\pm,0}$ and $\ket{1^\pm,1^\pm}$ (or $\ket{1^\pm,1^\pm}$ and $\ket{0,2^\pm}$): $(E_{2^\pm}+E_{0})-2E_{1^\pm}=\mp(2-\sqrt{2})g_{b}\neq0$. This energy gap suppresses polariton hopping (see figure\,4(a)(right) for the energy-level diagram).
Note that a polariton blockade can be applied to the ${\it l}$-polariton case. The energy gap between $\ket{l^\pm}$ and $\ket{(l-1)^\pm}$ can be calculated as
\begin{equation}
\delta E_{l} = \omega\pm(\sqrt{l}-\sqrt{l-1})g_{b}.
\end{equation}
However, this indicates that as the polariton number $l$ grows, it becomes harder to block the transition $\ket{(l-1)^\pm}\leftrightarrow\ket{l^\pm}$.

The experimental sequence is shown in figure\,4(b). After sideband cooling, the quantum state of the ions is $\ket{\psi_{\rm Init}}=\ket{\downarrow_{1},0}\otimes\ket{\downarrow_{2},0}$. Since $\ket{\downarrow_{i},0}$ is a superposition of the 1-polariton states, $\ket{1^+}$ and $\ket{1^-}$, no additional pulses are required for state preparation. Then, the ions are illuminated with blue-sideband pulse. For detection, we also employ the same pulse sequences used in the single-polariton experiment.

We first show the numerically simulated results for the quantum dynamics of two polaritons in a two-ion chain in figure\,5(a-c). Values for the parameters of $(\kappa_{12}, 2g_{\rm b})/{\rm 2}\pi$ = (2, 15) kHz are used for the numerical calculations. As an initial state, the quantum states of the ions are prepared in $\ket{\psi_{\rm Init}}=\ket{\downarrow_{1},0}\otimes\ket{\downarrow_{2},0}$. In this simulation, we do not include any decoherence processes. Note that in this case the dynamics of the two ions, as well as their initial states, are expected to be identical to each other due to the symmetry with respect to the exchange of the ions. Therefore, we only show the state populations for one of the ions.

\begin{figure*}[h]
\centering
  \includegraphics[width=16.0cm]{Fig5_rev.pdf}
\caption{\label{fig5} (a--c) Numerical simulation of a polariton blockade. (a) Simulated populations in $\ket{\uparrow_{i},0}$ (blue). (b) Simulated populations in $\ket{\uparrow_{i},1}$ (black), $\ket{\downarrow_{i},0}$ (orange), as well as their sum (red). (c) Simulated populations in $\ket{\uparrow_{i},2}$ (black) and $\ket{\downarrow_{i},1}$ (orange), as well as their sum (red). (d) Results of the single-polariton blockade experiments of Ion1 (top) and Ion 2 (bottom). Measured populations $\ket{\uparrow_{i},0}$ (blue), $\ket{\uparrow_{i},1}$ (black), and $\ket{\downarrow_{i},0}$ (orange), as well as the sum of $\ket{\uparrow_{i},1}$ and $\ket{\downarrow_{i},0}$ (red) are shown. Each point is an average of 50 measurements. The dotted curves represent numerically calculated populations. The solid curves correspond to the numerically calculated populations expected for each of the three actual measurement sequences in figure\,4(b). The gray dotted lines represent a population of 1.}
\end{figure*}

Figure\,5(a) shows the population in $\ket{\uparrow_i,0}$, or equivalently that in the 0-polariton manifold, as a blue solid curve. In figure\,5(b), the black and orange solid curves represent the simulated populations in $\ket{\uparrow_{i},1}$ and $\ket{\downarrow_{i},0}$, respectively, and the red solid curve corresponds to the population in the 1-polariton manifold. We also show the populations in the 2-polariton states in figure\,5(c). The black and orange solid curves represent the populations in $\ket{\uparrow_{i},2}$ and $\ket{\downarrow_{i},1}$, respectively. The red solid curves corresponds to the 2-polariton population ($\bra{\uparrow_{i},2}\rho_{i}\ket{\uparrow_{i},2}+\bra{\downarrow_{i},1}\rho_{i}\ket{\downarrow_{i},1}$). As can be seen in figure\,5(a--c), the population in the 1-polariton manifold at each ion site remains high while the population in 0-polariton and 2-polariton manifolds remains negligible.

