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Journal of Physics B Atomic Molecular and Optical Physics

Self-bound droplets with uncorrelated disordered potentials

Karima Abbas, Abdelâali Boudjemâa

Published Feb 2, 2024• 2 citations
Publisher

Abstract

Abstract We investigate the effects of an external random δ -correlated potential on the bulk properties of self-bound droplets in three-dimensional binary Bose–Einstein condensates. The ground-state energy and the quantum fluctuation induced by disorder are computed utilizing the Bogoliubov theory. We provide a comprehensive stability phase-diagram for the resulting dirty droplets. At finite temperature, we calculate the free energy, and the thermal equilibrium density in terms of the disorder parameters. We show that the intriguing interplay of the thermal correction and the disorder may dissolve the droplet.

DOI
10.1088/1361-6455/ad2548

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Abstract We investigate the effects of an external random δ -correlated potential on the bulk properties of self-bound droplets in three-dimensional binary Bose–Einstein condensates. The ground-state energy and the quantum fluctuation induced by disorder are computed utilizing the Bogoliubov theory. We provide a comprehensive stability phase-diagram for the resulting dirty droplets. At finite temperature, we calculate the free energy, and the thermal equilibrium density in terms of the disorder parameters. We show that the intriguing interplay of the thermal correction and the disorder may dissolve the droplet.
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We investigate the effects of higher-order quantum fluctuations on the bulk properties of self-bound droplets in three-, two- and one-dimensional binary Bose mixtures using the Hartree–Fock–Bogoliubov theory. We calculate higher-order corrections to the equation of state of the droplet at both zero and finite temperatures. We show that our results for the ground-state energy are in a good agreement with recent quantum Monte Carlo simulations in any dimension. Our study extends to the finite temperature case where it is found that thermal fluctuations may destabilize the droplet state and eventually destroy it. In two dimensions, we reveal that the droplet occurs at temperatures well below the Berezinskii–Kosterlitz–Thouless transition temperature.
Abstract 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.
We systematically study the effects of higher-order quantum and thermal fluctuations on the stabilization of self-bound droplets in Bose mixtures employing the time-dependent Hartree-Fock-Bogoliubov theory. We calculate the ground-state energy, the droplet equilibrium density, the depletion and anomalous density of the droplets as well as the critical temperature as a function of the relevant parameters. Our findings are compared with previous analytical predictions and diffusion Monte Carlo simulations. We employ our theory together with the local density approximation for quantum and thermal fluctuations to obtain an extended finite-temperature Gross-Pitaevskii equation. The density profiles and breathing modes of the droplet are deeply examined in terms of the interaction strength and the temperature by numerically solving the developed generalized Gross-Pitaevskii equation.
We discuss the bulk and surface properties of ultradilute self-bound quantum droplets in a heteronuclear Bose-Bose mixture in the presence of higher-order quantum and thermal fluctuations. Within the realm of the Hartree-Fock-Bogoliubov theory, we calculate beyond the Lee-Huang-Yang corrections to the ground-state energy, the droplet equilibrium density, the surface tension, and the critical number of particles. Our predictions are compared with recent diffusion Monte Carlo simulation and density functional theory method and excellent agreement is found. We address in addition the effects of temperature on the formation and on the robustness of the heteronuclear self-bound mixtures.
We systematically investigate the properties of three-dimensional dipolar binary Bose mixture at low temperatures. A set of coupled self-consistent equations of motion are derived for the two condensates. In the homogeneous case, useful analytical formulas for the condensate depletion, the anomalous density, the ground-state energy, and the equation of state are obtained. The theory is extended to the inhomogeneous case and the importance of the inhomogeneity is highlighted. Our results open up an avenue for studying dipolar mixture droplets. Impacts of the dipole-dipole interaction on the stability, density profiles, and the size of the self-bound droplet are deeply discussed. The finite-temperature behavior of such a state is also examined.