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:quant-ph/0003110

Stability properties of trapped Bose-Fermi gases mixture

X. X. Yi, C. P. Sun

Published Mar 23, 2000• 0 citations
arXivHTMLPDF

Abstract

The stability of Bose-Fermi gases trapped in an isotropic potentials at ultracold temperature is strongly influenced by the interaction between the fermions and the bosons. At zero temperature, the stability criterion is given in this paper using variation method, the results show that whether a fermion-boson mixture is stable depends mainly on the interaction between the fermions and the bosons. For finite temperature, however, the stability is not only related to the coupling constants, but also to the temperature. The stability conditions for finite temperature are also derived and discuss in details in this paper.

DOI
10.48550/arxiv.quant-ph/0003110

Related papers

Phase separation of a trapped Bose-Fermi gas mixture: Beyond the Thomas-Fermi approximation

X. X. Yi, C. P. Sun

Phase separation of a Bose-Fermi gas mixture in a trapping potential is strongly influenced by the interaction between the fermion and the boson. The stability condition for the mixture at zero temperature is deduced. It is found that mixture stability depends on the fermion-boson interaction, the total number of the bosons and the fermions, and the trapping frequencies. The stability conditions for the mixture at finite temperature are also derived and discussed.

Physical Review A•Sep 1, 2001•24 citations

Stability of Bose-Fermi mixtures in two dimensions: A lowest-order constrained variational approach

Anonymous, L. Pisani, P. Pieri

We investigate the problem of mechanical stability in two-dimensional Bose-Fermi mixtures at zero temperature, focusing on systems with a tunable Bose-Fermi (BF) interaction and a weak but finite boson-boson (BB) repulsion. The analysis is carried out within the framework of the lowest-order constrained variational (LOCV) approach, which allows for a nonperturbative treatment of strong interspecies correlations while retaining analytical transparency. The BF interaction is modeled by a properly regularized attractive contact potential, enabling the exploration of both the attractive and repulsive energy branches. We determine the minimal BB repulsion required to ensure mechanical stability of the mixture by evaluating the inverse compressibility matrix over the full range of BF coupling strengths, within the domain of validity of the LOCV approximation. The interaction contribution to the energy is benchmarked against available experimental data and quantum Monte Carlo results in the single-impurity limit, showing good agreement. Our analysis reveals how the critical BB coupling depends on interaction strength, density imbalance, and mass ratio. In particular, we find that mixtures with equal boson and fermion masses exhibit enhanced stability, requiring the smallest BB repulsion to prevent mechanical instability. In this case, a relatively small BB interaction is sufficient to stabilize attractive mixtures for all values of the BF interaction. These results provide a theoretical framework for assessing stability conditions in experimentally realizable two-dimensional Bose-Fermi mixtures with tunable interactions.

arXiv:2602.15598•Physical Review A•Aug 6, 2026•0 citations

Critical temperature of Bose Einstein condensation in trapped atomic Bose Fermi mixtures

A P Albus, S Giorgini, F Illuminati +1 more

We calculate the shift in the critical temperature of Bose–Einstein condensation for a dilute Bose–Fermi mixture confined by a harmonic potential, to lowest order in both the Bose–Bose and Bose–Fermi coupling constants. The relative importance of the effect on the critical temperature of the boson–boson and boson–fermion interactions is investigated as a function of the parameters of the mixture. The possible relevance of the shift of the transition temperature in current experiments on trapped Bose–Fermi mixtures is discussed.

arXiv:cond-mat/0210339•Journal of Physics B Atomic Molecular and Optical Physics•Nov 11, 2002•7 citations

Finite-temperature effects on the collapse of trapped Bose-Fermi mixtures

Xia-Ji Liu, Michele Modugno, Hui Hu

By using the self-consistent Hartree-Fock-Bogoliubov-Popov theory, we present a detailed study of the mean-field stability of spherically trapped Bose-Fermi mixtures at finite temperature. We find that, by increasing the temperature, the critical particle number of bosons (or fermions) and the critical attractive Bose-Fermi scattering length increase, leading to a significant stabilization of the mixture.

arXiv:cond-mat/0307639•Physical Review A•Nov 4, 2003•31 citations

Bose-Einstein condensation temperature of a trapped interacting Bose-Fermi gas mixture

Yong-li Ma, S. T. Chui

We calculate the critical temperature of a trapped interacting Bose-Fermi gas mixture by means of a first-order perturbation method in a local-density approximation. An explicit analytical expression is derived for the dependence of the critical temperature on the numbers of bosons and fermions, the strengths of boson-boson and boson-fermion interactions, and the trapping frequencies.

