Speckle Potentials Research Articles

Anderson localization of elementary excitations in disordered binary Bose mixtures: Effects of the Lee-Huang-Yang quantum and thermal corrections

We investigate analytically and numerically the Anderson localization of quasiparticles in binary Bose mixtures in the presence of the Lee-Huang-Yang quantum and thermal corrections subjected to correlated disordered potentials. We calculate the density profiles, the Bogoliubov quasiparticle modes, and the localization length in both the mixture and droplet phases. We show that for one-dimensional speckle potentials, the peculiar interplay of disorder and the Lee-Huang-Yang fluctuations may enhance localization in one component while inducing delocalization in the other. Our results reveal also that thermal fluctuations lead to the emergence of two and multiple localization maxima. In the droplet state, our findings indicate that the Anderson localization of quasiparticles is weak in the flat-top region since its excitation modes are restricted to those below the particle-emission threshold. Published by the American Physical Society 2024

Anderson localization and quenched induced dynamics of spin orbit coupled Bose–Einstein condensate in a random potential

We consider the localization and dynamical properties of a one dimensional spin orbit coupled Bose–Einstein condensate trapped by a disordered speckle potential. We numerically solve coupled Gross–Pitaevskii equation to obtain ground sate solutions. The effects of spin–orbit coupling and detuning parameter on localization are investigated. It is found that the increase of spin–orbit coupling delocalizes the condensate while the increase of detuning favors localization. After achieving the numerical ground state solutions, we examine the quench induced dynamics of the condensate by the complete cessation of the spin–orbit coupling. We show that at parameters where the ground state is not localized, the dynamics of the system is chaotic.

Self-bound liquid droplets in one-dimensional optical speckle potentials

We present a comprehensive description of the equilibrium properties of self-bound liquid droplets in one-dimensional optical speckle potentials at both zero and finite temperatures. Using the Bogoliubov theory we calculate analytically the equation of state, fluctuations induced by disorder, and the equilibrium density. In particular, we show that the peculiar competition between the speckle disordered, the interactions and the Lee-Huang-Yang quantum fluctuations may strongly affect the stability and the formation of the self-bound droplet. We address also the static and dynamical properties of such a disordered droplet using the generalized disorder-dependent Gross-Pitaevskii equation. Notably, impacts of a weak speckle potential are treated numerically for both small droplets of an approximately Gaussian shape and large droplets with a flat-top plateau.

Localization landscape for interacting Bose gases in one-dimensional speckle potentials

While the properties and the shape of the ground state of a gas of ultracold bosons are well understood in harmonic potentials, they remain for a large part unknown in the case of random potentials. Here we use localization-landscape (LL) theory to study the properties of the solutions to the Gross-Pitaevskii equation (GPE) in one-dimensional (1D) speckle potentials. In the cases of attractive interactions, we find that the LL allows one to predict the position of the localization center of the ground state (GS) of the GPE. For weakly repulsive interactions, we point out that the GS of the quasi-1D GPE can be understood as a superposition of a finite number of single-particle states, which can be computed by exploiting the LL. For intermediate repulsive interactions, we introduce a Thomas-Fermi-like approach for the GS which holds in the smoothing regime, well beyond the usual approximation involving the original potential. Moreover, we show that, in the Lifshitz glass regime, the particle density and the chemical potential can be well estimated by the LL. Our approach can be applied to any positive-valued random potential endowed with finite-range correlations and can be generalized to higher-dimensional systems.

Quantum localization corrections from the Bethe–Salpeter equation

We investigate coherent matter wave transport in isotropic 3D speckle potentials by using the Bethe–Salpeter equation and the self-consistent theory of localization. This model constitutes an efficient tool to properly evaluate corrections to Boltzmann diffusion by taking into consideration quantum interference terms between the multiple-scattering paths. We calculate analytically and numerically the static current density, the density of states, the dipolar contribution and the reduced diffusion coefficient. Our results reveal that quantum corrections to diffusive transport, known as weak localization may not only lead to shift the above quantities but affect also the position of the mobility edge.

