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:2005.10047 · SciPost Physics

Beyond Lee-Huang-Yang description of self-bound Bose mixtures

Miki Ota, G. E. Astrakharchik

Published Aug 18, 2020• 72 citations
arXivHTMLPDF

Abstract

We investigate the properties of self-bound ultradilute Bose-Bose mixtures, beyond the Lee-Huang-Yang description. Our approach is based on the determination of the beyond mean-field corrections to the phonon modes of the mixture in a self-consistent way and calculation of the associated equation of state. The newly obtained ground state energies show excellent agreement with recent quantum Monte Carlo calculations, providing a simple and accurate description of the self-bound mixtures with contact type interaction. We further show numerical results for the equilibrium properties of the finite size droplet, by adjusting the Gross-Pitaevskii equation. Our analysis is extended to the one-dimensional mixtures where an excellent agreement with quantum Monte Carlo predictions is found for the equilibrium densities. Finally, we discuss the effects of temperature on the stability of the liquid phase.

DOI
10.21468/scipostphys.9.2.020

Related papers

Quantum droplets in one-dimensional Bose-Bose mixtures: beyond the Lee-Huang-Yang description

Abdelâali Boudjemâa, Karima Abbas

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.

New Journal of Physics•Sep 1, 2023•10 citations

Many-body and temperature effects in two-dimensional quantum droplets in Bose–Bose mixtures

Abdelâali Boudjemâa

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.

arXiv:2111.04025•Scientific Reports•Nov 5, 2021•23 citations

Universality in ultradilute liquid Bose-Bose mixtures

Viktor Cikojević, Leandra Vranješ Markić, G. E. Astrakharchik +1 more

We have studied dilute Bose-Bose mixtures of atoms with attractive interspecies and repulsive intraspecies interactions using quantum Monte Carlo methods at $T=0$. Using a number of models for interactions, we determine the range of validity of the universal equation of state of the symmetric liquid mixture as a function of two parameters: the $s$-wave scattering length and the effective range of the interaction potential. It is shown that the Lee-Huang-Yang correction is sufficient only for extremely dilute liquids with the additional restriction that the range of the potential is small enough. Based on the quantum Monte Carlo equation of state we develop a density functional which goes beyond the Lee-Huang-Yang term and use it together with the local density approximation to determine density profiles of realistic self-bound drops.

arXiv:1811.04436•Physical Review A•Feb 13, 2019•81 citations

Quantum droplets and bright solitons in mixtures of Bose-Einstein condensates

Elena Poli

The ultracold and ultradilute bosonic heteronuclear mixture (41K - 87Rb) of Bose-Einstein condensates with tunable interspecies interaction at zero temperature is studied in the self-bound regime, using numerical simulations based on Density Functional Theory within the Local Density Approximation. In particular, the beyond mean-field effects embodied in the Lee-Huang-Yang energy contribution are explicitly included in the total energy functional. The thermodynamic properties of the homogeneous system are investigated to set the stability conditions of the self-bound droplet. The surface properties are discussed with (i) a variational approach, (ii) a numerical method and (iii) by solving the two coupled Gross-Pitaevskii equations associated to the two components of the mixture. The validity of the liquid-drop model is verified by computing the total ground state energy for systems with a different number of particles and, after the confinement in a quasi-1D configuration by means of an optical waveguide, we also discuss the transition between quantum droplets and bright solitons, two localized states of different nature.

•Sep 1, 2020•0 citations

Ultradilute quasi-two-dimensional Bose-Bose liquid mixtures

Leandra Vranješ Markić, Ivan Poparić, Krešimir Dželalija +2 more

We study ultradilute $^{39}$K Bose-Bose bulk mixtures and droplets in an external harmonic potential that confines them in one spatial direction towards the two-dimensional (2D) limit. Equations of state for several confinements are obtained with quantum Monte Carlo (QMC) at $T=0$, using interaction potentials that include information on the $s$-wave scattering length $a$ and the effective range $r_{\rm eff}$. Performing the calculations using two different interaction potential models we have determined the range of confinements for which equations of state are universal in terms of $a$ and $r_{\rm eff}$. Based on the QMC equation of state, we develop a 2D QMC density functional for each confinement strength and use it together with the local density approximation to determine properties of the self-bound drops. For moderate squeezing, energies and droplet profiles obtained using the 2D QMC functional agree well with those obtained using 3D functionals, while offering a substantial reduction in computational cost, and a consistent approach in crossover to 2D. Noticeably, our results approach 2D mean-field (MF) + Lee-Huang-Yang (LHY) predictions only for the most strongly confined systems for which universality in terms of $a$ and $r_{\rm eff}$ is observed. This implies a very narrow range of confinements for which 2D LHY functionals are applicable, which has important consequences for the study of vortices.

