text:
\section*{Abstract}
We investigate weak force sensing based on coherent quantum noise cancellation in a nonlinear hybrid optomechanical system. The optomechanical cavity contains a moveable mechanical mirror, a fixed semitransparent mirror, an ensemble of ultracold atoms, and an optical parametric amplifier (OPA). Using the coherent quantum noise cancellation (CQNC) process, one can eliminate the back action noise at all frequencies. Also by tuning the OPA parameters, one can suppress the quantum shot-noise at lower frequencies than the resonant frequency. In the CQNC scheme, the damping rate of the mechanical oscillator matches the damping rate of the atomic ensemble, which is experimentally achievable even for a low-frequency mechanical oscillator with a high-quality factor. Elimination of the back action noise and suppression of the shot noise significantly enhance force sensing and thus overcome the standard quantum limit of weak force sensing. This hybrid scheme can play an essential role in the realization of quantum optomechanical sensors and quantum control.

\end{abstract}

\maketitle

\narrowtext
\section{Introduction} \label{I}
Weak force sensing at the quantum limit of sensitivity has attracted a lot of attention in recent decades \cite{braginsky1980quantum,braginsky1995quantum}. This tendency leads to the development of quantum cavity optomechanics and the possibility of using quantum phenomena in macroscopic dimensions \cite{aspelmeyer2014cavity}. Optomechanical sensors have given accurate results to measure mass \cite{bin2019mass,liu2019realization}, acceleration \cite{krause2012high,qvarfort2018gravimetry}, displacement \cite{wilson2015measurement,rossi2018measurement}, and force
\cite{caves1980measurement,schreppler2014optically,ghobadi2015weak}. However, the measurement accuracy of optomechanical sensors is limited by the shot noise and the back-action noise, in which their competition are collectively called the standard quantum limit (SQL) \cite{bowen2015quantum}. The quantum non-demolition measurement \cite{thorne1978quantum} via quantum entanglement \cite{ma2017proposal} or squeezing \cite{clark2016observation,otterpohl2019squeezed} can be used to surpass the SQL. Also, the squeezed states are traditionally  employed to detect gravitational waves via supersensitive interferometry \cite{hollenhorst1979quantum,aasi2013enhanced,dodonov1980nondemolition}.

In the optomechanical sensor, as the intensity of the optical field increases, the measurement strength and the shot noise decrease while the back-action noise increases. Therefore, to increase the force sensitivity, it is necessary to reduce or eliminate the back-action noise. It is suggested \cite{hertzberg2010back} that measuring only a single quadrature of motion can increase the force sensitivity. In this method, the effect of the back-action noise on the orthogonal quadrature in the measurement is isolated. Woolly and Clerk \cite{woolley2013two} proposed a three-mode optomechanical system to evade the back-action noise, in which two mechanical oscillators are coupled to a single cavity mode.
Hammerer $\it{et~al.}$ \cite{hammerer2009establishing} introduced an anti-noise path in the system to cancel the back-action noise of light via quantum interference. They showed that an ancillary atomic oscillator could exhibit an opposite and equal response to the optical field in the optomechanical cavity. In this way, the CQNC process can delete the back-action noise, which is induced by the radiation pressure at all frequencies, and surpass the SQL \cite{tsang2010coherent,tsang2012evading}. The atomic ensemble can be coupled to the optomechanical systems, internally or externally, to improve the optomechanical cooling \cite{genes2009micromechanical,hammerer2010optical,genes2011atom,camerer2011realization} and create the best regime relevant to force sensing at the low mechanical frequency with a high-quality factor \cite{wimmer2014coherent}.

In addition, the interaction between the atomic ensemble and mechanical oscillator has been used to provide entanglement, entangled Einstein-Podolsky-Rosen (EPR) states, and squeezed states in the hybrid optomechanical system \cite{hammerer2009establishing}. The combination of the optomechanical system, the atomic two-level system and also the OPA can be utilized as an applicable candidate for force sensing \cite{wasilewski2010quantum,muschik2011dissipatively,polzik2015trajectories}.
Recently, the cavity optomechanical system with the OPA is used to implement ultrahigh-precision position detection \cite{peano2015intracavity}. The advantage of this scheme is that the information is imprinted on the momentum quadrature, which is not amplified. It leads to a limited suppression of signal but simultaneously reduces the noise dramatically. Then, one can obtain the SQL without losing quantum efficiency at a mechanical resonance in the squeezed resonator. On the other hand, using the OPA, the SQL can be attained in a dissipative cavity optomechanical system \cite{huang2017robust}. So far, the hybrid optomechanical system, including the OPA and the atomic ensemble, is not used to enhance force sensing.

He \textit{et~al.} \cite{he2020normal} used the hybrid optomechanical system, containing the degenerate OPA and the atomic ensemble, to investigate the displacement spectrum of the moveable mirror and the spectrum of squeezed cavity quadrature field.
They showed that this hybrid optomechanical system leads to a wider spacing between the two peaks in the normal mode splitting and a more significant degree of the squeezing spectrum compared with the case of the optomechanical system with just one of the atomic ensemble or the OPA. Furthermore, the peak in the squeezed spectrum diminishes at lower temperatures due to the reduction of mechanical thermal noise.

Under these considerations, the present paper aims to study the CQNC force sensing in the hybrid optomechanical system containing both the OPA and the atomic ensemble. The mechanical oscillator, coupled to the atomic ensemble as the oscillator with the effective negative mass, is used for force sensing. Based on the scheme of Tsang $\it{et~al.}$ \cite{tsang2010coherent,tsang2012evading}, the coupling between the optomechanical cavity and the atomic ensemble is necessary for the CQNC process. On the other hand, tuning the OPA parameters can improve the precision of force sensing and reach the sub-SQL sensitivity at small values of the optomechanical coupling without losing quantum efficiency \cite{zhao2020weak}. The rest of the present paper is organized as follows. In section \ref{II}, we present the hybrid optomechanical system and model for optomechanical force sensing and derive the equations of motion. The central conditions for ideal CQNC and shot noise reduction are given based on the physical parameters of the system.  In section \ref{III}, we discuss force sensing and the feasibility of physical parameters of the system. A summary of our main results is provided in section \ref{IV}.

\section{Hybrid optomechanical system and model} \label{II}
We consider the hybrid optomechanical system, which contains a moveable mirror known as a mechanical oscillator, a trapped ultracold atomic ensemble and an optical parametric amplifier (OPA), as shown in Fig.~\ref{Fig1}. The atomic ensemble is driven by the intracavity field and a classical field. It can generate a strong atom-field coupling to store and transfer quantum states through the collective atomic excitation \cite{akulshin1998electromagnetically,li2004group,ian2008cavity,chang2011multistability}. The optical amplifier is used to prevent a loss in the injected squeezed light. The single-mode Fabry-Perot optical cavity includes the fixed semitransparent mirror and the movable fully reflective mirror, equivalent to a quantum harmonic oscillator with mass $m$ and frequency $\omega_m$. The optical cavity interacts with the moveable mirror through the radiation pressure. The optical cavity is driven by applying a strong laser field to the semitransparent mirror.

\begin{figure}[t]
      \includegraphics [width =1\columnwidth]{fig1.pdf}
         \caption{(Color online) Overview of the hybrid optomechanical system which consists of an optomechanical cavity, a degenerate optical parametric amplifier (OPA), and an ensemble of ultracold atoms.} \label{Fig1}
\end{figure}

Hamiltonian of the optomechanical system (OMS), Hamiltonian of the OPA \cite{zhao2020weak}, Hamiltonian of the atomic ensemble, and the Hamiltonian of the laser driving field \cite{motazedifard2019force} can be written as the following expressions:
\begin{align}
\label{e1}
& H_{OMS}=\hbar \Delta_a a^{\dag} a+\frac{\hbar \omega_m}{2}(X^2+P^2)+\hbar g_{0} a^{\dag} a X,
\end{align}
\begin{align}
\label{e2}
H_{OPA}=i \hbar G(e^{i\theta}a^{\dag2} - e^{-i\theta}a^{2}),
\end{align}
\begin{align}
\label{e3}
& H_{at}=-\hbar \omega_m d^{\dag} d+\frac{\hbar G'}{2}(a+a^{\dag})(d+d^{\dag}),
\end{align}
and
\begin{align}
\label{e4}
& H_{L}=i\hbar E_{L}(a^{\dag}-a),
\end{align}
where $a$ is the annihilation operator of the optical field, $X$ and $P$ are the dimensionless position and momentum operators of the mechanical oscillator which are normalized to zero point motion $X_{zp}=\sqrt{\hbar /(m \omega_m)}$ and zero point momentum $P_{zp}=\hbar /X_{zp}$, respectively. The parameters $g_{0}$ and $G$ are the single photon optomechanical coupling and the nonlinear gain of the degenerate OPA, and $\theta$ is the phase of the OPA pump field. $E_{L}=\sqrt{P\kappa/\omega_{L}}$ stands for the pump rate of external driving laser in which $P$, $\omega_{L}$, and $\kappa$ are the input laser driving power, the input laser frequency, and the input photon decay rate, respectively. We also used $d$ and $G'$ to denote the effective atomic bosonic annihilation operator and the effective atom-field coupling for the atomic ensemble which are thoroughly discussed in Ref. \cite{motazedifard2016force}. Hamiltonian of the system in the interaction picture containing the two level atomic ensemble and the OPA can be written as
\begin{align}
\label{e5}
& H_{I}=\hbar \Delta_a a^{\dag} a+\frac{\hbar \omega_m}{2}(X^2+P^2)+\hbar g_{0} a^{\dag} a X \nonumber\\&+i \hbar G(e^{i\theta}a^{\dag2}+e^{-i\theta}a^{2})-\hbar \omega_m d^{\dag} d
\nonumber\\&+\frac{\hbar G'}{2}(a+a^{\dag})(d+d^{\dag})+i\hbar E_{L}(a^{\dag}-a).
\end{align}
Here, $\Delta_a=\omega_{a}-\omega_{L}$ is the detuning of the optical mode from the driving laser frequency in which $\omega_{a}$ is the frequency of the optical cavity \cite{bariani2015atom,motazedifard2016force}. Using the quantum Heisenberg-Langevin equations of motion, the equations of motion for the present system can be given as the following nonlinear equations
\begin{align}
\label{e6}
&\dot{X}=\omega_m P,\\
\label{e7}
&\dot{P}=-\omega_m X-g_{0}a^{\dag} a-\gamma_m P+\sqrt{2\gamma_m}(\hat{F}_{th}+F_{ext}),\\
\label{e8}
&\dot{a}=-(i\Delta_a+\frac{\kappa}{2})-ig_{0}X a+2Ge^{i\theta}a^{\dag} \nonumber\\&-\frac{iG'}{2}(d+d')+\sqrt{\kappa}a_{in},\\
\label{e9}
&\dot{d}=i\omega_m d-\frac{G'}{2}(a+a^{\dag})-\frac{\Gamma}{2}+\sqrt{\Gamma}d_{in},
\end{align}
where $\gamma_m$, $\kappa$ and $\Gamma$ are the mechanical damping rate, the cavity photon decay rate and the collective atomic dephasing rate, respectively. The mechanical noise term is $\hat{F}_{th}$, and $F_{ext}$ is the external force to be measured which is applied to the mechanical oscillator, as shown in Fig. \ref{Fig1}. The external force is normalized to $\sqrt{\hbar m \omega_m \gamma_m}$ that is expressed in units of $\sqrt{\rm Hz}$. The equations of motion contain the dissipation and fluctuation noise terms associating with the parameters of the system.