Wave localization in number-theoretic landscapes

We investigate the localization of waves in aperiodic structures that manifest the characteristic multiscale complexity of certain arithmetic functions with a central role in number theory. In particular, we study the eigenspectra and wave localization properties of tight-binding Schr\"{o}dinger equation models with on-site potentials distributed according to the Liouville function $\lambda(n)$, the M\"{o}bius function $\mu(n)$, and the Legendre sequence of quadratic residues modulo a prime (QRs). We employ Multifractal Detrended Fluctuation Analysis (MDFA) and establish the multifractal scaling properties of the energy spectra in these systems. Moreover, by systematically analyzing the spatial eigenmodes and their level spacing distributions, we show the absence of level repulsion with broadband localization across the entire energy spectra. Our study introduces deterministic aperiodic systems whose eigenmodes are all strongly localized in realistic finite one-dimensional systems and provides opportunities for novel quantum and classical devices of particular importance to cold-atom experiments in engineered speckle potentials and enhanced light-matter interactions.

Spectral functions and localization-landscape theory in speckle potentials

Spectral function is a key tool for understanding the behavior of Bose-Einstein condensates of cold atoms in random potentials generated by a laser speckle. In this paper we introduce a method for computing the spectral functions in disordered potentials. Using a combination of the Wigner-Weyl approach with the localization-landscape theory, we build an approximation for the Wigner distributions of the eigenstates in the phase space and show its accuracy in all regimes, from the deep quantum regime to the intermediate and semiclassical. Based on this approximation, we devise a method to compute the spectral functions using only the landscape-based effective potential. The paper demonstrates the efficiency of the proposed approach for disordered potentials with various statistical properties without requiring any adjustable parameters.

Anderson localization of a spin–orbit coupled Bose–Einstein condensate in disorder potential

We present numerical results of a one-dimensional spin–orbit coupled Bose–Einstein condensate expanding in a speckle disorder potential by employing the Gross–Pitaevskii equation. Localization properties of a spin–orbit coupled Bose–Einstein condensate in zero-momentum phase, magnetic phase and stripe phase are studied. It is found that the localizing behavior in the zero-momentum phase is similar to the normal Bose–Einstein condensate. Moreover, in both magnetic phase and stripe phase, the localization length changes non-monotonically as the fitting interval increases. In magnetic phases, the Bose–Einstein condensate will experience spin relaxation in disorder potential.

Quantum Reservoir Computing for Speckle Disorder Potentials

Quantum reservoir computing is a machine learning approach designed to exploit the dynamics of quantum systems with memory to process information. As an advantage, it presents the possibility to benefit from the quantum resources provided by the reservoir combined with a simple and fast training strategy. In this work, this technique is introduced with a quantum reservoir of spins and it is applied to find the ground state energy of an additional quantum system. The quantum reservoir computer is trained with a linear model to predict the lowest energy of a particle in the presence of different speckle disorder potentials. The performance of the task is analyzed with a focus on the observable quantities extracted from the reservoir and it is shown to be enhanced when two-qubit correlations are employed.

Dynamic evolution of expanding Bose–Einstein condensates in the presence of a three-dimensional random optical speckle potential

We study the diffusion of an expanding Bose–Einstein condensate released from a harmonic trap in a three-dimensional speckle disorder potential. To this end, we use the first Born approximation and examine the density profiles at short and long times. Analytical results are presented in different regimes. The evolution of the density profiles in space and time is deeply examined. We find that at long times and for a fixed disorder strength, the profile of the average atomic density decreases in power law. The time evolution of the typical size of the condensate is explored numerically.