In this experiment, for the full determination of the polariton states, we need to measure the 0-, 1-, and 2-polariton states. This requires measurements in five different basis states: $\ket{\uparrow_{i},0}$ for the 0-polariton state, $\{\ket{\uparrow_{i},1},\ket{\downarrow_{i},0}\}$ as the 1-polariton states, and $\{\ket{\uparrow_{i},2},\ket{\downarrow_{i},1}\}$ as the 2-polariton states. Fully determining the polariton state using state-dependent fluorescence detection requires many auxiliary levels and extensive pulse sequences similar to those used in phonon-number-resolving detection \cite{9} (see Discussion for details). However, in the present experimental setup, the decoherence of the relevant transitions required for the phonon-number-resolving detection is not negligible, and the overall results may result in the lower contrasts.

However, the measurement scheme can be simplified if we can assume that the system stays in the subspace with two polaritons in total. In this case, the population in the 0-polariton manifold at either of the two ion sites is equal to that in the 2-polariton manifold at the other ion site. Therefore, a simplified measurement scheme similar to that used in the observation of single-polariton hopping, where only $\ket{\uparrow_i,0}$, $\ket{\uparrow_i,1}$, and $\ket{\downarrow_i,0}$ are determined, would give the full information of the system with respect to the polariton number at each ion site.

Of course, the assumption given above is not exactly satisfied in reality, and we should consider deviations from it. Deviations toward smaller numbers of polaritons (i.e., zero or one polariton in total) can be covered by the simplified scheme given above, while those toward larger numbers of polaritons (i.e., three or more polaritons in total) should be considered separately. In our estimation, the maximum population that the system has residing in the subspaces with three polaritons or more in total is $\sim0.084$. This residual population can be estimated by considering imperfect preparation and population leakages due to the motional heating. The predominant cause of imperfect preparation is residual motional excited-state populations after sideband cooling of the relevant radial mode. The finite average quantum number is 0.04, indicating that residual populations of 0.08 exist for three polaritons or more in total. Leakage due to heating of the radial modes can be evaluated from independent measurements of the system's heating rate. Our previous study gives 5 quanta/s for a four-ion chain \cite{10}, and typically a smaller value is expected for the two ions used here. If we choose to use the same heating rate and a maximum total duration of the time sequence of $\sim840$ $\mu$s, we can obtain an upper bound of 0.004 for the current study. As a result, the maximum total population that the system has residing in the subspace with three polaritons or more is estimated to be $\sim0.084$. Although this amount is not negligible, we can interpret the qualitative behavior of the polaritonic system in the presence of such an imperfection.

Figure\,5(d) shows the experimentally observed populations in $\ket{\uparrow_{i},0}$ (blue), $\ket{\uparrow_{i},1}$ (black), $\ket{\downarrow_{i},0}$ (orange)\footnote{For the same reason as in the case of single-polariton hopping, these three populations are not normalized with respect to their sum.}, and the 1-polariton manifold (red). Each point is an average of 50 measurements. The dotted curves are numerically simulated populations in each state or manifold. The infidelity of the initial preparation and the dephasing of the Rabi oscillation at the carrier, blue-sideband, and shelving transitions are included in the simulation. The blue-sideband Rabi frequency used in the numerical simulations for each quantum state is 15.7 kHz. The experimental data show good agreement with the simulated data.

In addition to the deviations of the total number of polaritons mentioned above, there are two other major errors. The first is the fluctuation of the blue-sideband Rabi frequency, which results in some data points for the population in the 1-polariton manifold (red), exceeding 1. As discussed in the single-polariton hopping experiment, this can be attributed to a temporal shift in the position of the ions. The second derives from miscounting the state populations due to an incomplete experimental sequence. The experimental sequence used in this work is optimized for evaluating 0- and 1-polariton state. However, populations in higher polariton manifolds are also partially mapped to $\ket{\downarrow_{i}}$. These residual populations can cause measurement errors. To verify this error, we numerically calculate the populations expected for each of the three actual measurement sequences in figure\,4(b). The simulated populations are shown as solid curves in figure\,5(d). The simulated results incorporating the actual measurement sequences show better agreement with the experimental results, while the remaining discrepancies can be ascribed to the other error sources discussed above. The concentration of the population to the 1-polariton manifolds confirmed here indicates the occurrence of polariton blockades.

\section{Discussion}

Although the mapping sequences used in the present experiments are not exhaustive for detecting multiple polaritons, we speculate that we can characterize the polariton states using sufficient mapping sequences. This is because the populations in 0-polariton and 2-polariton manifolds are expected to be small and, therefore, we can distinguish the 3-polariton states with such non-exhaustive measurements. Nonetheless, we need a detection method to precisely evaluate the $n$-polariton state to explore the different polariton dynamics in the future, especially in regions where hopping is dominant compared with the polariton--polariton interaction. In this parameter region, the polariton hopping results in the superposition of different polariton states.