In the presence of strong optical drive, the quantum dynamics of the system can be well described by the linearizing the nonlinear Heisenberg-Langevin equations of motion, as shown in Refs. \cite{genes2008ground,vitali2007optomechanical}. Therefore, we expand each operator, in Eqs. \eqref{e6}-\eqref{e9}, as a steady state part and a quantum fluctuating part, as discussed theoretically \cite{huang2017robust,gebremariam2020enhancing} and experimentally \cite{safavi2013squeezed,shomroni2019two}. Then, we suppose that each operator in Eqs. \eqref{e6}-\eqref{e9} contains the steady state values ($\bar{O}$) and the fluctuating part ($\hat{O}$), including $P=\bar{P}+\hat{P}$, $X=\bar{X}+\hat{X}$, $a=\alpha+\hat{a}$, and $d=\bar{d}+\hat{d}$. We take the amplitude of intra cavity mode as a c-number, $\alpha= \vert{\alpha}\vert e^{i\phi}$, with a phase $\phi$. In order to summarize the equations of motion, the standard position and momentum quadratures of the cavity and atomic fields are defined as $\hat{x}_{i}=(\hat{a}_{i}+\hat{a}_{i}^{\dag})/\sqrt{2}$ and $\hat{p}_{i}=(\hat{a}_{i}-\hat{a}_{i}^{\dag})/(i\sqrt{2})$, and in addition, there are similar definitions for the amplitude and phase of the input quantum noises as $\hat{x}_{i}^{in}=(\hat{a}_{i}^{in}+\hat{a}_{i}^{in,\dag})/\sqrt{2}$ and $\hat{p}_{i}^{in}=(\hat{a}_{i}^{in}-\hat{a}_{i}^{in,\dag})/(i\sqrt{2})$, where $i$ stands for the cavity field mode ($\hat{a}$) and the atomic field mode ($\hat{d}$).

After straightforward calculations in the strong driving regime ($\\vert{\alpha}\vert\gg 1$), the quantum fluctuation parts of the  linearized quantum Heisenberg-Langevin equations of motion are obtained in terms of the standard quadratures as
\begin{align}
\label{e10}
&\dot{\hat{X}}=\omega_m \hat{P},\\
\label{e11}
&\dot{\hat{P}}=-\omega_m \hat{X}-\gamma_m \hat{P}-g \cos{\phi} \hat{x}_a+g \sin{\phi} \hat{p}_a \nonumber\\& +\sqrt{2\gamma_m} (\hat{F}_{th}+F_{ext}),\\
\label{e12}
&\dot{\hat{x}}_a=g \sin{\phi} \hat{X}+c_{-} \hat{x}_a+s_{+}\hat{p}_a+\sqrt{\kappa}\hat{x}^{in}_a,\\
\label{e13}
&\dot{\hat{p}}_a=-g \cos{\phi} \hat{X}+s_{-}\hat{x}_a-c_{+}\hat{p}_a-G'\hat{x}_d+\sqrt{\kappa}\hat{p}^{in}_a,\\
\label{e14}
&\dot{\hat{x}}_d=-\frac{\Gamma}{2}\hat{x}_d-\omega_{m}\hat{p}_d+\sqrt{\Gamma}\hat{x}^{in}_d,\\
\label{e15}
&\dot{\hat{p}}_d=-G'\hat{x}_a+\omega_{m}\hat{x}_d-\frac{\Gamma}{2}\hat{p}_d+\sqrt{\Gamma}\hat{p}^{in}_d.
\end{align}
where parameters are defined as $g=\sqrt{2}g_0\vert{\alpha}\vert$ known as the effective linearized optomechanical coupling, $c_{\pm}=\pm \frac{\kappa}{2}+2G\cos{\theta}$ and $s_{\pm}=\pm \Delta+2G\sin{\theta}$. The laser driving power, $P$, is proportional to $g^2$ as the measurement strength. The equations of motion, Eqs. \eqref{e10}-\eqref{e15}, describe the CQNC which are similar to the equations of motion in Refs. \cite{wimmer2014coherent,bariani2015atom}.

The atomic ensemble, as the quantum oscillator, is coupled to the optomechanical cavity but interacts with the cavity field in the exactly opposite way with an effective negative mass. Now, in order to cancel the back action noise we assume that the system is set at the resonance condition, $\Delta=0$, the $\alpha$ is real which means the intracavity phase is zero, $\phi=0$, and finally we assume the case of zero pump phase, $\theta=0$, of the optomechanical system, then Eqs. \eqref{e10}-\eqref{e15} are changed to
\begin{align}
\label{e16}
&\dot{\hat{X}}=\omega_m \hat{P},\\
\label{e17}
&\dot{\hat{P}}=-\omega_m \hat{X}-\gamma_m \hat{P}-g \hat{x}_a+\sqrt{2\gamma_m}(\hat{F}_{th}+F_{ext}),\\
\label{e18}
&\dot{\hat{x}}_a=(-\frac{\kappa}{2}+2G)\hat{x}_a+\sqrt{\kappa}\hat{x}^{in}_a,\\
\label{e19}
&\dot{\hat{p}}_a=-g \hat{X}+(-\frac{\kappa}{2}-2G)\hat{p}_a-G'\hat{x}_d+\sqrt{\kappa}\hat{p}^{in}_a,\\
\label{e20}
&\dot{\hat{x}}_d=-\frac{\Gamma}{2}\hat{x}_d-\omega_{m}\hat{p}_d+\sqrt{\Gamma}\hat{x}^{in}_d,\\
\label{e21}
&\dot{\hat{p}}_d=-G'\hat{x}_a+\omega_{m}\hat{x}_d-\frac{\Gamma}{2}\hat{p}_d+\sqrt{\Gamma}\hat{p}^{in}_d.
\end{align}

It can be seen from Eq. \eqref{e19} that the optical field momentum quadrature ($p_a$) depends on the position ($X$) of the mechanical oscillator and in turn the position is controlled by the momentum ($P$) of the mechanical oscillator. The external force can be detected by monitoring the optical mode. The equations of motion, Eqs. \eqref{e16}-\eqref{e21}, can be solved for the operators in the frequency domain to calculate $p_a(\omega)$ as a function of the input noises. A quantum operator in the Fourier domain can be written as
\begin{align}
\label{e22}
\hat{O}(\omega)=\frac{1}{\sqrt{2\pi}}\int{dt\hat{O}(t)e^{-i\omega t}},
\end{align}
then using Eq. \eqref{e22}, Eqs. \eqref{e16}-\eqref{e21} can be given in the Fourier space as
\begin{align}
\label{e23}
&\hat{X}=\chi_m(-g\hat{x}_a+\sqrt{2\gamma_m} (\hat{F}_{th}+F_{ext})),\\
\label{e24}
&\hat{P}=\frac{i\omega}{\omega_m} \hat{X},\\
\label{e25}
&\hat{x}_a=\sqrt{\kappa}\lambda_{+}\hat{x}_a^{in},\\
\label{e26}
&\hat{p}_a=g^2\chi_m\lambda_{-}\lambda_{+}\sqrt{\kappa}\hat{x}_a^{in}-g\chi_m\lambda_{-}\sqrt{2\gamma_m} (\hat{F}_{th}+F_{ext}) \nonumber\\& -G'\lambda_{-}\hat{x}_d+\lambda_{-}\sqrt{\kappa}\hat{p}_a^{in} ,\\
\label{e27}
&\hat{x}_d=-\omega_{m}\chi_d \hat{p}_d+\chi_d\sqrt{\Gamma}\hat{x}^{in}_d,\\
\label{e28}
&\hat{p}_d=-G'\xi \lambda_{+}\sqrt{\kappa}\hat{x}_a^{in}-\chi'_d \sqrt{\Gamma}\hat{x}_d^{in}+\xi\sqrt{\Gamma}\hat{p}^{in}_d,
\end{align}
where, the parameters are defined as
\begin{align}
\label{e29}
& \lambda_{\pm}=(\chi_a^{-1}\mp2G)^{-1}, \\
\label{e30}
& \xi=(i\omega+\Gamma/2+\omega_m^2 \chi_d)^{-1}.
\end{align}
Also, the effective susceptibilities can be written as
\begin{align}
\label{e33}
&\chi_m=\frac{\omega_m}{\omega_m^2-\omega^2+i\omega \gamma_m},\\
\label{e34}
&\chi_a=\frac{1}{i\omega+\kappa/2},\\
\label{e35}
&\chi_d=\frac{1}{i\omega+\Gamma/2},\\
\label{e36}
&\chi'_d=-\omega_{m}\xi \chi_d=\frac{-\omega_m}{\omega_m^2-\omega^2+i\omega \Gamma/2+\Gamma^2/4},
\end{align}
for the mechanical oscillator, the meter optical cavity, the atomic ensemble, and the last one stands for the generalized susceptibility of the atomic ensemble, respectively.

\section{Force sensing and CQNC} \label{III}
Solving Eqs. \eqref{e23}-\eqref{e28},we can find the phase quadrature of the cavity field, $p_a$, and finally using the standard input-output relation as
\begin{align}
\label{e37}
\hat{p}_a^{out}=\sqrt{\kappa}\hat{p}_a-\hat{p}_a^{in},
\end{align}
the detected phase quadrature of the cavity field mode can be expressed in terms of the input noises as the following expression
\begin{align}
\label{e38}
&\hat{p}_a^{out}=-g\chi_m \lambda_{-}\sqrt{2\gamma_m\kappa} (\hat{F}_{th}+F_{ext})
\nonumber\\& +(g^2\chi_m+G^{'2} \chi'_d)\lambda_{+}\lambda_{-}\kappa\hat{x}_a^{in}+(\lambda_{-}\kappa-1)\hat{p}_a^{in}
\nonumber\\& -G'\lambda_{-}\sqrt{\kappa \Gamma}[\chi_d(\omega_m\chi'_d+1)\hat{x}_d^{in}+\chi_d'\hat{p}_d^{in}].
\end{align}
The first term in Eq. \eqref{e38} represents the thermal noise and the external force where the external force is independent of the detected frequency, the second line contains the back-action noise and the shot noise of the field, and the third line describes the atomic noise. If we choose the conditions such that
\begin{align}
\label{e39}
g^2\chi_m+G^{'2} \chi'_d=0
\end{align}
for all frequencies, then the first term in the second line of Eq. \eqref{e38}, the back-action term, will be entirely canceled in Eq. \eqref{e38} and also in the external force measurement. In the CQNC scheme, we essentially have $g=G^{'}$ and $\chi_m=-\chi'_d$ or, in other words, the contributions to the back-action noise from the mechanical oscillator and the atomic ensemble cancel each other for all frequencies. They are the noise and anti-noise contributions to the signal obtained by assuming the use of an atomic ensemble as an oscillator with the effective negative mass. In addition to the above assumptions, we assume that the mechanical resonator and the atomic ensemble have the same damping rates ($\gamma_m=\Gamma/2$) and also the mechanical oscillator has a high-quality factor such that $\Gamma\ll \omega_m$, then we can ignore the last term in the denominator of the generalized atomic susceptibility in Eq. \eqref{e36}. Therefore, the susceptibilities of mechanics and generalized atomic ensemble completely match, which leads to the perfect coherent back-action noise cancellation.