arXiv:2607.25558•Jul 28, 2026•0 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
We investigate the properties of self-bound ultradilute Bose-Bose mixtures, beyond the Lee-Huang-Yang description. Our approach is based on the determination of the beyond mean-field corrections to the phonon modes of the mixture in a self-consistent way and calculation of the associated equation of state. The newly obtained ground state energies show excellent agreement with recent quantum Monte Carlo calculations, providing a simple and accurate description of the self-bound mixtures with contact type interaction. We further show numerical results for the equilibrium properties of the finite size droplet, by adjusting the Gross-Pitaevskii equation. Our analysis is extended to the one-dimensional mixtures where an excellent agreement with quantum Monte Carlo predictions is found for the equilibrium densities. Finally, we discuss the effects of temperature on the stability of the liquid phase.
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 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 have studied dilute Bose-Bose mixtures of atoms with attractive interspecies and repulsive intraspecies interactions using quantum Monte Carlo methods at T=0T=0T=0. Using a number of models for interactions, we determine the range of validity of the universal equation of state of the symmetric liquid mixture as a function of two parameters: the sss-wave scattering length and the effective range of the interaction potential. It is shown that the Lee-Huang-Yang correction is sufficient only for extremely dilute liquids with the additional restriction that the range of the potential is small enough. Based on the quantum Monte Carlo equation of state we develop a density functional which goes beyond the Lee-Huang-Yang term and use it together with the local density approximation to determine density profiles of realistic self-bound drops.
The ultracold and ultradilute bosonic heteronuclear mixture (41K - 87Rb) of Bose-Einstein condensates with tunable interspecies interaction at zero temperature is studied in the self-bound regime, using numerical simulations based on Density Functional Theory within the Local Density Approximation. In particular, the beyond mean-field effects embodied in the Lee-Huang-Yang energy contribution are explicitly included in the total energy functional. The thermodynamic properties of the homogeneous system are investigated to set the stability conditions of the self-bound droplet. The surface properties are discussed with (i) a variational approach, (ii) a numerical method and (iii) by solving the two coupled Gross-Pitaevskii equations associated to the two components of the mixture. The validity of the liquid-drop model is verified by computing the total ground state energy for systems with a different number of particles and, after the confinement in a quasi-1D configuration by means of an optical waveguide, we also discuss the transition between quantum droplets and bright solitons, two localized states of different nature.
We study ultradilute 39^{39}39K Bose-Bose bulk mixtures and droplets in an external harmonic potential that confines them in one spatial direction towards the two-dimensional (2D) limit. Equations of state for several confinements are obtained with quantum Monte Carlo (QMC) at T=0T=0T=0, using interaction potentials that include information on the sss-wave scattering length aaa and the effective range reffr_{\rm eff}reff​. Performing the calculations using two different interaction potential models we have determined the range of confinements for which equations of state are universal in terms of aaa and reffr_{\rm eff}reff​. Based on the QMC equation of state, we develop a 2D QMC density functional for each confinement strength and use it together with the local density approximation to determine properties of the self-bound drops. For moderate squeezing, energies and droplet profiles obtained using the 2D QMC functional agree well with those obtained using 3D functionals, while offering a substantial reduction in computational cost, and a consistent approach in crossover to 2D. Noticeably, our results approach 2D mean-field (MF) + Lee-Huang-Yang (LHY) predictions only for the most strongly confined systems for which universality in terms of aaa and reffr_{\rm eff}reff​ is observed. This implies a very narrow range of confinements for which 2D LHY functionals are applicable, which has important consequences for the study of vortices.
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.