We numerically study the expansion dynamics of ultracold atoms in a one-dimensional disordered potential in the presence of a weak position measurement of the atoms. We specifically consider this position measurement to be realized by a combination of an external laser and a periodic array of optical microcavities along a waveguide. The position information is acquired through the scattering of a near-resonant laser photon into a specific eigenmode of one of the cavities. The time evolution of the atomic density in the presence of this light-scattering mechanism is described within a Lindblad master equation approach, which is numerically implemented using the Monte Carlo wave function technique. We find that an arbitrarily weak rate of photon emission leads to a breakdown of Anderson localization of the atoms.
We numerically study the expansion dynamics of ultracold atoms in a one-dimensional disordered potential in the presence of a weak position measurement of the atoms. We specifically consider this position measurement to be realized by a combination of an external laser and a periodic array of optical microcavities along a waveguide. The position information is acquired through the scattering of a near-resonant laser photon into a specific eigenmode of one of the cavities. The time evolution of the atomic density in the presence of this light-scattering mechanism is described within a Lindblad master equation approach, which is numerically implemented using the Monte Carlo wave function technique. We find that an arbitrarily weak rate of photon emission leads to a breakdown of Anderson localization of the atoms.
We propose to observe Anderson localization of ultracold atoms in the presence of a random potential made of atoms of another species or spin state and trapped at the nodes of an optical lattice, with a filling factor less than unity. Such systems enable a nearly perfect experimental control of the disorder, while the possibility of modeling the scattering potentials by a set of pointlike ones allows an exact theoretical analysis. This is illustrated by a detailed analysis of the one-dimensional case.
Abstract We study the elastic scattering time τ s of ultracold atoms propagating in optical disordered potentials in the strong scattering regime, going beyond the recent work of Richard et al (2019 Phys. Rev. Lett. 122 100403). There, we identified the crossover between the weak and the strong scattering regimes by comparing direct measurements and numerical simulations to the first order Born approximation. Here we focus specifically on the strong scattering regime, where the first order Born approximation is not valid anymore and the scattering time is strongly influenced by the nature of the disorder. To interpret our observations, we connect the scattering time τ s to the profiles of the spectral functions that we estimate using higher order Born perturbation theory or self-consistent Born approximation. The comparison reveals that self-consistent methods are well suited to describe τ s for Gaussian-distributed disorder, but fails for laser speckle disorder. For the latter, we show that the peculiar profiles of the spectral functions, as measured independently in Volchkov et al (2018 Phys. Rev. Lett. 120 060404), must be taken into account. Altogether our study characterizes the validity range of usual theoretical methods to predict the elastic scattering time of matter waves, which is essential for future close comparison between theory and experiments, for instance regarding the ongoing studies on Anderson localization.
Common belief, confirmed by existing experiments, is that arbitrarily weak disorder should lead to spatial localization of eigenmodes of scalar wave equations when wave propagation is two-dimensional (2D). We predict that contrary to this belief, a localization-delocalization transition can take place for light scattered by two-level atoms placed at random positions in the middle plane of a parallel-plate 2D waveguide fed by its fundamental transverse-magnetic (TM) mode (electric field polarized perpendicular to the waveguide and atomic planes). This transition, driven by near-field dipole-dipole interactions between atoms, occurs upon increasing the areal number density of atoms beyond some critical value. A finite-size scaling analysis of the transition yields an estimate of its critical exponent ν = 1.4 ± 0.2.