By rewriting Eq. \eqref{e38}, the relation between the external force, $F_{ext}$, and the measured phase quadrature, $\hat{p}_a^{out}$, can be given as the following expression
 \begin{align}
\label{e40}
F_{ext}+\hat{F}_{add}=\frac{-1}{g\chi_m \lambda_{-}\sqrt{2\gamma_m\kappa}}\hat{p}_a^{out}
\end{align}
where the added force noise, $\hat{F}_{add}$, is defined as
\begin{align}
\label{e41}
& \hat{F}_{add}=\hat{F}_{th}-\frac{\lambda_{-}\kappa-1}{g\chi_m \lambda_{-}\sqrt{2\gamma_m\kappa}}\hat{p}_a^{in}
\nonumber\\& +\frac{G' \chi_d' \sqrt{\kappa \Gamma}}{g\chi_m \sqrt{2\gamma_m\kappa}}[\frac{\chi_d}{\chi_d'}(\omega_m\chi'_d+1)\hat{x}_d^{in}+\hat{p}_d^{in}].
\end{align}
It should be noted that the back-action noise term is canceled. Simplifying Eq. \eqref{e41}, we have
\begin{align}
\label{e42}
& \hat{F}_{add}=\hat{F}_{th}-\frac{\lambda_{-}\kappa-1}{g\chi_m \lambda_{-}\sqrt{2\gamma_m\kappa}}\hat{p}_a^{in}
\nonumber\\& +[-\frac{i\omega+\Gamma/2}{\omega_m}\hat{x}_d^{in}+\hat{p}_d^{in}].
\end{align}
The added noise contains the thermal Langevin force coupled to a thermal reservoir at temperature $T$ (first term), the shot noise in the phase quadrature of the optical field (second term) and the atomic noise (third term).

Using the definition of spectral density of the added noise \cite{wimmer2014coherent}, $S_{F,add}(\omega)$, we can find the sensitivity of the force measurement as
\begin{align}
\label{e43}
S_{F,add}(\omega)\delta(\omega-\omega')=\frac{1}{2}(\left\langle \hat{F}_{add}(\omega)\hat{F}_{add}(-\omega')\right\rangle +c.c. ),
\end{align}
then, using the conditions of the CQNC and for $\omega \ll \kappa$, we find the spectral noise as
\begin{align}
\label{e44}
& S_{F,add}(\omega)=\frac{k_BT}{\hbar\omega_m}+\frac{1}{2} \frac{1}{g^2|\chi_m(\omega)|^2 (2\gamma_m\kappa)}|\frac{\lambda_{-}(\omega)\kappa-1}{\lambda_{-}(\omega)}|^2
\nonumber\\& +\frac{1}{2}(\frac{\omega^2+\Gamma^2/4}{\omega_m^2}+1).
\end{align}
After some calculation, the spectral density can be more simplified as
\begin{align}
\label{e45}
& S_{F,add}(\omega)=\frac{k_BT}{\hbar\omega_m}+\frac{1}{2}[\frac{(\kappa/2-2G)^2}{g^2|\chi_m(\omega)|^2 (2\gamma_m\kappa)}
\nonumber\\&(\frac{\omega^2+\Gamma^2/4}{\omega_m^2}+1)],
\end{align}
where obviously the back-action noise term, scaling to $g^2$, is deleted. This result can be compared to that of the standard optomechanical system, discussed in Refs. \cite{aspelmeyer2014cavity,wimmer2014coherent,bariani2015atom}, as the following equation
\begin{align}
\label{e46}
 S_{F}(\omega)=\frac{k_BT}{\hbar\omega_m}+\frac{1}{2} [ \frac{\kappa}{\gamma_m}\frac{1}{g^2|\chi_m|^2}\frac{1}{4}+4g^2\frac{1}{\kappa\gamma_m}]
\end{align}
which contains the shot noise and the back-action noise terms proportional to $1/g^2$ and $g^2$, respectively. The thermal Brownian noise results in a constant background noise to the force sensitivity independent of the input laser power.
At $T=0$, we can minimize the right hand side of Eq. \eqref{e46} with respect to $g^2$ or proportionally the input laser power, $P=2\hbar \omega_L \kappa(g/g_0)^2$, gives the SQL for continuous force sensing,
\begin{align}
\label{e47}
 S_{F,SQL}=\frac{1}{\gamma_m|\chi_m|}
\end{align}
and equivalently the minimized noise spectral density can be found for the CQNC at $T=0$ as
\begin{align}
\label{e48}
 S_{F,CQNC}=\frac{1}{2}\frac{\omega^2+\omega_m^2+\Gamma^2/4}{\omega_m^2}.
\end{align}
The noise spectral densities are normalized by the factor, $\hbar m\omega_m\gamma_m$, then they are given in units of N$^2$Hz$^{-1}$. However, in this work, we have considered the noise spectral densities as dimensionless for simplicity.

The noise spectral densities for the standard optomechanical system (SQL), the optomechanical system with OPA (dashed lines) and the CQNC schemes (CQNC) are represented in Fig. \ref{Fig2}. The spectral density for the CQNC scheme is limited to the shot noise term over the whole detection bandwidth, which is the main advantage of the CQNC scheme. Fig. \ref{Fig2} shows the variation of the noise spectral density of the optomechanical system versus the detection frequency for different values of the OPA pump gain, $G$. At the resonance condition ($\Delta=0$), the noise spectral density of the standard optomechanical system and that of the optomechanical system with the OPA equal the noise spectral density of the CQNC scheme. Fig. \ref{Fig2} shows that with the increase of relative OPA pump gain, $G/\kappa$, the SQL can be suppressed at frequencies below and as well above the mechanical resonance. The force noise spectral density is decreased by nearly two orders of magnitude on both sides of the low and high-frequency domains. Recently, Korobko \textit{et~al.} \cite{korobko2019quantum} proposed an optical approach to expand the detection bandwidth for gravitational-wave observatories in which quantum uncertainty can be squeezed inside one of the optical resonators at high frequencies. At the same time, the low-frequency sensitivity was remained unchanged. On the other hand, as mentioned in section \ref{I}, Zhao \textit{et~al.} \cite{zhao2020weak} investigated weak-force sensing in a squeezed cavity and theoretically showed that the SQL could be suppressed at frequencies below the mechanical resonance; however, the back-action noise remained unchanged in the system.

\begin{figure}[t]
 \includegraphics [width = 1\columnwidth]{fig2.pdf}
   \caption{(Color online) Noise power spectral densities calculated for the standard optomechanical system (black solid line), $S_{SQL}$, the optomechanical system with the OPA (colored dashed line) with different $G$, and the coherent quantum noise cancellation (red dashed line), $S_{CQNC}$, in optimal power versus the detection frequency. The spectral densities are normalized to $\hbar m\omega_m\gamma_m$. The parameters are given in Table \ref{1} and we have $Q=\omega_m/\gamma_m=10^4$.} \label{Fig2}
\end{figure}

The spectral densities are depicted in Fig. \ref{Fig3}(a) and Fig. \ref{Fig3}(b) as functions of the laser driving power, scaling to the optomechanical coupling $g^2$, for on-resonance ($\omega=\omega_m$) and off-resonance ($\omega=\omega_m+4\gamma_m$) cases, respectively. Fig. \ref{Fig3}(a) shows that at the higher driving power, the noise spectral density decreases over the bandwidth significantly. At lower values of the coupling strength, the shot noise term is dominant, and the noise spectral density of the normal optomechanical system (SQL) first decreases with the driving power increasing until the minimum point. After that, the back-action noise is dominant, and the noise spectral density of the normal optomechanical system increases. In the normal optomechanical system, the noise spectral density of the SQL represented by Eq. \eqref{e47} can be reached to the minimum point at $g_{SQL}=\sqrt{\kappa}/(2\sqrt{|\chi_m|})$, whereas this point in the normal system can be lowered by using the OPA pump with gain $G$, which gives $g_{SQ}^{\theta=0}=|\kappa-4G|/(2 \sqrt{\kappa|\chi_m|})$ \cite{zhao2020weak}. The CQNC scheme cancels the back-action noise. It improves the sensitivity in a broad bandwidth at higher values of the driving power. In the absence of OPA pumping ($G=0$), on-resonance, the CQNC system needs a higher driving power to reach the same sensitivity of the standard setup. In contrast, as the OPA pump gain $G$ increases, the sensitivity of the CQNC-OPA arrangement rapidly becomes superior to the normal optomechanical system and surpasses the SQL at lower values of the driving power. In addition to the cancellation of the back-action noise, the CQNC-OPA arrangement reduces the shot noise by about two orders of magnitude. It improves the measurement accuracy at lower driving power domain. On the other side, away from the resonance case with detuning $4\gamma_m$, the spectral density of the system, $S_{F}$, decreases with increasing the values of the OPA pump gain $G$, as depicted in Fig. \ref{Fig3}(b). We have used experimentally accessible parameters \cite{bariani2015atom,bowen2015quantum,wimmer2014coherent} in our calculations which are collected in Table \ref{1}.

\begin{table}
\caption{Parameters of the hybrid system.}
\label{1}
\begin{tabular}{l l l}
\toprule
Parameter    &  Symbole &  Value (unit) \\
\hline
Mirror mass & $m$ & 50 ng \\
Single photon optomechanical coupling & $g_0/2\pi$ & 300 Hz \\
Mechanical resonance & $\omega_m/2\pi$ & 300 kHz \\
Mechanical damping rate & $\gamma_m/2\pi$ & 30 Hz\\
Optical cavity damping rate & $\kappa/2\pi$ & 1 MHz\\
Laser source power & $P$ & 100 mW \\
Laser frequency & $\omega_L /2\pi$ & 384 THz \\
\hline
\hline
\end{tabular}
\end{table}

\twocolumngrid\
\begin{center}\
\begin{figure}[h]\
\includegraphics[scale=1]{Fig3a.pdf}\
\includegraphics[scale=1]{Fig3b.pdf}\
\caption{(Color online) Noise spectral density for weak force measurement (a) on mechanical resonance ($\omega=\omega_m$) and (b) off-resonance with $4\gamma_m$ detuning ($\omega=\omega_m+4\gamma_m$) as function of the input driving power ($P=2\hbar \omega_L \kappa(g/g_0)^2$) for the standard optomechanical system and for the present hybrid system, containing the OPA and the atomic ensemble, with different values of the relative parametric gain as $G/\kappa=0$, 0.05, 0.1, 0.15, and 0.2. The parameters are given in Table \ref{1}.}\
\label{Fig3}
\end{figure}\
\end{center}\
\twocolumngrid\

To reach the SQL, we have considered the impact of $g^2/g^2_{SQL}$, the frequency $\omega$, and the parametric gain $G$ on the noise spectral density of the present hybrid system. Fig. \ref{Fig4}(a) and Fig. \ref{Fig4}(b) depict the noise spectral densities for the hybrid system as functions of the relative optomechanical coupling $g^2/g^2_{SQL}$ and relative frequency $\omega/\omega_m$ with $G/\kappa=0$ and 0.1, respectively. Fig. \ref{Fig4}(a) with $G/\kappa=0$ indicates that the noise spectral density is close to the minimum value in a limited range in the vicinity of the resonance, and it increases in areas farther than the resonance region. While, the noise spectral density, as shown in Fig. \ref{Fig4}(b) with $G/\kappa=0.1$, is close to the minimum value in a wider area, and it increases with a lower slope in areas farther than the resonance region, especially in areas with a frequency lower than the resonant frequency. Fig. \ref{Fig4}(a) shows that the noise spectral density reaches the minimum values in the narrow area in the vicinity of the resonant frequency, which slightly increases at higher values of $g^2/g^2_{SQL}$. While, Fig. \ref{Fig4}(b) with $G/\kappa=0.1$ shows that the spectral noise density approaches to the minimum values of the SQL in a wider range of lower values of $g^2/g^2_{SQL}$ which is interesting for feasible experimental scenarios.

