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:2302.00385 · Physical Review A

Superfluid-droplet crossover in a binary boson mixture on a ring: Exact diagonalization solutions for few-particle systems in one dimension

L. Chergui, J. Bengtsson, J. Bjerlin, Philipp Stürmer, G. M. Kavoulakis, S. M. Reimann

Published Aug 21, 2023• 13 citations
arXivHTMLPDF

Abstract

We investigate the formation of self-bound quantum droplets in a one-dimensional binary mixture of bosonic atoms, applying the method of numerical diagonalization of the full Hamiltonian. The excitation spectra and ground-state pair correlations signal the formation of a few-boson droplet when crossing the region of critical interspecies interactions. The self-binding affects the rotational excitations, displaying a change in the energy dispersion from negative curvature, associated with superfluidity in the many-body limit, to a nearly parabolic curvature indicative of rigid body rotation. We exploit two global symmetries of the system to further analyze the few-body modes in terms of transition matrix elements and breathing mode dynamics. The ground and excited state energies reported here are exact within the respective Hilbert spaces, which have been adapted according to a given set of single-particle basis states and a specific importance threshold of the employed truncation method. We compare these data to the usual ad hoc inclusion of higher-order contributions in the extended Gross-Pitaevskii equation. For the given parameters we find a remarkable agreement between the few-body regime and the thermodynamic limit in one dimension.

DOI
10.1103/physreva.108.023313

Related papers

Droplet-superfluid compounds in binary bosonic mixtures

M. Nilsson Tengstrand, S. M. Reimann

While quantum fluctuations in binary mixtures of bosonic atoms with short-range interactions can lead to the formation of a self-bound droplet, for equal intracomponent interactions but an unequal number of atoms in the two components, there is an excess part that cannot bind to the droplet. Imposing confinement, as here through periodic boundary conditions in a one-dimensional setting, the droplet becomes amalgamated with a residual condensate. The rotational properties of this compound system reveal simultaneous rigid-body and superfluid behavior in the ground state and uncover that the residual condensate can carry angular momentum even in the absence of vorticity. In contradiction to the intuitive idea that the superfluid fraction of the system would be entirely made up of the excess atoms not bound by the droplet, we find evidence that this fraction is higher than what one would expect in such a picture. Our findings are corroborated by an analysis of the elementary excitations in the system, and shed new light on the coexistence of localization and superfluidity.

arXiv:2110.15675•Physical Review A•Mar 24, 2022•30 citations

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

Microscopic pairing theory of a binary Bose mixture with interspecies attractions: Bosonic BEC-BCS crossover and ultradilute low-dimensional quantum droplets

Hui Hu, Jia Wang, Xia-Ji Liu

Ultradilute quantum droplets are an intriguing new state of matter, in which the attractive mean-field force can be balanced by the repulsive force from quantum fluctuations to avoid collapse. Here, we present a microscopic theory of ultradilute quantum droplets in three-, one-, and two-dimensional two-component Bose-Bose mixtures by generalizing the conventional Bogoliubov theory to include the bosonic pairing arising from the interspecies attraction. Our pairing theory is fully equivalent to a variational approach and hence gives an upper bound for the energy of quantum droplets. In three dimensions, we predict the existence of a strongly interacting Bose droplet at the crossover from Bose-Einstein condensates (BECs) to BCS superfluids and map out the bosonic BEC-BCS crossover phase diagram. In one dimension, we find that the energy of the one-dimensional Bose droplet calculated by the pairing theory is in excellent agreement with the latest diffusion Monte Carlo simulation [L. Parisi et al., Phys. Rev. Lett. 122, 105302 (2019)] for nearly all the interaction strengths at which quantum droplets exist. In two dimensions, we show that Bose droplets disappear and may turn into a solitonlike many-body bound state, when the interspecies attraction exceeds a critical value. Below the threshold, the pairing theory predicts more or less the same results as the Bogoliubov theory derived by D. S. Petrov and G. E. Astrakharchik [Phys. Rev. Lett. 117, 100401 (2016)]. The predicted energies from both theories are higher than the diffusion Monte Carlo results due to the weak interspecies attraction and the increasingly important role played by the beyond-Bogoliubov-approximation effect in two dimensions. Our pairing theory provides an ideal starting point to understand interesting ground-state properties of quantum droplets in various dimensions, including their shape and collective oscillations.

arXiv:2006.00434•Physical Review A•Oct 2, 2020•46 citations

Quantum self-bound droplets in Bose-Bose mixtures: Effects of higher-order quantum and thermal fluctuations

Nadia Guebli, Abdelâali Boudjemâa

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.

arXiv:2108.08632•Physical Review A•Aug 11, 2021•39 citations

Microscopic derivation of the extended Gross-Pitaevskii equation for quantum droplets in binary Bose mixtures