Observing the loss and revival of long-range phase coherence through disorder quenches

Relaxation of quantum systems is a central problem in nonequilibrium physics. In contrast to classical systems, the underlying quantum dynamics results not only from atomic interactions but also from the long-range coherence of the many-body wave function. Experimentally, nonequilibrium states of quantum fluids are usually created using moving objects or laser potentials, directly perturbing and detecting the system's density. However, the fate of long-range phase coherence for hydrodynamic motion of disordered quantum systems is less explored, especially in three dimensions. Here, we unravel how the density and phase coherence of a Bose-Einstein condensate of 6Li2 molecules respond upon quenching on or off an optical speckle potential. We find that, as the disorder is switched on, long-range phase coherence breaks down one order of magnitude faster than the density of the quantum gas responds. After removing it, the system needs two orders of magnitude longer times to reestablish quantum coherence, compared to the density response. We compare our results with numerical simulations of the Gross-Pitaevskii equation on large three-dimensional grids, finding an overall good agreement. Our results shed light on the importance of long-range coherence and possibly long-lived phase excitations for the relaxation of nonequilibrium quantum many-body systems.

One- and two-particle problem with correlated disorder potential

Motivated by the recent experimental and theoretical progresses in the exploration of the effect of disorder in interacting system, we examine the effect of two types of correlated disorder, the quasi-periodic potential and speckle disorder potential, on one- and two-particle problem with exact diagonalization (ED) method. We give the phase diagram for single particle in the presence of quasi-periodic potential and also analyse the effect of strong interaction on the phase diagram for ground state in two dimensions. For the speckle disorder potential case, we examine both the effect of correlation length and disorder strength on single particle ground state energy and two-particle binding energy. The transport property for different interaction strength under speckle disorder potential is also calculated and discussed at last.

Many-body localization in a one-dimensional optical lattice with speckle disorder

The many-body localization transition for Heisenberg spin chain with a speckle disorder is studied. Such a model is equivalent to a system of spinless fermions in an optical lattice with an additional speckle field. Our numerical results show that the many-body localization transition in speckle disorder falls within the same universality class as the transition in an uncorrelated random disorder, in contrast to the quasiperiodic potential typically studied in experiments. This hints at possibilities of experimental studies of the role of rare Griffiths regions and of the interplay of ergodic and localized grains at the many-body localization transition. Moreover, the speckle potential allows one to study the role of correlations in disorder on the transition. We study both spectral and dynamical properties of the system focusing on observables that are sensitive to the disorder type and its correlations. In particular, distributions of local imbalance at long times provide an experimentally available tool that reveals the presence of small ergodic grains even deep in the many-body localized phase in a correlated speckle disorder.

Enhanced transport of spin-orbit-coupled Bose gases in disordered potentials.

Anderson localization is a single-particle localization phenomena in disordered media that is accompanied by an absence of diffusion. Spin-orbit coupling (SOC) describes an interaction between a particle's spin and its momentum that directly affects its energy dispersion, for example, creating dispersion relations with gaps and multiple local minima. We show theoretically that combining one-dimensional spin-orbit coupling with a transverse Zeeman field suppresses the effects of disorder, thereby increasing the localization length and conductivity. This increase results from a suppression of backscattering between states in the gap of the SOC dispersion relation. Here, we focus specifically on the interplay of disorder from an optical speckle potential and SOC generated by two-photon Raman processes in quasi-one-dimensional Bose-Einstein condensates. We first describe backscattering by using a Fermi golden rule approach, and then numerically confirm this picture by solving the time-dependent one-dimensional Gross-Pitaevskii equation for a weakly interacting Bose-Einstein condensate with SOC and disorder. We find that on the tens of millisecond timescale of typical cold atom experiments moving in harmonic traps, initial states with momentum in the zero-momentum SOC gap evolve with negligible backscattering, while without SOC these same states rapidly localize.