\twocolumngrid\
\begin{center}\
\begin{figure}[h]\
\includegraphics[scale=0.75]{Fig4a.pdf}\
\includegraphics[scale=0.75]{Fig4b.pdf}\
\caption{(Color online) Noise spectral density for weak force measurement as function of the relative squared optomechanical coupling ($(g/g_{SQL})^2$) and the relative detection frequency ($\omega/\omega_m$) for the present hybrid system, containing the OPA and the atomic ensemble with different values of the relative parametric gain as (a) $G/\kappa=0$ and (b) $G/\kappa=0.1$. The parameters are given in Table \ref{1}.}\
\label{Fig4}
\end{figure}\
\end{center}\
\twocolumngrid\

\section {Summary and conclusion} \label{IV}
In summary, we have presented the analysis of the coherent quantum noise cancellation (CQNC) and shot noise reduction scheme in the optomechanical system assisted by the ensemble of ultracold atoms and the optical parametric amplifier (OPA). The ensemble of ultracold atoms is chosen as the effective oscillator with the effective negative mass, which destructively interacts with the optical cavity mode leading to the perfect cancellation of the back-action noise. On the other hand, the quantum squeezing in the optomechanical cavity reduces shot noise in the low driving power and the broad range of detection frequency. In this hybrid system, the CQNC and shot noise reduction cooperatively occur when the effective linearized optomechanical coupling and the nonlinear gain of the OPA, the mechanical susceptibility and the generalized susceptibility of the atomic ensemble, and eventually the damping rates of the mechanical oscillator and the atomic ensemble coincide with each other, respectively.  Finally, we have also used a set of possible experimental parameters which shows the elimination of the back-action noise and the reduction of the shot noise at frequencies below the mechanical resonance.

\section*{References}

redpajama_set_name: RedPajamaArXiv


It was the late Antonio Carluccio who was largely responsible for drawing the British people into a love affair with Italian food. The famous cookery writer, who died in November 2017, was a leading authority on Italian cookery and wrote no less than 19 recipe books.
Here's his traditional lasagne recipe, a dish which originated in Naples in the Middle Ages but has been a British dinner-time staple for decades.
With layers upon layer of deliciousness, it can be prepared in advance and popped in the oven whenever you need it. It's also relatively simple to make.


text:
A simple example demonstrating the usage of the Kafka plugin API with
the automatic (hash-based) partitioning.

### Requirements

To start the example, you have to have the Kafka broker running first.
if you don't have it installed locally you can use the following docker
image:
```
sudo docker run -p 2181:2181 -p 9092:9092 --name kafka --rm \
   --env ADVERTISED_HOST=172.17.0.1 --env ADVERTISED_PORT=9092 spotify/kafka
```

It will bring up the Kafka broker listening on port 9092 for client
communication.

### Usage

To run the example, type:
```
go run main.go deps.go [-kafka-config <config-filepath>]
```

If `kafka-config` is unspecified, the application will try to search
for `kafka.conf` in the current working directory.
If the configuration file cannot be loaded or is not defined, default
configuration will be used.

redpajama_set_name: RedPajamaGithub


text:
package com.android.internal.http.multipart;

import java.io.File;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import org.apache.http.util.EncodingUtils;
import org.apache.commons.logging.Log;
import org.apache.commons.logging.LogFactory;

/**
 * This class implements a part of a Multipart post object that
 * consists of a file.
 *
 * @author Matthew Albright
 * @author Jeff Dever
 * @author Adrian Sutton
 * @author Michael Becke
 * @author Mark Diggory
 * @author Mike Bowler
 * @author Oleg Kalnichevski
 *
 * @since 2.0
 *
 */
public class FilePart extends PartBase {

    /** Default content encoding of file attachments. */
    public static final String DEFAULT_CONTENT_TYPE = "application/octet-stream";

    /** Default charset of file attachments. */
    public static final String DEFAULT_CHARSET = "ISO-8859-1";

    /** Default transfer encoding of file attachments. */
    public static final String DEFAULT_TRANSFER_ENCODING = "binary";

    /** Log object for this class. */
    private static final Log LOG = LogFactory.getLog(FilePart.class);

    /** Attachment's file name */
    protected static final String FILE_NAME = "; filename=";

    /** Attachment's file name as a byte array */
    private static final byte[] FILE_NAME_BYTES =
        EncodingUtils.getAsciiBytes(FILE_NAME);

    /** Source of the file part. */
    private PartSource source;

    /**
     * FilePart Constructor.
     *
     * @param name the name for this part
     * @param partSource the source for this part
     * @param contentType the content type for this part, if null the
     * {@link #DEFAULT_CONTENT_TYPE default} is used
     * @param charset the charset encoding for this part, if null the
     * {@link #DEFAULT_CHARSET default} is used
     */
    public FilePart(String name, PartSource partSource, String contentType, String charset) {

        super(
            name,
            contentType == null ? DEFAULT_CONTENT_TYPE : contentType,
            charset == null ? "ISO-8859-1" : charset,
            DEFAULT_TRANSFER_ENCODING
        );

        if (partSource == null) {
            throw new IllegalArgumentException("Source may not be null");
        }
        this.source = partSource;
    }

    /**
     * FilePart Constructor.
     *
     * @param name the name for this part
     * @param partSource the source for this part
     */
    public FilePart(String name, PartSource partSource) {
        this(name, partSource, null, null);
    }

    /**
     * FilePart Constructor.
     *
     * @param name the name of the file part
     * @param file the file to post
     *
     * @throws FileNotFoundException if the file is not a normal
     * file or if it is not readable.
     */
    public FilePart(String name, File file)
    throws FileNotFoundException {
        this(name, new FilePartSource(file), null, null);
    }

    /**
     * FilePart Constructor.
     *
     * @param name the name of the file part
     * @param file the file to post
     * @param contentType the content type for this part, if null the
     * {@link #DEFAULT_CONTENT_TYPE default} is used
     * @param charset the charset encoding for this part, if null the
     * {@link #DEFAULT_CHARSET default} is used
     *
     * @throws FileNotFoundException if the file is not a normal
     * file or if it is not readable.
     */
    public FilePart(String name, File file, String contentType, String charset)
    throws FileNotFoundException {
        this(name, new FilePartSource(file), contentType, charset);
    }

     /**
     * FilePart Constructor.
     *
     * @param name the name of the file part
     * @param fileName the file name
     * @param file the file to post
     *
     * @throws FileNotFoundException if the file is not a normal
     * file or if it is not readable.
     */
    public FilePart(String name, String fileName, File file)
    throws FileNotFoundException {
        this(name, new FilePartSource(fileName, file), null, null);
    }

     /**
     * FilePart Constructor.
     *
     * @param name the name of the file part
     * @param fileName the file name
     * @param file the file to post
     * @param contentType the content type for this part, if null the
     * {@link #DEFAULT_CONTENT_TYPE default} is used
     * @param charset the charset encoding for this part, if null the
     * {@link #DEFAULT_CHARSET default} is used
     *
     * @throws FileNotFoundException if the file is not a normal
     * file or if it is not readable.
     */
    public FilePart(String name, String fileName, File file, String contentType, String charset)
    throws FileNotFoundException {
        this(name, new FilePartSource(fileName, file), contentType, charset);
    }

    /**
     * Write the disposition header to the output stream
     * @param out The output stream
     * @throws IOException If an IO problem occurs
     * @see Part#sendDispositionHeader(OutputStream)
     */
    @Override
    protected void sendDispositionHeader(OutputStream out)
    throws IOException {
        LOG.trace("enter sendDispositionHeader(OutputStream out)");
        super.sendDispositionHeader(out);
        String filename = this.source.getFileName();
        if (filename != null) {
            out.write(FILE_NAME_BYTES);
            out.write(QUOTE_BYTES);
            out.write(EncodingUtils.getAsciiBytes(filename));
            out.write(QUOTE_BYTES);
        }
    }

    /**
     * Write the data in "source" to the specified stream.
     * @param out The output stream.
     * @throws IOException if an IO problem occurs.
     * @see Part#sendData(OutputStream)
     */
    @Override
    protected void sendData(OutputStream out) throws IOException {
        LOG.trace("enter sendData(OutputStream out)");
        if (lengthOfData() == 0) {

            // this file contains no data, so there is nothing to send.
            // we don't want to create a zero length buffer as this will
            // cause an infinite loop when reading.
            LOG.debug("No data to send.");
            return;
        }

        byte[] tmp = new byte[4096];
        InputStream instream = source.createInputStream();
        try {
            int len;
            while ((len = instream.read(tmp)) >= 0) {
                out.write(tmp, 0, len);
            }
        } finally {
            // we're done with the stream, close it
            instream.close();
        }
    }

    /**
     * Returns the source of the file part.
     *
     * @return The source.
     */
    protected PartSource getSource() {
        LOG.trace("enter getSource()");
        return this.source;
    }

    /**
     * Return the length of the data.
     * @return The length.
     * @see Part#lengthOfData()
     */
    @Override
    protected long lengthOfData() {
        LOG.trace("enter lengthOfData()");
        return source.getLength();
    }

