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Atoms

Ultradilute Quantum Droplets in the Presence of Higher-Order Quantum Fluctuations

Abdelâali Boudjemâa, Karima Abbas, Nadia Guebli

Published Jun 17, 2022• 6 citations
Publisher

Abstract

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.

DOI
10.3390/atoms10020064

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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.
We study the equilibrium properties of self-bound droplets in two-dimensional Bose mixtures employing the time-dependent Hartree-Fock-Bogoliubov theory. This theory allows one to understand both the many-body and temperature effects beyond the Lee-Huang-Yang description. We calculate higher-order corrections to the excitations, the sound velocity, and the energy of the droplet. Our results for the ground-state energy are compared with the diffusion Monte Carlo data and good agreement is found. The behavior of the depletion and anomalous density of the droplet is also discussed. At finite temperature, we show that the droplet emerges at temperatures well below the Berezinskii-Kosterlitz-Thouless transition temperature. The critical temperature strongly depends on the interspecies interactions. Our study is extended to the finite size droplet by numerically solving the generalized finite-temperature Gross-Pitaevskii equation which is obtained self-consistently from our formalism in the framework of the local density approximation.
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 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.
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 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.
Abstract We theoretically investigate the temperature effect in a Bose–Bose mixture with attractive inter-species interactions, in the regime where a self-bound ultradilute quantum droplet forms due to the subtle balance between the attractive mean-field force and the repulsive force provided by Lee–Huang–Yang quantum fluctuations. We find that in contrast to quantum fluctuations, thermal fluctuations destabilize the droplet state and completely destroy it above a threshold temperature. We show that the threshold temperature is determined by the intra-species interaction energy. For a three-dimensional Bose–Bose mixture, the threshold temperature is less than one-tenth of the Bose–Einstein condensation temperature under the typical experimental conditions. With increasing temperature, the droplet’s equilibrium density gradually decreases and can be reduced by several tens of percent upon reaching the threshold temperature. We also consider a one-dimensional quantum droplet and find a similar destabilization effect due to thermal fluctuations. The threshold temperature in one dimension is roughly set by the binding energy of the inter-species dimer. The pronounced thermal instability of a self-bound quantum droplet predicted in our work could be examined in future experiments, by measuring the temperature dependence of its central density and observing its sudden disappearance at the threshold temperature.