Session C4: Disorder and Optical Lattices

Dissipative Transport of a Bose-Einstein Condensate in an Optical Speckle Disorder Potential

Very recent experiments involving ultra-cold atoms have proved very successful at probing the effects of disorder in an extremely controlled fashion. Most impressive is the observation of Anderson localization of bosonic atoms in the presence of a disorder potential created using an optical speckle pattern. These experiments are, for the first time, able to directly image the localized single particle wavefuniton. Other recent experiments, such as the one at RICE, are able to provide rich information with regards to transport in the presence of disorder. While such experiments are novel with no known analogues in the solid state context, a definitive understanding of the experimental results has been missing. In the present work, we provide a theoretical model suitable for describing such experiments. We illustrate the strength of our method by clearly identifying the distinct time scales, associated with the disorder induced dissipative transport, in striking agreement with experimental observations. Analytic expressions derived in our work provide clear insight into the physical mechanism responsible for dissipation.   

Dipolar Bose-Einstein condensates as discrete superfluids

We investigate the superfluid properties of a dipolar Bose-Einstein condensate (BEC) in a fully three-dimensional trap. Specifically, we calculate a superfluid critical velocity for this system by applying the Landau criterion to its discrete quasiparticle spectrum. We test this critical velocity by direct numerical simulation of condensate depletion as a blue-detuned laser moves through the condensate. In both cases, the presence of the roton in the spectrum serves to lower the critical velocity beyond a critical particle number. Since the shape of the dispersion, and hence the roton minimum, is tunable as a function of particle number, we thereby propose an experiment that can simultaneously measure the Landau critical velocity of a dipolar BEC and demonstrate the presence of the roton in this system.   

Fermions in a 3-D Disordered Potential

We report our progress toward a study of ultra-cold, fermionic $^{40}$K in a 3-D disordered potential [1]. The potential is formed by crossing two optical speckle fields which create fine-grained disorder in three-dimensions having a length scale of about 700 nm. Transport of the non-interacting cloud through the potential will be discussed. We will also present the use of a hybrid magneto-optical trap [2] to cool $^{40}$K. \\[4pt] [1] M. White \textit{et al.}, Phys. Rev. Lett. \textbf{102}, 055301 (2009). \\[0pt] [2] Y.-J. Lin \textit{et al.}, Phys. Rev. A \textbf{79}, 063631 (2009).   

Anderson Localization in a Bose-Einstein Condensate with Tunable Interactions

The wave nature of matter can often lead to spectacular and counterintuitive phenomena. In a disordered system, it can lead to the surprising result that interference from multiply scattered matter waves can lead to a localized, insulating state, even for very weak disorder. This so-called Anderson localization is a general wave phenomena, and has been observed in wave systems as varied as ultrasonic, light, microwave, and ultra-cold atoms. One of the most interesting modifications of the Anderson model is the inclusion of an interparticle interaction. Questions as to whether the addition of this interaction leads to the break-down of localization at long times is still unanswered. We perform expansion experiments of an ultra-cold gas of $^7$Li with tunable interactions in a one-dimensional guide with superimposed optical speckle for disorder. We have investigated the nature of the localization versus atomic momentum and in addition, will report on the progress of expansion measurements designed to investigate the role interactions play in localization.   

The Effects of Disorder on a Quasi-2D System of Ultra-Cold Atoms

An ultra-cold gas of atoms can be used to create many different model Hamiltonians. When tightly confined in one spatial dimension, the gas can become effectively two-dimensional. At low temperature, a quasi-2D Bose gas undergoes a Berezinskii-Kosterlitz-Thouless phase transition to a superfluid, mediated by the binding and unbinding of vortex pairs. As disorder affects vortex transport properties, a slight amount of fine-grain disorder in the potential energy may alter the properties of this phase transition. We will present experimental observations of a 2D Bose gas of rubidium atoms in the presence of disorder created by a laser speckle field.   