}


text:
Home » Analysis
Credit: Nikkei Asia
Japan's new whisky regulations: What do they mean?
Plans to protect the reputation of Japanese whisky have been unveiled, but do they go far enough? Shay Waterworth looks at the implications.
The release of a new set of regulations for the production of Japanese whisky in February brought a sigh of relief from major players in the category. The Japan Spirits & Liqueurs Makers Association announced the rules, stating that to be labelled "Japanese whisky" the product must be made from malted barely, use local water and be fermented, distilled, aged and bottled in Japan, while also being aged in wooden casks for three years and bottled at a minimum 40% abv. This prompted the creation of a tongue-in-cheek bottle shot of Nikka Whisky from the Ben Nevis, which made the rounds on social media. The edited picture was poking fun at the open secret that Japanese distiller Nikka has previously shipped whisky from its Ben Nevis distillery in Scotland for use in its Japanese blends.
To many consumers this would be a shock, but actually Japanese brands have a history of importing whiskies from around the world to use in their blends and it's certainly not frowned upon by the local industry. A combination of the rise in popularity of Japanese whisky and a deep running corporate competitiveness has prevented distilleries from selling stocks to other domestic producers, therefore they rely on overseas whiskies to generate volumes. The use of foreign whiskies is actually acknowledged as part of the category's culture by the JSLMA, but under its new regulations this looks set to change.
According to the association, the new regulations will aim to "contribute to the appropriate selection of whisky products by consumers in Japan and abroad, and to thereby protect the interests of consumers, ensure fair competition and improve quality". So it seems that, while it's taken a lot longer than expected, the association is planning for the future by protecting the reputation and integrity of Japanese whisky before word gets out among consumers.
However, while the principles are in place, they won't be enforced until March 31, 2024 and even then the regulations are voluntary, not law. This means that not only can brands still use foreign whiskies, but some may continue producing misleading products for the local and international markets.
In the long term it seems unlikely that the association will ever be in a position to truly enforce these regulations and therefore the integrity of Japanese whisky will largely rely on the leadership of big brands. Following the announcement, Beam Suntory, the biggest producer of Japanese whisky, gave this statement: "We fully support the implementation of these new standards of identity for Japanese whisky. We believe that these standards will help to further distinguish the Japanese whisky category."
Hideki Kanda, chief executive of Suntory Spirits, adds: "We believe the new definition will allow us to further promote the quality of Suntory whisky overseas, as well as help differentiating Japanese whisky from other whiskies around the world."
With the influence of major brands and a basic framework set out by JSLMA, the regulation of Japanese whisky has taken a big step forward. However, without any significant power and a three-year window of grace for brands, it's hardly a cutthroat solution. And as prices of Japanese whisky continue to boom internationally, it seems unlikely the selling of stocks to other domestic producers will be prioritised and therefore the reliance on foreign whiskies will remain in order to satisfy the demand.
Keywords: new, whisky, production, japan, regulations, february, japanese, relief, japanese whisky, shay waterworth, players, sigh, waterworth looks, japan spirits, major players, new whisky regulations, shay waterworth looks
Japanese whisky gets new production regulations
Scotland: New scotch whisky regulations come into play
New Scotch whisky regulations announced
The Lakes Distillery appoints new whisky maker
BrewDog Distilling Co's first whisky cask sale breaks records on Whisky Hammer

redpajama_set_name: RedPajamaCommonCrawl


text:
\section{INTRODUCTION}

\noindent Vanadium spinels AV$_2$O$_4$ (A=Mg, Zn, Cd) are being studied extensively
in recent years \cite{wheeler,motome,radaelli,tcherny,tm-rv,gianluca} as they provide a very
interesting playground for the study of competing interactions on a frustrated
lattice in 3-dimension. The Vanadium (V) ions at the B-sites of the spinel structure
form a pyrochlore lattice, with corner sharing tetrahedra, which is geometrically
frustrated. In its $3+$ valence state, V ion has
two electrons in the d-shell which, because of a strong Hund's coupling, align
parallel to each other thereby imparting a high spin state
($S=1$) to the ion. Thus in this family of spinels, there is a magnetic ion on
a geometrically
frustrated lattice resulting in competing ground states. Things get more
involved when the partial occupancy of triply degenerate $t_{2g}$ orbitals by
the two d-electrons makes the orbital degree of freedom unfrozen.
As both spin and orbital degrees
of freedom remain active, there is a high possibility of spin-orbit (SO) coupling
playing important role in the low energy physics of this family of systems.
Role of this interaction has been a matter of debate recently
\cite{motome,tcherny, wheeler}.
The manifestation of the interplay of orbital, spin and lattice degrees of
freedom in these systems culminates in experiments as a sequence of phase
transitions\cite{wheeler, reehuis, garlea}. A structural transition, often followed by magnetic transition
as the temperature is lowered, signifies competing interactions trying to
stabilize a particular ground state with gradual lifting of the frustration.

MgV$_2$O$_4$, with a normal spinel structure, has been reported to undergo a
structural transition at 51 K from cubic to tetragonal phase and a
magnetic transition at 42 K from non-magnetic to an antiferromagnetic(AFM) phase consisting of alternating
antiferromagnetic chains of V atoms running parallel to {\bf a} and {\bf b} directions
 as one goes along {\bf c}-axis\cite{wheeler,mamiya}. The high
temperature (HT) phase
has a cubic spinel structure with $F\bar{4}3m$ symmetry where the V ion
is surrounded by an almost perfect $O_6$ octahedron with all the six V-O bonds
having same length. This leads to a sizable ($\sim2.5$ eV)
$t_{2g}$ - $e_{g}$ crystal field splitting of the d levels.
There is of course a small
trigonal distortion also present in this phase. Experimental results further
reveal that the structural transition to
the tetragonal phase at 51 K  is accompanied by a compression along c-axis with c/a=0.9941. This
lowers the symmetry to space
group $I\bar{4}m2$. Hence, in addition to
the $t_{2g}$ - $e_{g}$  splitting arising from roughly $O_6$ octahedral
coordination, a further splitting occurs due to the tetragonal compression
where the low lying $t_{2g}$ triplet splits into a lower energy singlet
($d_{xy}$ orbital) and a higher
energy doublet of $d_{yz}$ and $d_{zx}$ orbitals. The orbital degeneracy is thereby partially lifted with this structural distortion. Now out of the two d
electrons, one goes to the lower energy $d_{xy}$
orbital while the other still has a choice as it occupies the doubly degenerate
$d_{yz}$ and $d_{zx}$ orbitals. This opens up a possibility of orbital order
in this system. Structural transition also partially lifts the frustration of
the $V-V$ bonds in the pyrochlore lattice. This then brings in the second
transition, at lower temperature of 42 K where a long
range antiferromagnetic order sets in\cite{wheeler}. Thus the presence of any
orbital order and the magnetic order observed at low temperatures in all the
Vanadium spinels are interrelated.

Several theoretical models have been
proposed in the last few years to explain the possible orbital order in Vanadium
spinels so as to be consistent with the observed antiferromagnetic order.
Among these, the model proposed by Tsunetsugu and Motome
\cite{motome} is based on strong coupling Kugel-Khomskii
Hamiltonian and predicts an orbital order where at each V site,
d$_{xy}$ orbital is occupied by one electron and the second electron occupies
either d$_{xz}$ or d$_{yz}$ orbital, alternately, along the c-axis. However,
this type
of orbital order was found to be of lower symmetry than that ($I4_1/amd$) observed
experimentally for ZnV$_2$O$_4$. In an alternative
theoretical model, Tchernychov\cite{tcherny} considered a dominant SO interaction
which then led to the proposal that the second electron would occupy
a complex orbital of type d$_{xz}$$\pm$id$_{yz}$ at each V site. This
orbital order is found to be consistent with the underlying crystal symmetry.
Also it explains the low magnetic moment per V ion observed in these systems
as a large negative orbital moment is expected from a strong SO
coupling.
These findings were also corroborated by electronic structure calculations
\cite{tm-rv} for ZnV$_2$O$_4$.

However, recent measurements on other members of the Vanadium spinel family
raise doubts about the presence of a strong spin-orbit interaction effect.
In fact, there has been a tremendous effort, from both
theoreticians and experimentalists
working on these systems, to bring out a unified picture in terms of the
important interactions which underlie the two phase transitions (one
structural and the other magnetic). In
ZnV$_2$O$_4$ the SO coupling is found to be significant both from theory as
well as experiments\cite{tcherny,tm-rv, cheong} whereas in case of MnV$_2$O$_4$
there seems to be very little or no effect of the SO interaction on the orbital order
\cite{tm-tsd,baek}. Recently Wheeler et al.\cite{wheeler} performed neutron diffraction
measurements on MgV$_2$O$_4$
single crystal and speculated on the
basis of their observations that MgV$_2$O$_4$ might come intermediate between
ZnV$_2$O$_4$ and MnV$_2$O$_4$ as far as strength of SO coupling is concerned. Hence it is expected that in MgV$_2$O$_4$ the
occupied orbitals,
instead of being completely real (Tsunetsugu and Motome model) or completely
complex (Tchernychov model), could be a mixture of real and complex orbitals.
In the previous theoretical study on MgV$_2$O$_4$\cite{pandey}, the issue of impact of SO coupling on orbital order has not been investigated. However, as stated above, SO coupling in MgV$_2$O$_4$ is
expected to be non-negligible from experimental observations.
In order to investigate thoroughly the effect of SO interaction on magnetic and orbital
order in MgV$_2$O$_4$, we have carried out
first principle electronic structure calculations incorporating SO coupling.
Such a calculation is definitely expected to unfurl the strength
of SO coupling in this system, the nature of orbital order (if there is any)
and correlation of experimentally observed magnetic order with the orbital
order, if present.

\section{METHODOLOGY}

\noindent We undertake an electronic structure calculation
using full-potential linearized augmented-plane-wave method with the basis chosen to be linearized augmented plane waves as
implemented in WIEN2K code\cite{wien2k}.
The calculations have
been carried out with no shape approximation to the potential and charge
density. These calculations were performed at
three levels of sophistication using local spin density approximation (LSDA),
Coulomb correlated LSDA+U approximation, and with SO interaction i.e. LSDA+U+SO approximation.
To remove the self-Coulomb and self-exchange-correlation energy included in
LSDA approximation, we use self-interaction corrected scheme (LSDA+U(SIC))
\cite{anisimov},
which is appropriate for the strongly correlated systems. The corrected
energy functional is written as\cite{anisimov}
\begin{equation}\nonumber
E= E^{LSDA}
  -[UN(N-1)/2-JN(N-2)/4] + 1/2\sum_{m,m',\sigma} U_{mm'}n_{m\sigma}n_{m'-\sigma} + 1/2\sum_{m\neq m',m',\sigma}(U_{mm'}-J_{mm'})n_{m\sigma}n_{m'\sigma}
\end{equation}

\noindent Here E$^{LSDA}$ is the standard LSDA energy functional, U represents the on-site Coulomb interaction, J is the exchange parameter and
n$_{m\sigma}$ are the occupations of the localized orbitals. N is the total
number of localized electrons.

In the LSDA+U+SO calculations, SO coupling was considered within the scalar
relativistic approximation and the second variational method was employed
\cite{koelling}. In this method, the eigen value problem
is first solved separately for spin up and spin down states without
inclusion of the SO interaction term (H$_{SO}$) in the total
Hamiltonian. The resulting eigen values
and eigen functions are then used to solve new eigen value problem with the
H$_{SO}$ term in the total Hamiltonian. This method is more efficient and
computationally less expensive than the
calculation in which H$_{SO}$ is included in the total Hamiltonian by doubling the
dimension of the original eigenvalue problem in order to calculate the
non-zero matrix elements between spin-up and spin-down states. In this method,
the calculation of H$_{SO}$ matrix elements involves much less number of
basis functions than in the original basis set.

\begin{figure}
\includegraphics[width=8cm]{Fig1.eps}
\caption{ Corner sharing network of V$_4$O$_4$ cubes in the low temperature
structure of MgV$_2$O$_4$ showing the experimentally observed magnetic order.
The solid and dotted lines joining the V atoms (shown in one cube) represent
the shorter V-V FM bonds (2.971\AA) and longer V-V AFM bonds (2.98 \AA)
respectively. }
\end{figure}

MgV$_2$O$_4$ crystallizes in tetragonal structure with symmetry $I\bar{4}m2$
(space group 119) at low temperatures\cite{wheeler}. Atomic positions and lattice constants were taken from the
experimental data\cite{wheeler}. The atomic sphere radii were chosen to be
1.96, 1.99, and 1.78 a.u. for Mg, V, and O, respectively. We have used
50 {\bf k} points in the irreducible part of the Brillouin zone for the self-consistent calculations. In order to model
the low temperature magnetic order observed in the experiment, we have
constructed a supercell (with 8 inequivalent  Vanadium atoms). The lowering of
symmetry of this unit cell arises due to the experimentally observed antiferromagnetic ordering.
The network of corner sharing
V$_4$O$_4$ cubes of low temperature structure is shown in Fig. 1 with the magnetic order. The 8 inequivalent  Vanadium atoms considered in the calculation are also
marked in the figure with the corresponding
orientation of spins at that particular site. One can see the antiferromagnetic
chains along {\bf a} $(...V3-V7-V3-V7...)$  and {\bf b} $(...V6-V2-V6-V2...)$ axes alternating along c-axis.
 In each V$_4$O$_4$ cube there are 4 inequivalent
V atoms. Due to the presence of cooperative trigonal distortion
along c-axis resulting in alternating compression and expansion of cube
faces, there is a further symmetry breaking and hence successive cubes along
c-axis no longer remain equivalent. Furthermore, the V$_4$O$_4$ cube containing
V1, V5, V2 and V6 does not have the same spin arrangement as that containing
V3, V7, V4 and V8. Therefore to model the experimentally observed magnetic order one needs to consider 8 inequivalent V atoms in the unit
cell.

