Session C04: Localization and Transport in Atomic Systems

Scale-invariant phase transition of disordered bosons in one dimension

The disorder-induced quantum phase transition between superfluid and non-superfluid states of bosonic particles in one dimension is generally expected to be of the Berezinskii-Kosterlitz-Thouless (BKT) type. In this talk, we show that hard-core lattice bosons with power-law hopping decaying with distance as 1/r^α -- corresponding in spin language to a XY model with power-law couplings – undergo a non-BKT continuous phase transition instead, in the experimentally relevant regime 2<α <=3. By scaling analysis near the transition point, we demonstrate a new universal behavior of disordered bosons in one dimension. We discuss possible realizations in cold atomic and molecular systems.    

Probing localization in the 2D Aubry-Andre model using ultracold atoms in an optical lattice

The Aubry-Andre model is a quasiperiodic system where a weak, periodic, but incommensurable modulation is applied on the onsite energies of a periodic lattice. It displays novel properties such as a localization transition and topological phenomena and its phase diagram contains the localized Bose glass in addition to the conventional superfluid and Mott insulting phases found in periodic lattices.  We implement a 2D Aubry-Andre model by superimposing four retro-reflecting laser beams with different amplitudes under 45 degrees in the horizontal plane.  By loading a BEC of bosonic ³⁹K atoms with widely tunable scattering length into this optical lattice, we study the interplay between disorder and interaction on the localization transition of this system.  We map out the superfluid to Bose glass/Mott insulator transition phase diagram by measuring the coherence of the atoms through their matter-wave diffraction pattern in time-of-flight imaging. For vanishing interactions, the localization transition is in good agreement with the single-particle prediction.  For increasing repulsive interaction we initially observe that superfluidity is preserved for larger disorder strength, similar to our previous experiment on the eight-fold symmetrical quasicrystal. For strong interactions, this trend reverses and the Bose glass transition blends into the Mott transition.    

From trilobite molecules to tight-binding models

When a Rydberg atom and a ground state "perturber" atom encounter one another, they interact via an oscillatory potential mediated by the scattering of the Rydberg electron off of the perturber. The wells in this potential can trap the perturber, binding the two atoms together into a molecule. This same mechanism can also cause trimers, tetramers, and larger clusters to form. As the number of perturbers increases, it becomes impractical to describe this Rydberg composite within the framework of molecular physics, as its properties start to mirror those of a solid-state system. A clear example of this is the modified spectrum of the Rydberg electron in the presence of a dense environment of immobile perturbers. Because this spectrum of an isolated Rydberg atom is highly degenerate due to its SO(4) symmetry, an exact mapping exists between the perturbed Rydberg states and the states of a particle in a tight-binding lattice. Using this mapping, we demonstrate how to realize a thermodynamic limit in the Rydberg electron. This thermodynamic limit and the control over the properties of the tight-binding lattice through the arrangement of the perturbers allow us to prove that the Rydberg electron can undergo Anderson localization in a disordered perturber landscape. The confluence of the infinite-ranged Coulomb potential and the zero-range electron-atom potentials leads to a plethora of possible lattice parameters, ranging from nearest-neighbor hopping to all-to-all coupling between sites.   

Driving versus disorder: interplay of dynamic localization and Aubry-André localization in a cold atom quasicrystal

We report the experimental study of an ultracold atomic gas in a bichromatic optical lattice subjected to both dipolar driving and quasi-disorder. We measure a rich localization phase diagram as a function of drive amplitude and quasi-disorder strength which arises due to the competition between these two localizing effects. The observed quantum phase transition displays multiple lobes which can be understood as arising from a competition between quasi-disorder and effective tunneling energy, but also comprises several features which are not present in this first-order theory. We argue, with the support of numerics, that these exotic features arise from higher-order terms beyond the high-frequency-drive approximation.   

Mobility edges in long-range hopping models

The experimental platform of one-dimensional momentum state lattices (MSLs) offering individual control over lattice Hamiltonian terms has proven to be a versatile platform for studying various lattice models. In this talk, I will discuss our progress toward implementing the long-range hopping model with quasi-periodic site energy disorder. In the 1D quasi-periodic energy case, the model becomes the celebrated Aubry–André (AA) model, which is self-dual, and hence has no mobility edge. In the presence of long-range hopping terms, the AA model loses its self-duality and has a mobility edge. The control over the lattice parameters paves the way for engineering transport in this one-dimensional quasi-periodic lattice.   

