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arXiv:2410.17884

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

Zohra Mehri, Abdelâali Boudjemâa

Published Oct 23, 2024• 0 citations
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Abstract

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 quasiparticles 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 uncover 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.

DOI
10.48550/arxiv.2410.17884

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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 quasiparticles 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 uncover 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.
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
Abstract The static and dynamic properties of self-bound quantum droplets in a one-dimensional Bose-Bose mixture are discussed in the spirit of the Hartree–Fock-Bogoliubov theory. This latter enables us to provide beyond the Lee-Huang-Yang (LHY) quantum corrections to the equation of state at both zero and finite temperatures. In the uniform case our results for the ground-state energy and the critical temperature are confirmed through comparison with Quantum Monte-Carlo simulation and with available theoretical results. The density profiles are supported by numerical simulations of the generalized Gross-Pitaevskii equation which selfconsistently includes higher-order terms originating from the normal and anomalous fluctuations under the local density approximation. We show that the density exhibits a dip near its center in the flat-top plateau region for large interspecies interactions. We exemplify the impact of the beyond LHY corrections on the spatiotemporal evolution of the self-bound droplet in the presence of excitation induced by periodic density modulation. It is found that higher-order corrections may lead to the formation of a train of small droplets. We then extend our study for the case of inhomogeneous droplets in quasi one-dimensional Bose mixtures.
We study the Anderson localization of Bogoliubov quasiparticles (elementary many-body excitations) in a weakly interacting Bose gas of chemical potential $\ensuremath{\mu}$ subjected to a disordered potential VVV. We introduce a general mapping (valid for weak inhomogeneous potentials in any dimension) of the Bogoliubov--de Gennes equations onto a single-particle Schr\"odinger-like equation with an effective potential. For disordered potentials, the Schr\"odinger-like equation accounts for the scattering and localization properties of the Bogoliubov quasiparticles. We derive analytically the localization lengths for correlated disordered potentials in the one-dimensional geometry. Our approach relies on a perturbative expansion in $V/\ensuremath{\mu}$, which we develop up to third order, and we discuss the impact of the various perturbation orders. Our predictions are shown to be in very good agreement with direct numerical calculations. We identify different localization regimes: For low energy, the effective disordered potential exhibits a strong screening by the quasicondensate density background, and localization is suppressed. For high-energy excitations, the effective disordered potential reduces to the bare disordered potential, and the localization properties of quasiparticles are the same as for free particles. The maximum of localization is found at intermediate energy when the quasicondensate healing length is of the order of the disorder correlation length. Possible extensions of our work to higher dimensions are also discussed.
We study the properties of self-bound liquid droplets of three-dimensional Bose mixtures in a weak random potential with Gaussian correlation function at both zero and finite temperatures. Using the Bogoliubov theory, we derive useful formulas for the ground-state energy, the equilibrium density, the depletion, and the anomalous density of the droplet. The quantum fluctuation induced by the disorder known as the glassy fraction is also systematically computed. At finite temperature, we calculate the free energy, the thermal equilibrium density, and the critical temperature in terms of the disorder parameters. We show that when the strength and the correlation length of the disorder potential exceed a certain critical value, the droplet evaporates and is eventually entirely destroyed. We calculate the density profiles of this exotic state by means of numerical simulations of the corresponding generalized disorder Gross-Pitaevskii equation. Our predictions reveal that as the strength of the disorder gets larger, the atomic density varies rapidly in the plateau region. We point out in addition that the peculiar interplay of the disorder and the repulsive Lee-Huang-Yang corrections play a pivotal role in the collective modes of the self-bound droplet.
We theoretically investigate the finite-temperature structure and collective excitations of a self-bound ultradilute Bose droplet in a flat space realized in a binary Bose mixture with attractive inter-species interactions on the verge of mean-field collapse. As the droplet formation relies critically on the repulsive force provided by Lee–Huang–Yang quantum fluctuations, which can be easily compensated by thermal fluctuations, we find a significant temperature effect in the density distribution and collective excitation spectrum of the Bose droplet. A finite-temperature phase diagram as a function of the number of particles is determined. We show that the critical number of particles at the droplet-to-gas transition increases dramatically with increasing temperature. Towards the bulk threshold temperature for thermally destabilizing an infinitely large droplet, we find that the excitation-forbidden, self-evaporation region in the excitation spectrum, predicted earlier by Petrov using a zero-temperature theory, shrinks and eventually disappears. All the collective excitations, including both surface modes and compressional bulk modes, become softened at the droplet-to-gas transition. The predicted temperature effects of a self-bound Bose droplet in this work could be difficult to measure experimentally due to the lack of efficient thermometry at low temperatures. However, these effects may already present in the current cold-atom experiments.
We study liquid quantum droplets in a mixture of two-component Bose-Einstein condensates under variable confinement introduced along one or two spatial dimensions. Although the atom-atom scattering has a three-dimensional character, discreteness of the available modes in the reduced dimension(s) strongly influences the zero-point energy, which for a weakly interacting three-dimensional system is given by the Lee-Huang-Yang term. Here, we generalize the result of Lee, Huang, and Yang and calculate the higher order corrections to the mean-field energy for a single component Bose-Einstein condensate under condition of a tight confinement in one or two spatial directions. We apply our results to the two-component mixture of bosonic species under conditions favorable for the creation of quantum liquid droplets, which constitute a perfect playground for studies of the beyond mean-field effects. Our findings allow one to analyze the properties of quantum droplets at the dimensional crossover and provide demanding conditions for accessing quasilow dimensions. They also pave a way for experimental exploration of this state of matter in reduced dimensions.