\section{RESULTS}

\begin{figure}
\includegraphics[width=9cm]{Fig2.eps}
\caption{ Spin polarized (a) total DOS within LSDA,
(b) partial DOS for V d-states around the Fermi level
within LSDA+U, (c) partial d-DOS within LSDA+U+SO (U-J = 2 eV)in the low temperature AFM phase.}
\end{figure}

\noindent Our LSDA calculations of experimentally observed antiferromagnetically
ordered
phase show that total energy of this phase is indeed lower than that of the
corresponding
ferromagnetic (FM) phase by 0.4 eV per formula unit. The density of states (DOS) of
this antiferromagnetic
state (within LSDA) is shown in Fig. 2(a). It is observed that LSDA
gives a metallic state whereas the system is known to be a Mott insulator\cite{mamiya}.
Thus AFM interaction alone is not able to open up the gap. Around the Fermi
level, mainly V d-states are seen to be present. In an effort to have the
insulating gap as observed experimentally, we included Coulomb correlation
in our calculations within LSDA+U approximation. We performed
calculations with U$_{eff}$ (=U-J) values in the range 1 to 4 eV as found to be relevant
from the literature on
Vanadium spinel systems\cite{tm-rv,
tm-tsd,pandey}. We present the results for U$_{eff}$ = 2 eV in the
following, nevertheless it may be noted that our conclusions remain valid in the whole range of U$_{eff}$  values considered by us.
In Fig. 2(b) we show
 the partial DOS of five d-orbitals as these are the states present
around the Fermi level. As expected, the application of Coulomb correlation $U$ is able to open up
a small gap of 0.12 eV which increases with the increase in $U$. The
gap originates because of the
the splitting of the t$_{2g}$ levels in addition to the t$_{2g}$-$e_g$
splitting due to octahedral field.
The further splitting of t$_{2g}$ is
primarily caused by the antiferromagnetic interactions which
get enhanced in the presence of Coulomb correlations.

Another observation that can clearly be made from the partial DOS of d-orbitals (Fig. 2(b)) is that among the occupied t$_{2g}$ orbitals, one orbital
(i.e. d$_{x^2-y^2}$) is more populated while the other two (d$_{xz}$ and d$_{yz}$)
essentially have the same occupancy and seem to be degenerate. The higher
occupancy of d$_{x^2-y^2}$ orbital is a result of the presence of
the tetragonal compression along c-axis at low temperatures. However,
closer analysis of occupancies of the apparently degenerate d$_{xz}$ and
d$_{yz}$ orbitals at each Vanadium site shows that there is a tendency towards
orbital ordering. Table I lists the orbital occupancies of
d$_{x^2-y^2}$, d$_{xz}$ and d$_{yz}$ for the 8 inequivalent V atoms
in the unit cell considered. One clearly observes that the occupancy of
d$_{xz}$ and d$_{yz}$
orbitals are different as one moves along the c-axis whereas that of
d$_{x^2-y^2}$ remains the same. The orbital polarization increases
on increasing the value of $U$ and alternates for the d$_{xz}$ and d$_{yz}$ orbitals
(see for example, V1 and V2) in successive Vanadium layers along
c-axis. This is similar to an A-type antiferro-orbital order where the
antiferromagnetic V chains
parallel to the ab-plane have {\it ferro-orbital} order (e.g. similar orbital occupancies of V1 and V5 ions or that of
V2 and V6 ions) whereas along c-axis there is an {\it antiferro-orbital}
order between d$_{xz}$ and d$_{yz}$ orbitals (see occupancies of V1 and V2 or
that of V5 and V6 in Table I). This is consistent with the previous theoretical
observation on the same system\cite{pandey}. The observed intra-chain ferro-orbital
order is also consistent with experimental antiferromagnetic order as
per Goodenough-Kanamori-Anderson rules \cite{goodenough}.The orbital order described above is also revealed in
the calculated real space electron density at each V site shown in Fig. 3(a).
This orbital order was predicted by Tsunetsugu and Motome
\cite{motome} for Vanadium spinels from their calculations based on Kugel-
Khomskii model in strong coupling limit.

As mentioned earlier, the influence of spin-orbit coupling
on the magnetic and orbital order in these systems is continuously debated
but no conclusion has been reached yet. In order to investigate the effect of
spin-orbit interaction in this particular system, we also performed a
calculation with spin-orbit coupling within LSDA+U+SO approximation. The
solution obtained within LSDA+U+SO has a lower energy than that obtained within
LSDA+U by 0.095 eV per formula unit for $U_{eff}$=2eV.
The partial DOS (Fig. 2(c)) clearly shows a non-negligible impact of SO in general,
with an increased energy gap compared to that with LSDA+U.

\begin{figure}
\includegraphics[width=7cm]{Fig3a.eps}
\includegraphics[width=7cm]{Fig3b.eps}
\includegraphics[width=7cm]{Fig3c.eps}
\includegraphics[width=7cm]{Fig3d.eps}
\caption{ Real space electron density at each V site within
(a) LSDA+U (b) LSDA+U+SO along two different directions. Isosurface
used for both corresponds to 0.5 e/\AA$^3$.}
\end{figure}
The analysis of orbital occupancies in this case indeed leads to some
important and interesting observations.
The apparent degeneracy of d$_{xz}$ and d$_{yz}$
orbitals observed within LSDA+U is no longer present and there is a complete lifting of degeneracy of all the
t$_{2g}$ orbitals (see Table I). Even though, likewise LSDA+U, the antiferromagnetic V chains parallel to the
ab-plane are
still ferro-orbitally ordered and along c-axis these chains are
anti-ferro orbitally ordered, the orbital polarizations in adjacent
chains along c-axes are significantly different in the presence of SO
interaction. For example, if we
compare the occupancies (Table I) for V1 and V2 with LSDA+U and LSDA+U+SO, we note that orbital occupancies of d$_{x^2-y^2}$ are no longer
same in presence of SO interaction. Furthermore, the polarization of the d$_{xz}$ and d$_{yz}$
orbitals are also very different (i.e. at V2 the polarization of d$_{yz}$
orbital w.r.t. d$_{xz}$ is much stronger than that at V1). This implies that V
chains in successive layers along
c-axis are affected differently by the SO interaction. This is also
reflected in the orbital moments of V ions (listed in Table II and depicted
in Fig. 4). The calculated electronic density at each V site is shown
in Fig. 3(b) which brings out the impact of SO interaction.

\begin{table}
\caption{Orbital occupancies and spin magnetic moment within  LSDA+U and LSDA+U+SO (U$_{eff}$=2 eV)}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
& \multicolumn{3}{|c|}{orbital occupation} & spin magnetic\\
\cline{2-4}
 & d$_{x^2-y^2}$ & d$_{xz}$ & d$_{yz}$ & moment ($\mu_B$) \\
\hline
 \multicolumn{5}{|c|}{With LSDA+U }\\
 \hline
V1 (V3) & 0.665 & 0.553 & 0.386  & 1.53 (-1.53) \\
V2 (V4) & 0.665 & 0.386 & 0.553 & 1.53 (-1.53) \\
V5 (V7) &  0.665 & 0.553 & 0.386 & -1.53 (1.53) \\
V6 (V8) &  0.665 & 0.386 &  0.553 & -1.53 (1.53) \\ \hline
 \multicolumn{5}{|c|}{With LSDA+U+SO }\\
\hline
V1 (V3) & 0.595 & 0.451 & 0.591  & 1.574 (-1.574)  \\
V2 (V4)& 0.759 & 0.214 & 0.665 &   1.571 (-1.571)  \\
V5 (V7)& 0.595 & 0.451 & 0.591 & -1.574 (1.574)  \\
V6 (V8)&  0.759 & 0.214 & 0.665 & -1.571 (1.571)  \\ \hline
\end{tabular}
\end{table}
\begin{table}
\caption{Calculated orbital moments, total magnetic moment (J) (in $\mu_B$)
and angle of J w.r.t. z-axis within LSDA+U+SO ($U_{eff}$ = 2 eV). The spin magnetic moment is along z axis and is listed in Table I}
\begin{tabular}{|c|c|c|c|c|c|}
\hline
& \multicolumn{3}{|c|}{$\mu_{orbital}$} & $\mu_{total}$ & $angle $ \\
\cline{2-4}

 & $x$ & $y$ & $z$ & J & \\
\hline
V1 &  -0.355 & 0.000 & -0.466 & 1.15 & 17.79 \\
V2 & -0.015 & -0.030 & -0.510 & 1.05 & 1.90\\
V5 &  -0.355 & 0.000 & 0.466 & -1.15 & 162.21 \\
V6 &  -0.015 & -0.030 &  0.510  & -1.05 & 178.10 \\ \hline
\end{tabular}
\end{table}
\begin{figure}
\includegraphics[width=9cm]{Fig4.eps}
\caption{ Electron densities for two successive Vanadium chains along c-axis within LSDA+U+SO showing the impact of SO interaction on them.
The directions of corresponding orbital and magnetic moments are also shown below
each chain.}
\end{figure}

In Fig. 4 we show two successive Vanadium chains along c-axis with
the calculated electron density at each Vanadium site in the presence
of both Coulomb correlation and SO interaction. We have also marked the
direction of orbital and magnetic moments at each site. Effect of SO
interaction is clearly different on the two chains and so is the arrangement
of the orbital moments. One chain shows the canted orbital arrangement and orbital moments are making an angle of 17.79$^{0}$ with the c-axis whereas in other chain orbital moment makes an angle of 1.90$^{0}$ (almost collinear orbital arrangement) with the c-axis (Table II). On one chain (V1-V5-V1-V5) due to canting of orbital
moment, the effect of SO interaction reduces whereas in the other chain
orbital moments align almost opposite to the magnetic moment implying
a substantial SO interaction.
The observation that the SO interaction appears to affect alternate V chains
along c-axis differently, is interesting. This also substantiates the
speculation of Wheeler et al. \cite{wheeler} that SO interaction in
MgV$_2$O$_4$ may not be as large as that in ZnV$_2$O$_4$ or as small as
that in MnV$_2$O$_4$ as discussed earlier.
 The magnitude of orbital moments observed in our calculation also corroborates this fact.
Thus our results show that a small but non-negligible
spin-orbit coupling, along with the significant trigonal distortion present in
MgV$_2$O$_4$ structure, has a substantial effect on the orbital order of this system.
This observation is consistent with the experimental observations by
Wheeler et al.\cite{wheeler} of antiferromagnetic chains with a strongly
reduced moment and the one-dimensional
behavior and a single band of excitations projected by the inelastic neutron scattering.