Delocalization of a disordered bosonic system by repulsive interactions

Anderson localization of ultracold atoms in disordered optical lattices, i.e. the transition from extended to exponentially localized states, was recently demonstrated for non-interacting samples. With the addition of atomic interactions, such a system becomes more complicated and is more difficult to describe theoretically. The effects of the disorder are expected to be gradually suppressed by repulsive interactions, and the possibility of different quantum phases arises. We employ a Bose-Einstein condensate of potassium, where the interaction can be tuned from negligible to large values via a Feshbach resonance and use a quasi-periodic lattice potential as a model of a controllable disordered system. This allows us to study the interplay of disorder and repulsive interactions in detail. We characterize the entire delocalization crossover through the study of the average local shape of the wavefunction, the spatial correlations, and the phase coherence. Three different regimes are identified and compared with theoretical expectations: an exponentially localized Anderson glass, the formation of locally coherent fragments, as well as a coherent, extended state.   

Pseudospin and spin-spin interactions in ultra-cold alkali

By Raman coupling two selected hyperfine states of alkali atoms in an external magnetic field cold atom experiments simulate magnetic-like spin 1/2 dynamics in a controlled quantum many-body environment. We describe the effective spin (or pseudospin) degrees of freedom in accordance with choosing one hyperfine state as ``spin-up,'' the other as ``spin-down.'' state We derive the corresponding short-ranged spin-spin interactions which are anisotropic and include the interaction of a particle pseudospin with an effective, short-ranged pseudospin independent internal pseudomagnetic field carried by the other particles. In the degenerate internal state approximation we find that a magnetically controlled Feshbach resonance can vary the ratio and relative sign of spin-independent to spin-dependent interactions. In contrast, the relative magnitudes of the spin-dependent interactions, such as anisotropy, are not affected by a Feshbach resonance. When including the indistinguishability of the interacting particles, we find that the effective interaction takes the form of short-range ising spin interactions. We discuss implications for experimental quantum magnetism simulations.   

Interaction effects of interconvertible two-component bosons in a state-dependent optical lattice

Mixtures of bosonic species in optical lattices are promising for the study of a number of topics, including spin-boson systems, the two-component Bose-Hubbard model, and quantum magnetism. We have implemented the two-component Bose-Hubbard model using two hyperfine states of $^{87}$Rb in a three-dimensional optical lattice with state-dependence along one axis. With optimal overlap of our quasi-stable, homonuclear mixture, we observe significant interspecies effects on the visibility. We have examined their dependence on the relative populations of the two species and the respective state-dependent lattice depths. Possible mechanisms for the observed many-body effects will be discussed.   

Dissipation of repulsively bound pairs in the Bose-Hubbard model

One of the most striking phenomena of the Bose-Hubbard model is the existence of repulsively bound atom pairs (dimers). These objects occur, if the on-site repulsion exceeds the tunneling bandwidth of the single particles by far, so that two atoms on the same site can't get rid of their interaction energy by just tunneling apart. The effective dynamics of dimers is governed by virtual intermediate processes of its constituents and can be described by a Hamiltonian which contains tunneling and nearest neighbor interactions. Additionally, the coupling of the dimers to the system of uncoupled atoms (monomers) leads to decay and/or generation of new dimers. The decay rates of isolated pairs and cluster of pairs is derived and the dynamics of the decay process is studied. In particular, it is shown that the decay of small cluster of pairs leads to temporary entanglement.   

Effective coherent four-body interactions in optical lattices

The interactions of neutral bosons with small scattering lengths confined in optical lattices are dominated by two-body collisions. When the scattering length is increased (say, via a Feshbach resonance), three-body interactions become important; however, even for small scattering lengths effective higher-body interactions---generated by virtual transitions to higher lattice orbitals---can play a surprisingly important role in some processes. For example, we recently showed that effective three-body interactions would have a significant influence on the collapse and revival of coherent states in 3D lattices [Johnson et al, NJP 11, 093022 (2009)]. Beautiful experimental evidence for this physics was recently presented in [Will et al, arXiv:0911.5066 (2009)]. Moreover, this data also shows clear signatures of four- and higher-body effective interactions. In this talk we describe how higher-body effective interactions arise in deep lattices and, in particular, we find the strength of the coherent four-body interactions which we compare to experiments.