Cloud shape of a molecular Bose–Einstein condensate in a disordered trap: a case study of the dirty boson problem

We investigate, both experimentally and theoretically, the static geometric properties of a harmonically trapped Bose–Einstein condensate of 6Li2 molecules in laser speckle potentials. Experimentally, we measure the in situ column density profiles and the corresponding transverse cloud widths over many laser speckle realizations. We compare the measured widths with a theory that is non-perturbative with respect to the disorder and includes quantum fluctuations. Importantly, for small disorder strengths we find quantitative agreement with the perturbative approach of Huang and Meng, which is based on Bogoliubov theory. For strong disorder our theory perfectly reproduces the geometric mean of the measured transverse widths. However, we also observe a systematic deviation of the individual measured widths from the theoretically predicted ones. In fact, the measured cloud aspect ratio monotonously decreases with increasing disorder strength, while the theory yields a constant ratio. We attribute this discrepancy to the utilized local density approximation, whose possible failure for strong disorder suggests a potential future improvement.

Full distribution of the superfluid fraction and extreme value statistics in a one-dimensional disordered Bose gas

The full statistical distribution of the superfluid fraction characterizing one-dimensional Bose gases in random potentials is discussed. Rare configurations with extreme fluctuations of the disorder potential can fragment the condensate and reduce the superfluid fraction to zero. The resulting bimodal probability distribution for the superfluid fraction is calculated numerically in the quasi-1D mean-field regime of ultracold atoms in laser speckle potentials. Using extreme-value statistics, an analytical scaling of the zero-superfluid probability as function of disorder strength, disorder correlation length and system size is presented. It is argued that similar results can be expected for point-like impurities, and that these findings are in reach for present-day experiments.

Anderson Localization for Very Strong Speckle Disorder

AbstractWe evaluate the localization length of the wave (or Schrödinger) equation in the presence of a disordered speckle potential. This is relevant for experiments on cold atoms in optical speckle potentials. We focus on the limit of large disorder, where the Born approximation breaks down and derive an expression valid in the “quasi‐metallic” phase at large disorder. This phase becomes strongly localized and the effective mobility edge disappears.

Localization and hybridization across an effective mobility edge in periodically driven speckle potentials

Disorder in a 1D quantum lattice induces Anderson localization of the eigenstates and blocks transport through the lattice. A time-periodic drive, when applied to a lattice with uncorrelated disorder, typically increases (as compared to the stationary states) localization length of the appearing Floquet states. We go beyond the uncorrelated disorder limit and address the experimentally relevant case of speckle potentials in which spatial correlations in on-site disorder are present. These correlations are responsible for the creation of an effective mobility edge in the spectrum of the stationary lattice Hamiltonian. We find that a slow driving leads to resonant hybridization of the Floquet states across the edge; i.e., it increases the width of the states in the localized band and decreases it for the states in the quasi-extended band. By increasing the drive amplitude, we observe homogenization of the bands so that finally all Floquet states become weakly localized and sparse.

Anderson Localization of Ultracold Atoms: Where is the Mobility Edge?

Recent experiments in noninteracting ultracold atoms in three-dimensional speckle potentials have yielded conflicting results regarding the so-called mobility edge, i.e., the energy threshold separating Anderson localized from diffusive states. At the same time, there are theoretical indications that most experimental data overestimate this critical energy, sometimes by a large amount. Using extensive numerical simulations, we show that the effect of anisotropy in the spatial correlations of realistic disorder configurations alone is not sufficient to explain the experimental data. In particular, we find that the mobility edge obeys a universal scaling behavior, independently of the speckle geometry.

Anderson Transition of Cold Atoms with Synthetic Spin-Orbit Coupling in Two-Dimensional Speckle Potentials.

We investigate the metal-insulator transition occurring in two-dimensional (2D) systems of noninteracting atoms in the presence of artificial spin-orbit interactions and a spatially correlated disorder generated by laser speckles. Based on a high order discretization scheme, we calculate the precise position of the mobility edge and verify that the transition belongs to the symplectic universality class. We show that the mobility edge depends strongly on the mixing angle between Rashba and Dresselhaus spin-orbit couplings. For equal couplings a non-power-law divergence is found, signaling the crossing to the orthogonal class, where such a 2D transition is forbidden.