\section{CONCLUSIONS}

\noindent To conclude, we
have studied the effect of spin-orbit interaction on magnetic
and orbital order in the low temperature tetragonal phase of MgV$_2$O$_4$. We
observe that even
though the orbital moments are relatively small compared to those of
ZnV$_2$O$_4$, the orbital order in successive Vanadium chains is differently
affected in the presence of SO interaction. In one chain (V1-V5-V1-V5, parallel to crystallographic {\bf a} axis) the three t$_{2g}$
orbitals are nearly equally populated giving rise to a canted (non-collinear)
arrangement
of orbital moments whereas in the other (V2-V6-V2-V6, parallel to {\bf b} axis), the orbitals
are highly polarized leading to a collinear arrangement of orbital
moments. These results imply that SO
interaction in  MgV$_2$O$_4$ is non-negligible and has a significant effect on orbital order. However it is not very strong unlike ZnV$_2$O$_4$ and at the same time not
very weak unlike MnV$_2$O$_4$.

\section{ACKNOWLEDGEMENT}

\noindent This work is supported by the DST (India) fast track project (grant no.: SR/FTP/PS-74/2008). RD acknowledges CSIR (India) for a research fellowship.


Todays post is a shorter one for those of you who aren't following me on Instagram (it's addicting I tell ya) and who think I'm not DIYing much lately. I know it appears like I haven't been doing much besides installing new things.
I have been doing little things here and there though. I promise and I'm planning and scheming things for sure.
One of the major things I'm thinking about and started to tackle already is our yucky master bathroom. Now we have two baths that look totally identical and I shortly blogged about one when I introduced you to our new shower head HERE. Now the photos look pretty good in that post. Something like this, right?
And when I removed the old vanity light strip I was shocked to see that the builder didn't even put an electrical box in the wall. The cable is just sticking out of the drywall. That's a no-no and needs to get fixed as well.
I have been trying to work on getting the bathroom to a blanks canvas and am deciding on several things. Here are my bathroom plans so far: I want to rip out the old vanity since the storage is simply not working for us at all. My husband and I both fell in love with the Ikea GODMORGON floating vanity. The two deep drawers are a storage dream and perfect for a small space.
Now the problem is that I will have to fill in the spot of missing tiles under the vanity. I do have enough left in storage to do just that but am actually considering ripping it all out and replacing it with something new and beautiful. I can keep the checker board in the other bathroom. No need to have two identical bathrooms, am I right?
And in a perfect world I would rip out that darn shower too and tile it to have a pretty walk-in shower. But I don't think my budget allows that. But I guess never say never. This all started with just wanting to paint this bathroom and putting in a new mirror and light and escalated into something much bigger.
I'm happy to say I have reached a point already where it's not an entire mess anymore and I'm considering picking up that vanity this week or next.
That's the rug I posted about two weeks ago and I love it on the tile put have a DIY in mind with it too.
That's it for today. I got lots of work to do. Finished most of my major tax work! Finally! Have to work on our annual huge photo book yet and of course the scary patio style challenge. With this weather, it's truly scary.
oh i can't wait to see! i love the sneak peek already and that rug!!! and i LOVE the new urban rugs! awesome finds!
Looking forward to this! I love you gold and white bathroom and can't wait to see what you do here!
Thanks Summer. I'm hoping for some great tiles! You know it!
I like the direction you are going. I really like the all white vanity/cabinet combo. It has great sleep lines. Looking forward to see what you do with the bathroom and what kind of fixture you will pick.
Oh fixture, I'm not sure yet. This will all move very slowly, I just know it.
Yay! Can't wait to follow along. I love that floating vanity!!
I've been eyeballing those UO rugs! Love them! what a bummer about the bad electrical situation. Can't wait to see the room finished up!
I'm loving where this is going Julia! That Ikea vanity is amazing and so is the new rug! I can't wait to see!
My hubby actually got really excited when he saw the vanity and that is so not like him. It's meant to be 😉 It was a miracle to get him into Ikea already. Never happens and he only did it because it was my birthday!
Love the floating vanity Julia. I think it'll be just perfect for your space. I love the towel holder and the rug. Cant wait to see it all done. It already looks so different.
Thanks Shavonda, so far it's been such simple little changes but they already make such a big difference and I actually enjoy walking into the bathroom again. I've hated it for so long!
I love that vanity Julia! Can't wait to see what you decide to do with the floor. Projects always tend to snowball into something bigger in my world too!
How about it. I don't know where to end it! I want to do everything.
That towel hook!! Gorgeous! And that last rug is fantastic, I love the colors.
Love that vanity–can't wait to see how everything comes together in here! We discovered a light with no junction box behind it at our old house, too…..makes you wonder/worry about what else is lurking behind the walls!
How about it. Scares me to death, especially since we had a neighbor with a house fire already. I think I know why they did it. The builder knew I wanted the light centered but there is a stud there so it made it impossible. That's the problem I have now because I don't want the light to be off center either. No clue what to do.
Can we just talk about how darling that little towel holder is? And, I think it's funny to see your pretty coral still sitting on the toilet tank in the middle of your work zone! 😉 Die hard accessory!
Can't wait to see this! That pink rug from UO is so pretty!
Love your plans!! It will be beautiful!
I'm liking where this is headed! Also, I want all of those rugs. I wish they came in runners!
I love the peeks. I have no doubt that this will be a fabulous room! You have such a strong eye for picking perfect fixtures.
That hexagon towel bar is total indication that the room is going to be spectacular!!


Arja Salafranca's new poetry collection offers portraits of people on trains in England, as well as recounting the experience of being a stranger in Spain, where she was born.
Vonani Bila's voice in Bilakhulu! is as buoyant and direct as ever; his emotional range is broad, incorporating humour and lament. These seven narrative poems, ranging from 3 to 35 pages in length, are grounded in the poet's family and village, at the same time making visible the wider forces that impinge on rural life.
A multi-lingual journal of new writing – poetry, short fiction, essays, reviews – and visual art. This edition contains the work of over 60 poets and writers from all over the country and expresses the range of themes and styles that are being explored in contemporary South African writing. A photographic essay on jazz musicians by Moshe Sekete and sketches by Ahmed Patel provide visual content.
Gail Dendy's new collection, Closer Than That, is full of delicate observations about the human condition, as are many anthologies, but these poems are crafted with the utmost skill and imbued with the musical soul of a dancer.
From the day the cell door closed on Nelson Mandela 40 years ago, poets took up the fight for freedom – not just his freedom, but that of an entire people. This book brings together almost 100 poets who turned their pens into political weapons without sacrificing their ability to arouse anger and give shape to dreams.
This is the third collection of poems curated by Patricia Schonstein. Her personal selection brings together a wide, rich range of love poems written by Nobel Laureates, well-established and emerging poets. They express love in all its guises and remind us of poetry's unique place in the landscape of the human heart.
Lyric, vigilant, hyper-alert to the surfaces, textures and sensations of the physical world, the poems in Moolman's sixth collection are beautiful and dangerous, a meditation on the fraught and even perilous relationship of mind and body.


text:
April 2019 — Volume 3, Issue 1 Back
Status of Vitamin D-25 Hydroxy Vitamin D {25 (OH)} in Patients with Multiple Myeloma
Donaryn Pasamonte, Flordeluna Z. Mesina
Apr 2019 DOI 10.35460/2546-1621.2018-0021 Access
Multiple myeloma (MM) causes generalized bone loss leading to lytic bone lesions and pathologic fractures. The increased osteoclast activity and reduced osteoblast function favors bone resorption and decrease bone formation. Vitamin D is vital in regulating calcium homeostasis and osteoclast-mediated bone resorption. Deficiency of Vitamin D among MM patients may complicate bone mineralization problems and fractures.
General Objective: To determine the status of Vitamin D in patients with multiple myeloma
Specific Objective: To determine the levels of Vitamin D, intact parathyroid hormone and ionized calcium among MM patients
This is a prospective, cross-sectional study which included patients who were 18-year old and above, male or female, diagnosed with multiple myeloma at the University of Santo Tomas Hospital, with or without treatment. Excluded in the study were those with Vitamin D and calcium supplementation. Eligible subjects were extracted blood for Vitamin D assay, intact parathyroid hormone and ionized calcium.
A total of 22 patients with multiple myeloma were included in the study. Sixteen patients (72.7%) had hypovitaminosis D. Among these sixteen patients, seven (31.8%) had vitamin D deficiency (Vitamin D levels <20 ng/mL [50 nmol/L]) and nine (40.9%) had vitamin D insufficiency (levels of 21-29 ng/mL [52.5-72.5 nmol/L]). Only 6 (27.3%) of them were found to have normal serum vitamin D (levels of >29 ng/mL [>72.5 nmol/L]). The mean age (p=0.069), intact PTH (p=0.062) and ionized calcium (p=0.188) of the three groups of patients did not differ.
This study found a high incidence of Vitamin D deficiency among multiple myeloma patients seen at the University of Santo Tomas Hospital. Vitamin D deficiency was independent of age, intact PTH and ionized calcium. It was more common in male subjects. Patients with hypovitaminosis D are at risk for having secondary hyperparathyroidism.
Vitamin D status should be determined among patients with multiple myeloma. Early recognition and treatment of hypovitaminosis D will prevent risk of having secondary hyperparathyroidism that can complicate skeletal-related events.
Kyle R, Gertz M, Witzig T, Lust J, et. al. Review of 1027 patients with newly diagnosed multiple myeloma. Mayo Clinic Proceedings. 2003;78(2):21–3.
Silbermann R, Roodman D. Myeloma bone disease: Pathophysiology and management. Journal of Bone Oncology. 2013Jun;2(2):59–69.
Raje N, Roodman GD. Advances in the biology and treatment of bone disease in multiple myeloma. Clinical Cancer Research. 2011 Mar 15;17(6):1278–86.
Christodoulou S, Goula T, Ververidis A, Drosos G. Vitamin D and bone disease. BioMed Research International. 2013;396541. Epub 2013/03/20. doi: 10.1155/2013/396541 PMID: 23509720.
Lips P, Van Schoor NM. The effect of vitamin D on bone and osteoporosis. Best Practice & Research Clinical Endocrinology & Metabolism. 2011 Aug 1;25(4):585–91.
Lauter B, Schmidt-Wolf IG. Prevalence, supplementation, and impact of vitamin D deficiency in multiple myeloma patients. Cancer Investigation. 2015 Nov 26;33(10):505–9.
Clement Z, Ashford M, Sivakumaran S. Vitamin D deficiency in a man with multiple myeloma. North American Journal of Medical Sciences. 2011:469–71.
Terpos E, Morgan G, Dimopoulos MA, Drake MT, Lentzsch S, Raje N, et al. International Myeloma Working Group recommendations for the treatment of multiple myeloma-related bone disease. Journal of Clinical Oncology. 2013 Jun 20;31(18):2347.
Rajkumar SV, Kyle RA, Connor RF. Clinical features, laboratory manifestations, and diagnosis of multiple myeloma. UpToDate. 2011 Jun.
Eisman JA, Bouillon R. Vitamin D: direct effects of vitamin D metabolites on bone: lessons from genetically modified mice. BoneKEy Reports. 2014 Feb 5;3.
Winzenberg T, van der Mei I, Mason RS, Nowson C, Jones G. Vitamin D: and the musculoskeletal health of older adults. Australian Family Physician. 2012 Mar;41(3):92.
Orosa R. 3 out of 5 Filipinos suffer from Vit-D deficiency. The Philippine Star. 2014 May 13;
Ng AC, Kumar SK, Rajkumar SV, Drake MT. Impact of vitamin D deficiency on the clinical presentation and prognosis of patients with newly diagnosed multiple myeloma. American Journal of Hematology. 2009;84(7):397–400.
Aribi M, Senouci-Bereksi S, Haddouche M, Mesli N. Vitamin D intake and light chain-lgG monoclonal antibodies in patients with multiple myeloma. 2012 Apr;
Maier GS, Seeger JB, Horas K, Roth KE, Kurth AA, Maus U. The prevalence of vitamin D deficiency in patients with vertebral fragility fractures. The Bone & Joint Journal. 2015;97-B(1):89–93.
Parathyroid Hormone (PTH), Serum [Internet]. Mayo Clinic Laboratories. Available from: https://www.mayocliniclabs.com/test-catalog/Clinical and Interpretive/28379
Badros A, Goloubeva O, Terpos E, Milliron T, Baer MR, Streeten E. Prevalence and significance of vitamin D deficiency in multiple myeloma patients. British Journal of Haematology. 2008;142(3):492–4.
Laroche M, Lemaire O, Attal M. Vitamin D deficiency does not alter biochemical markers of bone metabolism before or after autograft in patients with multiple myeloma. European Journal of Haematology. 2010;85:65–7.
Fisher P, Shieh A, Carmel A. Study finds high levels of Vitamin D needed for bone density drugs to work. Hospital for Special Surgery. 2011. Available from: https://www.hss.edu/newsroom_high-vitamin-bone-drugs-work.asp


