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:cond-mat/0505139 · Journal of Physics B Atomic Molecular and Optical Physics

Hydrodynamic modes in a trapped strongly interacting Fermi gas of atoms

Yeong E. Kim, Alexander L. Zubarev

Published Jul 4, 2005• 14 citations
arXivHTMLPDF

Abstract

The zero-temperature properties of a dilute two-component Fermi gas in the Bardeen–Cooper–Schrieffer phase–Bose–Einstein condensate crossover are investigated. On the basis of a generalization of the variational Schwinger method, we construct approximate semi-analytical formulae for collective frequencies of the radial and the axial breathing modes of the Fermi gas under harmonic confinement in the framework of the hydrodynamic theory. It is shown that the method gives nearly exact solutions.

DOI
10.1088/0953-4075/38/14/l02

Related papers

Collective excitations of strongly interacting Fermi gases of atoms in a harmonic trap

Yeong E. Kim, Alexander L. Zubarev

The zero-temperature properties of a dilute two-component Fermi gas in the BCS to Bose-Einstein Condensation crossover are investigated. On the basis of a generalization of the Hylleraas-Undheim method, we construct rigorous upper bounds to the collective frequencies for the radial and the axial breathing mode of the Fermi gas under harmonic confinement in the framework of the hydrodynamic theory. The bounds are compared to experimental data for trapped vapors of $^{6}\mathrm{Li}$ atoms.

arXiv:cond-mat/0502651•Physical Review A•Jul 18, 2005•35 citations

Collective oscillation modes of a superfluid Bose–Fermi mixture

Wen Wen, Ying Wang, Jianyong Wang

Abstract In this work, we present a theoretical study for the collective oscillation modes, i.e. quadrupole, radial and axial mode, of a mixture of Bose and Fermi superfluids in the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a molecular Bose–Einstein condensate (BEC) in harmonic trapping potentials with cylindrical symmetry of experimental interest. To this end, we start from the coupled superfluid hydrodynamic equations for the dynamics of Bose–Fermi superfluid mixtures and use the scaling theory that has been developed for a coupled system. The collective oscillation modes of Bose–Fermi superfluid mixtures are found to crucially depend on the overlap integrals of the spatial derivations of density profiles of the Bose and Fermi superfluids at equilibrium. We not only present the explicit expressions for the overlap density integrals, as well as the frequencies of the collective modes provided that the effective Bose–Fermi coupling is weak, but also test the valid regimes of the analytical approximations by numerical calculations in realistic experimental conditions. In the presence of a repulsive Bose–Fermi interaction, we find that the frequencies of the three collective modes of the Bose and Fermi superfluids are all upshifted, and the change speeds of the frequency shifts in the BCS–BEC crossover can characterize the different groundstate phases of the Bose–Fermi superfluid mixtures for different trap geometries.

arXiv:1902.05699•New Journal of Physics•Aug 21, 2019•4 citations

Collective Modes of a Quasi-Two-Dimensional Superfluid Fermi Gas in BCS-BEC Crossover

Yu Long Zhou, Xiaodong Ma, Guoxiang Huang

We investigate the collective modes of a quasi-two-dimensional (Q2D) superfluid Fermi gas in Bardeen–Cooper–Schrieffer Bose–Einstein condensation (BCS-BEC) crossover. For solving a generalized Gross–Pitaevskii equation by using a time-dependent variational method, we take a trial wavefunction with the form of hybrid Gaussian-parabolic type, which not only reflects the Q2D character of the system and also allows an essentially analytical approach of the problem. We present a Q2D criterion that is valid for various superfluid regimes and displays clearly the relation between the maximum condensed particle number and the parameters of trapping potential as well as atom–atom interaction. We show that due to the small particle number in the Q2D condensate, the contribution to oscillating frequencies by the quantum pressure in the strong confinement direction is significant and hence a Thomas–Fermi approximation can not be used.