Diffusion Measurements in a Strongly Correlated Lattice Gas

Ultracold lattice gases are an excellent platform for studying the transport properties of quantum systems. We present near-equilibrium transport measurements for a thermally active Mott insulator composed of bosonic ⁸⁷Rb confined in a cubic optical lattice. A small selection of atoms at the center of the gas are “tagged” by transferring them to a different spin state. This process uses tightly focused laser beams to induce stimulated Raman transitions without distorting the density profile. The spatio-temporal dynamics of the tagged atoms are measured using spin-resolved imaging. The effect of temperature on the dynamics is measured by varying the entropy per particle of the gas before loading into the lattice.   

Localization and multifractality in driven cold-atom quasicrystal and its relation to the driven integer quantum Hall matter

By independently controlling dipolar and phasonic modulations applied to atoms in an 1D incommensurate bichromatic lattice, we have experimentally demonstrated coherent tuning of the localization transition [1] and observed the competition between dynamic and Anderson localization. Here we elucidate the mapping between this system and a two-dimensional driven integer quantum Hall system, in which our combined modulation protocol maps to illumination by light with fully tunable polarization. As an application of the mapping, we discuss how to Floquet engineer an extended critical phase hosting multifractal wave functions, embedded in an interleaved localization phase diagram, simply by tuning the polarization of the driving light from linear to circular.   

2PI strong coupling approach to out of equilibrium dynamics of the clean and disordered Bose Hubbard model

Out of equilibrium phenomena in the Bose-Hubbard model (BHM), such as the spreading of correlations, thermalization and many-body localization have attracted considerable interest in recent years.  We have developed a two particle irreducible (2PI) strong coupling (2PISC) approach that allows us to access out of equilibrium phenomena in dimensions higher than one.  We have investigated the spreading of correlations in one, two and three dimensions and find quantitative agreement with measurements of the speed of spreading of single-particle correlations in both the one- and two-dimensional BHM realized with ultracold atoms. We demonstrate that there can be large differences between the phase and group velocities for the spreading of correlations and explore how the anisotropy in the velocity varies across the phase diagram of the BHM.  We have also applied the 2PISC approach to the disordered Bose-Hubbard model and obtained equations of motion for spatio-temporal correlations and explored their equilibrium solutions, including phase diagrams. We note that the disorder strengths where the emergence of non-ergodic dynamics was observed experimentally in the two dimensional disordered BHM [Choi et al., Science 352, 1547 (2016)] appears to correspond to the Mott insulator -- Bose glass phase boundary.  Our results establish the 2PISC approach as a powerful tool to study out-of-equilibrium dynamics in the BHM in dimensions greater than one.   

Anomalous Directed Percolation Universality of Rydberg Facilitation in a Gas

Rydberg atoms interact strongly over large distances leading to effects such as Rydberg blockade or facilitation. In the facilitation regime the dynamics of the system closely resembles those of epidemics, manifesting a non-equilibrium absorbing-state phase transition between large-scale spreading of excitations and an inactive system.

Using Monte-Carlo simulations of an optically driven Rydberg many body gas in the facilitation regime, we analyze the effects of thermal motion and the network character of the facilitation dynamics in a gas on the universality class of the phase transition. For very high temperatures the system shows mean field dynamics.  In the low temperature regime, we show that this phase transition falls into the universality class of directed percolation, provided the underlying network of ground state atoms is above the percolation threshold. With increasing temperature however, long-distance (Levy flight-type) excitations leads the system to display signatures of anomalous directed percolation. If the network of ground state atoms is below the percolation threshold the critical point of the phase transition is replaced by an extended Griffith phase.   

Effects of (non-)magnetic disorder in quasi-1D singlet superconductors

We study the competition between disorder and singlet superconductivity in a quasi-1d system. We investigate the applicability of the the Anderson theorem,  namely that time-reversal conserving (non-magnetic) disorder does not impact the critical temperature, by opposition to time-reversal breaking disorder (magnetic). To do so we examine a quasi-1d system with forward scattering disorder.