We revisit the problem of Anderson localization in a trapped Bose–Einstein condensate in 1D and 3D in a disordered potential, applying Quantum Monte Carlo technique because the disorder cannot be treated accurately in a perturbative way as even a small amount of disorder can produce dramatic changes in the physical properties of the system under investigation. Till date no unambiguous evidence of localization has been observed for matter waves in 3D. Matter waves made up of cold atoms are good candidates for such investigations. Simulations are performed for Rb gas in continuous space using canonical ensemble in the case of random and quasi-periodic potentials. To realize random and quasiperiodic potentials numerically we use speckle and bichromatic potentials, respectively. Owing to the high degree of control over the system parameters we specifically study the interplay of disorder and interaction in the system. A dilute Bose gas placed in a random environment falls into a fragmented localized state and the ergodicity (the repetitiveness of the wave function) is lost. An arbitrary Interaction can slowly overcome the effect of disorder and restore the ergodicity again. We observe that as the interaction strength increases, the wave functions become more and more delocalized. Since vanishing of Lyapunov exponent is only a necessary but not a sufficient condition for delocalization for probing the localization we calculate the mean square displacements as an alternative measure of localization. The path integral Monte Carlo technique in this paper numerically establishes the existing predictions of the scaling theory so far and paves a clear path for the further investigation of scaling theory to calculate more complicated properties like ‘critical exponents’ etc. in disordered quantum gases.
Anderson localization of particles -- the complete halt of wave transport through multiple scattering and phase coherence -- is a paradigmatic manifestation of quantum interference in disordered media. In three dimensions, the scaling theory predicts a quantum phase transition at a critical energy, the mobility edge, separating localized from diffusive states and underpinning metal-insulator transitions in electronic systems. Despite decades of experimental efforts, a direct observation of this emblematic transition for matter waves has remained elusive. Previous attempts with ultracold atoms were hindered by strong and uncontrolled energy broadening, resulting in indirect, sometimes inaccurate, and model-dependent estimates of the mobility edge. Here we implement a novel energy-resolved scheme to prepare atomic matter waves with a narrow energy distribution and track their expansion dynamics over long timescales. This allows for a direct observation of the three-dimensional Anderson transition in a laser-speckle disordered potential, and for a precise measurement of the mobility edge that is independent of any underlying theoretical modeling. Our measurements show excellent agreement with state-of-the-art numerical predictions over a wide range of disorder strengths, resolving long-standing discrepancies between prior experiments and theory. Beyond the three-dimensional Anderson transition, our approach opens new avenues for quantitative investigations of quantum critical phenomena in spatially disordered systems, including the roles of dimensionality, symmetry class, and interactions.
Bose-Einstein condensates (BECs) have proven to be remarkable systems with which to study some of the foundational models of condensed matter physics. The observation of a critical velocity for the breakdown of superfluidity in a BEC and the superfluid to Mott insulator transition observed in a BEC trapped by an optical lattice are but two examples of the, by now, dozens of exciting results in this field, which combines theoretical tools from condensed matter physics with state-of-the-art experimental techniques from ultra-cold atomic physics. However, any real condensed matter system has to contend with the effects of disorder, a phenomena notably absent in the inherently clean BEC systems. We have developed and implemented a way to add well characterized disorder in a controlled way to the otherwise clean BEC system using the light field from a laser speckle pattern. Using this system, we have investigated the effects of disorder or a single Gaussian defect, on the collective dipole motion of a BEC of 7Li in an optical trap. In addition, we perform transport experiments on a weakly interacting BEC expanding in a disordered one-dimensional atom wave-guide. We have observed that in such a system, the wave nature of matter can lead to spectacular and counterintuitive phenomena. Specifically, we verify that this system exhibits Anderson localization, a phenomena fundamentally resulting from the interference of multiply scattered matter waves. In such a state, the localized gas behaves as an insulator in a regime where it is classically expected to be conducting.\nWe also present results of experiments regarding a repulsive BEC scattering from a semi-permeable, single defect potential. We investigate the transport properties of such a system with special emphasis on the velocity and defect strength dependent dissipation of the collective dipole motion of the BEC. Finally, we present the results of our experiments on the scattering properties of bright matter wave solitons. We have observed fragmentation of the soliton in a disordered potential as well as both splitting and recombination of a soliton after interacting with a single repulsive defect potential.