# Inducing Transport in a Dissipation-Free Lattice with Super Bloch Oscillations 

Elmar Haller, 1 Russell Hart, 1 Manfred J. Mark, 1 Johann G. Danzl, 1 Lukas Reichs¨ollner, 1 and Hanns-Christoph N¨agerl 1 

$^{1}$Institut f¨ur Experimentalphysik and Zentrum f¨ur Quantenphysik, Universit¨at Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria 

(Dated: October 28, 2018) 

Particles in a perfect lattice potential perform Bloch oscillations when subject to a constant force, leading to localization and preventing conductivity. For a weakly-interacting Bose-Einstein condensate (BEC) of Cs atoms, we observe giant center-of-mass oscillations in position space with a displacement across hundreds of lattice sites when we add a periodic modulation to the force near the Bloch frequency. We study the dependence of these “super” Bloch oscillations on lattice depth, modulation amplitude, and modulation frequency and show that they provide a means to induce linear transport in a dissipation-free lattice. Surprisingly, we find that, for an interacting quantum system, super Bloch oscillations strongly suppress the appearance of dynamical instabilities and, for our parameters, increase the phase-coherence time by more than a factor of hundred. 

Understanding the conduction of electrons through solids is of fundamental concern within the physical sciences. The simplified situation of an electron under a constant force F within a perfect, non-dissipative, periodic lattice was origi- nally studied by Bloch and Zener [1] over 70 years ago. Their and subsequent studies revealed that the particle would un- dergo so-called Bloch oscillations (BOs), a periodic oscil- lation in position and momentum space, thereby quenching transport and hence resulting in zero conductivity. BOs can be viewed as periodic motion through the first Brillouin zone, resulting in a Bloch period T$_{B}$ = 2 ¯ hk / F , where k =$_{p}$ / d is the lattice wave vector for a lattice spacing d . They result from the interference of the particle’s matter wave in the presence of the periodic lattice structure, requiring a coherent evolution of the wave during the time T$_{B}$ . Generally, it is believed that conductance is restored via dissipative effects such as scatter- ing from lattice defects or lattice phonons [2, 3]. In bulk crys- tals, relaxation processes destroy the coherence of the system even before a single Bloch cycle is completed. These systems thus exhibit conductivity but prevent the observation of BOs. To observe BOs, the BO frequency n$_{B}$ = 1 / T$_{B}$ must be large compared to the rate of decoherence. In semiconductor super- lattices, where the Bloch frequency is enhanced, a few cycles have been observed [4]. 

A recent approach to observe and study BOs is to use sys- tems of ultracold atoms in optical lattice potentials with a force that is provided by gravity or by acceleration of the lat- tice potential. In these engineered potentials, generated by in- terfering laser waves, dissipation is essentially absent, and de- coherence can be well-controlled [5]. Essentially all relevant system parameters are tunable, e.g. lattice depth and spacing, particle interaction strength, and external force, i.e. lattice tilt. For sufficiently low temperatures, a well-defined, suf- ficiently narrow momentum distribution can initially be pre- pared. BOs have been observed for ultracold thermal samples [6–8], for atoms in weakly-interacting Bose-Einstein conden- sates (BECs) [5, 9, 10], and for ensembles of non-interacting quantum-degenerate fermions [11]. Non-interacting BECs [12, 13] are ideally suited to study BOs as interaction-induced 

PACS numbers: 03.75.Dg, 03.75.Lm, 05.30.Jp, 37.10.Jk 

dephasing effects are absent, allowing for the observation of more than 20000 Bloch cycles [12]. 

As for any oscillator, classical or quantum, it is natural that one investigates the properties of the oscillator under forced harmonic driving. In the context of ultracold atomic gases, this is readily possible, as n$_{B}$ is in the range of Hz to kHz. The dynamics of a harmonically driven Bloch oscilla- tor has recently been the subject of several theoretical [14–18] and experimental studies [19–22]. For example, modulation- enhanced tunneling between lattice sites [20, 21] and spatial breathing of incoherent atomic samples [22] have been ob- served. Here, for a weakly-interacting atomic BEC in a tilted lattice potential, we demonstrate that harmonic driving can lead to directed center-of-mass motion and hence to transport. In this dissipationless system we thereby recover transport and conductivity. More strikingly, for slightly off-resonant driving, we observe giant matter-wave oscillations that ex- tend over hundreds of lattice sites. These “super Bloch os- cillations” result from a beat between the usual BOs and the drive. They are rescaled BOs in position space and can also be used, by appropriate switching of the detuning or the phase, to engineer transport. Interestingly, forced driving leads to strongly reduced interaction-induced dephasing and greatly extends the time over which ordinary BOs can be observed. 

The experimental starting point is a tunable BEC of 1 . 2 × 10 5 Cs atoms in a crossed beam dipole trap [23] adiabatically loaded within 400 ms into a vertically oriented 1D optical lattice [12] as illustrated in Fig. 1(a). The lattice spacing is d =$_{l}$ / 2, where l = 1064 . 49 ( 1 ) nm is the wavelength of the light. Unless stated otherwise, we work with a shallow lat- tice with depth V = 3 . 0 ( 3 ) E$_{R}$ , where E$_{R}$ = h $^{2}$/ ( 2 m$_{l}$ $^{2}$) is the photon recoil energy for particles with mass m . The atoms are initially levitated against gravity by means of a magnetic field gradient and spread across approximately 50 lattice sites with an average density near 5 × 10 13 cm − 3 in the central region of the sample. We control the strength of the interaction as mea- sured by the s-wave scattering length a near a Feshbach reso- nance [23]. Throughout this work, unless stated otherwise, we work at a = 11 ( 1 ) a$_{0}$ , where a$_{0}$ is Bohr’s radius. We initiate 