text:
Bangladesh PM Sheikh Hasina grieves at ferry deaths
Dhaka, 28 November : Bangladesh Prime minister Sheikh Hasina, who is now in Port of Spain attending the Commonwealth summit, expressed her grief at Friday's launch disaster and ordered speedy rescue operation and investigation into the accident.
The president also expressed his sorrow at the tragedy and condolences for the grieving families. Hasina has sent condolences to the families of the victims, her deputy press secretary Mahbubul Huq Shakil said in Dhaka.
At least 32 killed after Bangladesh ferry accident
Launch sinks tragedy strikes Bhola on "Eid day"
Reuters, Dhaka, 28 November : Rescuers have retrieved 32 bodies, including at least 12 children, and are searching for scores of people missing after an overcrowded ferry sank in a river along the Bangladesh coast, police and witnesses said on Saturday.
They said the ferry M.V. Coco-4 was sailing to the coastal town of Bhola, some 300 km from Dhaka, on Friday night with around 1,500 people on board - about three times the number it was registered to carry. The death toll late on Friday had been put at five. Many of those on board were going home to celebrate the Muslim Eid al-Adha festival on Saturday. Media at the scene reported the ferry started taking in water after it hit a raised section of the river bed in heavy fog. Most of those on board swam to safety but up to 80 may still be missing, one survivor said. The ferry was listed with a capacity to carry about 450 people.
Officials and transport operators said they were still waiting for a rescue vessel to arrive. An investigation into the sinking has been ordered, the communications ministry said. Hundreds of people die every year in ferry accidents in Bangladesh, but no major ferry disasters have happened in the past two years after stricter enforcing of safety rules. န Photos : AFP, Reuters READ BBC STORY
Mamata lays foundation for country's first auto logistics hub in Howrah
Howrah, 28 November : Indian Railway Minister Mamata Banerjee on Saturday laid the foundation stone for the country's first automobile logistics hub near here and announced that nine more such centres will be set up at different places.
"After this, we will set up automobile hubs at Siliguri, Guwahati, Chennai, Pune, Mumbai, Ahmedabad, Kerala, Bangalore and Delhi as a pilot project in collaboration with Society of Indian Automobile Manufacturers (SIAM)," Mamata Banerjee said while laying the foundation stone near Shalimar railway station.
Tripura bans mobile in schools, Meghalaya in vehicles
Agartala, Shillong, 28 November : Tripura government has banned the use of mobile phones by students and teachers in schools across the northeastern state, an official said here Saturday. The Meghalaya government has banned the use of mobile phones by drivers.
The Tripura cabinet took the decision in a meeting chaired by Chief Minister Manik Sarkar. A Tripura education department official said: "If a student up to Class 12 is caught using a mobile in the school premises, he or she would be punished." He added that a notification to the effect is being issued. The official told reporters: "The Central Education Department issued the ban (to be applicable in all central government control and aided schools) a couple of months back and sent an advisory to all the state governments across the country to consider the issue."
Tripura School Education Minister Tapan Chakraborty said: "To maintain discipline in schools the ban on mobile phones was necessary." The minister urged parents and guardians of students not to give mobile phones to their schoolgoing children.
Interlocutor for Gorkhaland talks to visit Kolkata this weekend
Kolkata, 28 November : Vijay Madan, who has been appointed as the interlocutor in the talks between the WB state government and the Gorkha Janmukti Morcha is coming to Kolkata on 29 November. The next day he will have talks with senior officials of the state government including chief secretary Ashok Mohan Chakrabarti and home secretary Ardhendu Sen. On 1 December, he will have talks with Governor Gopalkrishna Gandhi. The tripartite talks between the Centre, GJM and the state government will be held on 21 December in Darjeeling.
Maoist leader Bikash call for 'dialogue' over phone
Kolkata, 28 November : Renewing the call for dialogue, Maoist leader Bikash today told Bengal Newz the central and West Bengal governments should stop the anti-Moists operations in West Midnapore and begin talks to resolve the problem.
"At this moment, the people want a solution through dialogue," Maoist leader Bikash said. He claimed that resistance was continuing since the central and state governments did not show willingness for peace by accepting demands for release of those arrested in West Midnapore.
The Maoist leader also said 'people's problems' would not be discussed in the forthcoming session of the state assembly beginning 30 November, but the tussle between the CPI(M) and Trinamool Congress and Congress would occupy the centrestage. န File Photo : Arpan Mukherjee
Eid celebrated across the Bengal
Children enjoy rides at Shishu Park in Dhaka on Eid Day >
Dhaka, Kolkata, 28 November : Muslims across the Bengal were celebrating Eid-ul-Azha on Saturday with prayers and sacrifice. Dressed in festive clothes, Muslims thronged mosques across the Bengal Saturday to pray on Eid.
The main Eid congregation in Bangladesh was held at the National Eidgah in Dhaka at 9:00am(BDST), attended by President Zillur Rahman among others. And in Kolkata thousands of devotees gathered to offer prayers at Road road. The celebrations began with millions of Muslims offering prayers at mosques and eidgahs throughout Bangladesh, West Bengal, Assam and Tripura for peace and prosperity.
The prayers were followed by the sacrificing of animals. Consequently, it has become a tradition to slaughter livestock and feed the poor to mark the occasion. န Photos : Firoz Ahmed, Avijit Mondal
India won't be affected much by Dubai crisis : Pranab
Reuters, Chandigarh, 28 November : Dubai's debt crisis will not affect India much but the government is keeping a close watch and will act to prevent any fallout, the Indian finance minister said on Saturday.
"The impact cannot be much as our stake is so small and the amount involved compared to the world economy is miniscule," Pranab Mukherjee told reporters in Chandigarh, where he was delivering a lecture. "Watchful and effective intervention at the appropriate time can avert some immediate crisis," he said. Indian stocks and the rupee were rattled on Friday after Dubai's woes stoked fears over corporate exposure to a key trading partner and that foreign funds would lose their appetite for risk.
The United Arab Emirates (UAE), of which Dubai is part, is the second-biggest export destination for India and accounts for 10-12 % of India's inward remittances. Mukherjee said the emirate's problems could force a return of Indian citizens, who make up more than 40% of the UAE's population.
India-Bangladesh talks from Monday
New Delhi, 28 November : India and Bangladesh will explore the possibility of signing an extradition treaty soon when the home secretaries of the two countries begin their three-day talks here on Monday.
Cross-border terrorism, infiltration, smuggling of fake currency and activities of north-east militants will also be high on the agenda. The Indian delegation, led by Indian home secretary G K Pillai, will seek cooperation from Bangladesh (led by home secretary Abdus Sobhan Sikder) to deal with security issues, especially anti-India jehadi organisations and north-east militants operating from its soil, sources said.
Though the proposal to sign an extradition treaty has been pending for long, New Delhi hopes to break some ice with Dhaka to finalize it quickly considering the positive signal given by the Sheikh Hasina government over the issue.
Life returns to normal in Assam's North Cachar Hills
ANI, North Cachar Hills (Assam), 28 November : The surrender of 'black widow' militants has created a positive influence in North Cachar Hills district of Assam, and there has been a gradual improvement in the security scenario.
The markets are now flooded with people, railway services have resumed and rock concerts are drawing a huge number of people. No untoward incident has been reported in NC Hills since 2 October this year, when Jewel Garlosa faction of Dima Halim Daogah or 'Black Widow' laid down their arms. Businessman and traders are happy as markets are filled with customers, which earlier remained empty because of frequent militant attacks. People along with their families do not hesitate anymore to move of their homes for night stroll. Besides, the night trains have resumed service and work on Lumding-Silchar railway gauge project has commenced.
A rock concert organized by a local musician Morningkey Phangso in the Valley attracted large audiences. With the situation improving in the region, people are beginning to enjoy life.
Maoists kill gram panchayat leader in W Midnapore
Jhargram, 28 November : Suspected Maoist guerrillas gunned down a local CPI(M) leader in trouble-torn West Midnapore district, police said Saturday.
According to sources, the incident took place Friday night in Jhargram sub-division's Jitushol area in the district when a group of unidentified miscreants killed Karuna Mahato. 'Mahato was a CPI(M) gram panchayat member in Shalboni region. The Maoist ultras called Mahato from his residence late Friday night and took him to a nearby forest. He was found dead this morning on National Highway-9 near Kalaboni forest region,' a district police officer said.
Forward Block demand renaming of Andaman Island
Port Blair, 28 November : The State Conference of All India Forward Block was held recently at Delanipur community hall. It was inaugurated by Naren Dey, Secretary, AIFB and Minister of Agriculture and Consumer's Affair, Govt. of West Bengal. In his address, the Minister urged the party workers to work relentlessly to attain their democratic and fundamental rights.
The conference also passed a resolution to press their demand for renaming Andaman & Nicobar Islands as 'Shaheed and Swaraj Dweep' as named by Netaji Subhash Chandra Bose. It also declared 23rd January, the birthday of Netaji as Netaji Jayanti/ Desh Prem Diwas. Besides, other issues for the development and welfare of the islanders were also discussed in the conference. Earlier, a district conference was held at Billiground.
A State Committee was constituted in the conference with Lingamayya as Chairman and A Pandyan, General Secretary besides five office bearers and eight committee members.