One of the possibilities is the extended scheme of the phonon-number-resolving detection \cite{9}. Here, we show the possible detection scheme for observing the 2-polariton state (figure\,6). For implementing the proposed detection scheme, four long lived states are required, and in the case of $^{40}\rm Ca^{+}$ ion, the zeeman sublevels of $D_{5/2}$ state are used. Here, each state is labelled as $\ket{D_{5/2},m_{j}=-5/2}\equiv\ket{e_{0}}, \ket{D_{5/2},m_{j}=-3/2}\equiv\ket{e_{1}}, \ket{D_{5/2},m_{j}=1/2}\equiv\ket{e_{2}}$, and $\ket{D_{5/2},m_{j}=3/2}\equiv\ket{e_{3}}.$ The detection process is as follows. (1) A shelving $\pi$ pulse is applied to transfer the probability amplitude of $\ket{\downarrow_i}$ to $\ket{e_{3i}}$. (2) Either a composite-pulse sequence or adiabatic passage over the blue-sideband transition is applied to realize the uniform transfer of the probability amplitude between the transitions $\ket{\downarrow_{i},0}\leftrightarrow\ket{\uparrow_{i},1}$ and $\ket{\downarrow_{i},1}\leftrightarrow\ket{\uparrow_{i},2}$. (3) We, then, flip the internal state ($\ket{\downarrow_{i}}\leftrightarrow\ket{\uparrow_{i}}$) by applying a carrier $\pi$ pulse. (4) The probability amplitude of $\ket{\downarrow_{i},0}$ is transferred to $\ket{e_{0i},0}$ by a shelving $\pi$ pulse. (5) The probability amplitude of $\ket{\uparrow_{i},1}$ is transferred to $\ket{\downarrow_{i},0}$ by a blue-sideband $\pi$ pulse, then, is subsequently transferred to $\ket{e_{1i},0}$ by a shelving $\pi$ pulse. (6) Likewise, the probability amplitude of $\ket{\uparrow_{i},0}$ is mapped onto the long-lived auxiriary state $\ket{e_{2i},0}$ by sequential carrier and shelving $\pi$ pulses. (7) The probability amplitude of $\ket{e_{3i}}$ is transferred back to $\ket{\downarrow_{i}}$. (8) Finally, a red-sideband $\pi$ pulse maps the probability amplitude of $\ket{\downarrow_{i},1}$ onto $\ket{\uparrow_{i},0}$. After the mapping sequence, the all probability amplitudes of 0-, 1-, and 2-polariton basis states are stored in the motional ground state, i.e. $\ket{\uparrow_{i},0}\rightarrow\ket{e_{0i},0}$, $\ket{\uparrow_{i},1}\rightarrow\ket{e_{2i},0}$, $\ket{\downarrow_{i},0}\rightarrow\ket{\downarrow_{i},0}$, $\ket{\uparrow_{i},2}\rightarrow\ket{e_{1i},0}$, and $\ket{\downarrow_{i},1}\rightarrow\ket{\uparrow_{i},0}$. These mapped states can be detected by applying a sequential detection pulse as performed in the previous study \cite{9}. In the present experimental setup, the decoherence of the relevant transitions required for implementing this measurement is not negligible; therefore, we employ another detection scheme.

\begin{figure*}[h]
\centering
  \includegraphics[width=15.0cm]{Fig6.png}
\caption{\label{fig6} Complete mapping sequence for detecting the 2-polariton state. The probability amplitude of each polariton basis state is mapped onto a Zeeman sublevel of the metastable state with the vibrational motion in the ground state.}
\end{figure*}

The polariton--polariton interaction may play important roles in various physical phenomena expected to obey the JCH (anti-JCH) model. For instance, for 2-polariton quantum dynamics, it has been theoretically predicted that a 2-polariton bound state is expected to be observed \cite{15}, which is analogous to the second-order tunneling of a bound two-boson realized with cold atoms \cite{16,17}. By providing site-dependent polariton--polariton interactions, so that the polaritons feel a tilted potential, it may be possible to observe the Bloch oscillation of polaritons, which has also been extensively studied in cold atoms trapped in optical lattices \cite{18}.

\section{Conclusions}
In conclusion, we have observed the 1-polariton and 2-polariton dynamics in the anti-JCH model with two ions. A single polariton hops between the ion sites, whereas the polariton--polariton interaction suppresses the hopping in the presence of a single polariton at each ion site.

\section*{Acknowledgments}
This work was supported by MEXT Quantum Leap Flagship Program (MEXT Q-LEAP) Grant Number JPMXS0118067477.

\section*{References}

redpajama_set_name: RedPajamaArXiv


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