Physical Review A•Nov 13, 2002•11 citations

Collective modes and stability of Bose-Fermi mixtures with a BCS-BEC crossover

Hiroyuki Shibata, Nobuhiko Yokoshi, Susumu Kurihara

We investigate an ultracold Bose-Fermi mixture with a Feshbach resonance between two hyperfine states of fermions. Using a functional integral method, we calculate collective modes associated with fermion pairs and bosons in the superfluid phase. We derive a stability condition of the mixtures that is valid in the entire region of the BCS-BEC crossover. This stability condition, which smoothly connects the well-known results obtained in both the BCS and Bose-Einstein Condensate (BEC) limits, shows that sufficiently strong fermion-boson (FB) interactions destabilize the mixtures. In order to investigate the consequence of this instability, we study the ground-state energy of both the uniformly mixed and the phase-separated states. We find that FB repulsion induces a phase separation, whereas FB attraction should cause a collapse of the mixture. The possibilities for the experimental observation of such instabilities are also discussed.

arXiv:cond-mat/0702094•Physical Review A•May 29, 2007•8 citations
The stability of Bose-Fermi gases trapped in an isotropic potentials at ultracold temperature is strongly influenced by the interaction between the fermions and the bosons. At zero temperature, the stability criterion is given in this paper using variation method, the results show that whether a fermion-boson mixture is stable depends mainly on the interaction between the fermions and the bosons. For finite temperature, however, the stability is not only related to the coupling constants, but also to the temperature. The stability conditions for finite temperature are also derived and discuss in details in this paper.
We investigate the problem of mechanical stability in two-dimensional Bose-Fermi mixtures at zero temperature, focusing on systems with a tunable Bose-Fermi (BF) interaction and a weak but finite boson-boson (BB) repulsion. The analysis is carried out within the framework of the lowest-order constrained variational (LOCV) approach, which allows for a nonperturbative treatment of strong interspecies correlations while retaining analytical transparency. The BF interaction is modeled by a properly regularized attractive contact potential, enabling the exploration of both the attractive and repulsive energy branches. We determine the minimal BB repulsion required to ensure mechanical stability of the mixture by evaluating the inverse compressibility matrix over the full range of BF coupling strengths, within the domain of validity of the LOCV approximation. The interaction contribution to the energy is benchmarked against available experimental data and quantum Monte Carlo results in the single-impurity limit, showing good agreement. Our analysis reveals how the critical BB coupling depends on interaction strength, density imbalance, and mass ratio. In particular, we find that mixtures with equal boson and fermion masses exhibit enhanced stability, requiring the smallest BB repulsion to prevent mechanical instability. In this case, a relatively small BB interaction is sufficient to stabilize attractive mixtures for all values of the BF interaction. These results provide a theoretical framework for assessing stability conditions in experimentally realizable two-dimensional Bose-Fermi mixtures with tunable interactions.
We calculate the shift in the critical temperature of Bose–Einstein condensation for a dilute Bose–Fermi mixture confined by a harmonic potential, to lowest order in both the Bose–Bose and Bose–Fermi coupling constants. The relative importance of the effect on the critical temperature of the boson–boson and boson–fermion interactions is investigated as a function of the parameters of the mixture. The possible relevance of the shift of the transition temperature in current experiments on trapped Bose–Fermi mixtures is discussed.
We investigate an ultracold Bose-Fermi mixture with a Feshbach resonance between two hyperfine states of fermions. Using a functional integral method, we calculate collective modes associated with fermion pairs and bosons in the superfluid phase. We derive a stability condition of the mixtures that is valid in the entire region of the BCS-BEC crossover. This stability condition, which smoothly connects the well-known results obtained in both the BCS and Bose-Einstein Condensate (BEC) limits, shows that sufficiently strong fermion-boson (FB) interactions destabilize the mixtures. In order to investigate the consequence of this instability, we study the ground-state energy of both the uniformly mixed and the phase-separated states. We find that FB repulsion induces a phase separation, whereas FB attraction should cause a collapse of the mixture. The possibilities for the experimental observation of such instabilities are also discussed.