Hui Hu, Xia-Ji Liu

An ultradilute quantum droplet is a self-bound liquidlike state recently observed in ultracold Bose-Einstein condensates. In most previous theoretical studies, it is described by a phenomenological low-energy effective theory, termed as the extended Gross-Pitaevskii equation. Here, we microscopically derive the Gross-Pitaevskii equation for the condensate and also for a pairing field in an inhomogeneous quantum droplet realized by Bose-Bose mixtures with attractive interspecies interaction. We show that the inclusion of the pairing field is essential, in order to have a consistent description of the droplet state. We clarify that the extended Gross-Pitaevskii equation used earlier should be understood as the equation of motion for the pairing field, rather than the condensate. The fluctuations of the pairing field give rise to low-energy collective excitations of the droplet. We also present the Bogoliubov equations for gapless phonon modes and gapped modes due to pairing in real space, which characterizes single-particle-like excitations of the droplet. The equations of motion derived in this work for the condensate and the pairing field serve as an ideal starting point to understand the structure and collective excitations of nonuniform ultradilute quantum droplets in ongoing cold-atom experiments.

arXiv:2006.05769•Physical Review A•Oct 2, 2020•23 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
We investigate the formation of self-bound quantum droplets in a one-dimensional binary mixture of bosonic atoms, applying the method of numerical diagonalization of the full Hamiltonian. The excitation spectra and ground-state pair correlations signal the formation of a few-boson droplet when crossing the region of critical interspecies interactions. The self-binding affects the rotational excitations, displaying a change in the energy dispersion from negative curvature, associated with superfluidity in the many-body limit, to a nearly parabolic curvature indicative of rigid body rotation. We exploit two global symmetries of the system to further analyze the few-body modes in terms of transition matrix elements and breathing mode dynamics. The ground and excited state energies reported here are exact within the respective Hilbert spaces, which have been adapted according to a given set of single-particle basis states and a specific importance threshold of the employed truncation method. We compare these data to the usual ad hoc inclusion of higher-order contributions in the extended Gross-Pitaevskii equation. For the given parameters we find a remarkable agreement between the few-body regime and the thermodynamic limit in one dimension.
While quantum fluctuations in binary mixtures of bosonic atoms with short-range interactions can lead to the formation of a self-bound droplet, for equal intracomponent interactions but an unequal number of atoms in the two components, there is an excess part that cannot bind to the droplet. Imposing confinement, as here through periodic boundary conditions in a one-dimensional setting, the droplet becomes amalgamated with a residual condensate. The rotational properties of this compound system reveal simultaneous rigid-body and superfluid behavior in the ground state and uncover that the residual condensate can carry angular momentum even in the absence of vorticity. In contradiction to the intuitive idea that the superfluid fraction of the system would be entirely made up of the excess atoms not bound by the droplet, we find evidence that this fraction is higher than what one would expect in such a picture. Our findings are corroborated by an analysis of the elementary excitations in the system, and shed new light on the coexistence of localization and superfluidity.
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.
Ultradilute quantum droplets are an intriguing new state of matter, in which the attractive mean-field force can be balanced by the repulsive force from quantum fluctuations to avoid collapse. Here, we present a microscopic theory of ultradilute quantum droplets in three-, one-, and two-dimensional two-component Bose-Bose mixtures by generalizing the conventional Bogoliubov theory to include the bosonic pairing arising from the interspecies attraction. Our pairing theory is fully equivalent to a variational approach and hence gives an upper bound for the energy of quantum droplets. In three dimensions, we predict the existence of a strongly interacting Bose droplet at the crossover from Bose-Einstein condensates (BECs) to BCS superfluids and map out the bosonic BEC-BCS crossover phase diagram. In one dimension, we find that the energy of the one-dimensional Bose droplet calculated by the pairing theory is in excellent agreement with the latest diffusion Monte Carlo simulation [L. Parisi et al., Phys. Rev. Lett. 122, 105302 (2019)] for nearly all the interaction strengths at which quantum droplets exist. In two dimensions, we show that Bose droplets disappear and may turn into a solitonlike many-body bound state, when the interspecies attraction exceeds a critical value. Below the threshold, the pairing theory predicts more or less the same results as the Bogoliubov theory derived by D. S. Petrov and G. E. Astrakharchik [Phys. Rev. Lett. 117, 100401 (2016)]. The predicted energies from both theories are higher than the diffusion Monte Carlo results due to the weak interspecies attraction and the increasingly important role played by the beyond-Bogoliubov-approximation effect in two dimensions. Our pairing theory provides an ideal starting point to understand interesting ground-state properties of quantum droplets in various dimensions, including their shape and collective oscillations.
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.
An ultradilute quantum droplet is a self-bound liquidlike state recently observed in ultracold Bose-Einstein condensates. In most previous theoretical studies, it is described by a phenomenological low-energy effective theory, termed as the extended Gross-Pitaevskii equation. Here, we microscopically derive the Gross-Pitaevskii equation for the condensate and also for a pairing field in an inhomogeneous quantum droplet realized by Bose-Bose mixtures with attractive interspecies interaction. We show that the inclusion of the pairing field is essential, in order to have a consistent description of the droplet state. We clarify that the extended Gross-Pitaevskii equation used earlier should be understood as the equation of motion for the pairing field, rather than the condensate. The fluctuations of the pairing field give rise to low-energy collective excitations of the droplet. We also present the Bogoliubov equations for gapless phonon modes and gapped modes due to pairing in real space, which characterizes single-particle-like excitations of the droplet. The equations of motion derived in this work for the condensate and the pairing field serve as an ideal starting point to understand the structure and collective excitations of nonuniform ultradilute quantum droplets in ongoing cold-atom experiments.
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.