Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2010.14729 · Chinese Physics B

Ultradilute self-bound quantum droplets in Bose–Bose mixtures at finite temperature*

Jia Wang, Xia-Ji Liu, Hui Hu

Published Dec 12, 2020• 14 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1674-1056/abd2ad

Related papers

Thermal destabilization of self-bound ultradilute quantum droplets

Jia Wang, Hui Hu, Xia-Ji Liu

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.

arXiv:2007.00888•New Journal of Physics•Oct 1, 2020•26 citations

Quantum liquid droplets in Bose mixtures with weak disorder

Karima Abbas, Abdelâali Boudjemâa

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.

arXiv:2303.04760•Physical Review A•Mar 7, 2023•13 citations

Consistent Theory of Self-Bound Quantum Droplets with Bosonic Pairing

Hui Hu, Xia-Ji Liu

We revisit the Bogoliubov theory of quantum droplets proposed by Petrov [Phys. Rev. Lett. 115, 155302 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.155302] for an ultracold Bose-Bose mixture, where the mean-field collapse is stabilized by the Lee-Huang-Yang quantum fluctuations. We show that a loophole in Petrov's theory, i.e., the ignorance of the softening complex Bogoliubov spectrum, can be naturally removed by the introduction of bosonic pairing. The pairing leads to weaker mean-field attractions, and also a stronger Lee-Huang-Yang term in the case of unequal intraspecies interactions. As a result, the equilibrium density for the formation of self-bound droplets significantly decreases in the deep droplet regime, in agreement with a recent observation from diffusion Monte Carlo simulations. Our construction of a consistent Bogoliubov theory paves the way to understand the puzzling low critical number of small quantum droplets observed in the experiment [C. Cabrera et al., Science 359, 301 (2018)SCIEAS0036-807510.1126/science.aao5686].

arXiv:2005.08581•Physical Review Letters•Nov 2, 2020•75 citations

Self-bound ultradilute Bose mixtures within local density approximation

Francesco Ancilotto, M. Barranco, M. Guilleumas +1 more

We have investigated self-bound ultradilute bosonic binary mixtures at zero temperature within density functional theory using a local density approximation. We provide the explicit expression of the Lee-Huang-Yang correction in the general case of heteronuclear mixtures, and investigate the general thermodynamic conditions which lead to the formation of self-bound systems. We have determined the conditions for stability against the evaporation of one component, as well as the mechanical and diffusive spinodal lines. We have also calculated the surface tension of the self-bound state as a function of the interspecies interaction strength. We find that relatively modest variations of the latter result in order-of-magnitude changes in the calculated surface tension. We suggest experimental realizations which might display the metastability and phase separation of the mixture when entering regions of the phase diagram characterized by negative pressures. Finally, we show that these droplets may sustain stable vortex and vortex pairs.

arXiv:1808.09197•Physical Review A•Nov 21, 2018•60 citations

Effects of higher-order fluctuations on the bulk and surface properties of quantum droplets in a heteronuclear Bose-Bose mixture

Abdelâali Boudjemâa, Nadia Guebli

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.

Physical Review A•Jul 10, 2023•2 citations

Lee-Huang-Yang droplet

Dmitry S. Petrov

According to the mean-field theory a condensed Bose-Bose mixture collapses when the interspecies attraction becomes stronger than the geometrical average of the intraspecies repulsions, $g_{12}^2>g_{11} g_{22}$. We show that instead of collapsing such a mixture gets into a dilute liquid-like droplet state stabilized by quantum fluctuations thus providing a direct manifestation of beyond mean-field effects. We study various properties of the droplet and find, in particular, that in a wide range of parameters its excitation spectrum lies entirely above the particle emission threshold. The droplet thus automatically evaporates itself to zero temperature, the property potentially interesting by itself and from the viewpoint of sympathetic cooling of other systems.

•Jun 28, 2015•0 citations
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.
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 revisit the Bogoliubov theory of quantum droplets proposed by Petrov [Phys. Rev. Lett. 115, 155302 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.155302] for an ultracold Bose-Bose mixture, where the mean-field collapse is stabilized by the Lee-Huang-Yang quantum fluctuations. We show that a loophole in Petrov's theory, i.e., the ignorance of the softening complex Bogoliubov spectrum, can be naturally removed by the introduction of bosonic pairing. The pairing leads to weaker mean-field attractions, and also a stronger Lee-Huang-Yang term in the case of unequal intraspecies interactions. As a result, the equilibrium density for the formation of self-bound droplets significantly decreases in the deep droplet regime, in agreement with a recent observation from diffusion Monte Carlo simulations. Our construction of a consistent Bogoliubov theory paves the way to understand the puzzling low critical number of small quantum droplets observed in the experiment [C. Cabrera et al., Science 359, 301 (2018)SCIEAS0036-807510.1126/science.aao5686].
We have investigated self-bound ultradilute bosonic binary mixtures at zero temperature within density functional theory using a local density approximation. We provide the explicit expression of the Lee-Huang-Yang correction in the general case of heteronuclear mixtures, and investigate the general thermodynamic conditions which lead to the formation of self-bound systems. We have determined the conditions for stability against the evaporation of one component, as well as the mechanical and diffusive spinodal lines. We have also calculated the surface tension of the self-bound state as a function of the interspecies interaction strength. We find that relatively modest variations of the latter result in order-of-magnitude changes in the calculated surface tension. We suggest experimental realizations which might display the metastability and phase separation of the mixture when entering regions of the phase diagram characterized by negative pressures. Finally, we show that these droplets may sustain stable vortex and vortex pairs.
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.
According to the mean-field theory a condensed Bose-Bose mixture collapses when the interspecies attraction becomes stronger than the geometrical average of the intraspecies repulsions, g122>g11g22g_{12}^2>g_{11} g_{22}g122​>g11​g22​. We show that instead of collapsing such a mixture gets into a dilute liquid-like droplet state stabilized by quantum fluctuations thus providing a direct manifestation of beyond mean-field effects. We study various properties of the droplet and find, in particular, that in a wide range of parameters its excitation spectrum lies entirely above the particle emission threshold. The droplet thus automatically evaporates itself to zero temperature, the property potentially interesting by itself and from the viewpoint of sympathetic cooling of other systems.