Chinese Physics Letters•Sep 27, 2006•3 citations

Collective modes of low-dimensional superfluid Fermi gases in the BCS-BEC crossover: Time-dependent variational analysis

Yu Long Zhou, Guoxiang Huang

We investigate collective modes and free expansions of quasi-one- and quasi-two-dimensional (Q1D and Q2D) ultracold Fermi gases in the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC). We solve a superfluid order parameter equation valid for the BCS-BEC crossover by employing a time-dependent variational method. We take a trial wave function of hybrid Gaussian-parabolic type, which not only reflects the low-dimensional character of the system but also allows an essentially analytical approach for the problem. We present Q1D and Q2D criteria that are valid in various superfluid regimes and show clearly the relation between the maximum condensed particle number and the parameters of the trapping potential as well as the atom-atom interaction. We demonstrate that, due to the small particle number in Q1D and Q2D condensates, the contribution to oscillating frequencies of collective modes by the quantum pressure in the strong-confinement direction is significant and hence the Thomas-Fermi approximation cannot be used. We also show that the free expansion of Q1D and Q2D superfluid Fermi gases in the strong-confinement direction is much faster than that in the weak-confinement direction.

Physical Review A•Feb 12, 2007•22 citations

Frequency shift and mode coupling of the collective modes of superfluid Fermi gases in the BCS-BEC crossover

Yu Long Zhou, Wen Wen, Guoxiang Huang

We investigate the dynamical behavior of large-amplitude collective modes in a superfluid Fermi gas in the crossover from Bardeen--Cooper--Schrieffer (BCS) superfluid to Bose--Einstein condensate (BEC) based on a hydrodynamic approach. We first solve the superfluid hydrodynamic equations that describe the time evolution of fermionic condensates in the BCS-BEC crossover and calculate explicitly the frequency shifts of the collective modes induced by nonlinear effects using the Lindstedt--Poincar\'e method. The result shows that the frequency shifts display different features in different superfluid regimes. We then study the second-harmonic generation of the collective modes under a phase-matching condition, which can be fulfilled by choosing appropriate parameters of the system. The analytical results obtained are checked by numerical simulations and good agreement is found.

Physical Review B•Mar 25, 2008•17 citations

Bulk properties and collective modes of a trapped strongly interacting fermi gas near the unitary limit regime

Zhenbang Lu, J. -S. Chen, J. R. Li

We investigate the properties of a trapped two-component, Fermi gas near the unitary limit regime. The bulk properties are discussed through a quasi-linear approximation with a medium dependent effective interaction. The obtained ground state energy for the unitary fermion system is in good agreement with existing theoretical predictions as well as experimental results. Within the framework of hydrodynamics, the radial and axial frequencies of the breathing modes are analyzed in detail. Applied to the cigar shaped harmonic trap, the theoretical results are reasonably consistent with the experimental measurements.

Laser Physics•Mar 10, 2010•6 citations
The zero-temperature properties of a dilute two-component Fermi gas in the Bardeen–Cooper–Schrieffer phase–Bose–Einstein condensate crossover are investigated. On the basis of a generalization of the variational Schwinger method, we construct approximate semi-analytical formulae for collective frequencies of the radial and the axial breathing modes of the Fermi gas under harmonic confinement in the framework of the hydrodynamic theory. It is shown that the method gives nearly exact solutions.
The zero-temperature properties of a dilute two-component Fermi gas in the BCS to Bose-Einstein Condensation crossover are investigated. On the basis of a generalization of the Hylleraas-Undheim method, we construct rigorous upper bounds to the collective frequencies for the radial and the axial breathing mode of the Fermi gas under harmonic confinement in the framework of the hydrodynamic theory. The bounds are compared to experimental data for trapped vapors of 6Li^{6}\mathrm{Li}6Li atoms.
Abstract In this work, we present a theoretical study for the collective oscillation modes, i.e. quadrupole, radial and axial mode, of a mixture of Bose and Fermi superfluids in the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a molecular Bose–Einstein condensate (BEC) in harmonic trapping potentials with cylindrical symmetry of experimental interest. To this end, we start from the coupled superfluid hydrodynamic equations for the dynamics of Bose–Fermi superfluid mixtures and use the scaling theory that has been developed for a coupled system. The collective oscillation modes of Bose–Fermi superfluid mixtures are found to crucially depend on the overlap integrals of the spatial derivations of density profiles of the Bose and Fermi superfluids at equilibrium. We not only present the explicit expressions for the overlap density integrals, as well as the frequencies of the collective modes provided that the effective Bose–Fermi coupling is weak, but also test the valid regimes of the analytical approximations by numerical calculations in realistic experimental conditions. In the presence of a repulsive Bose–Fermi interaction, we find that the frequencies of the three collective modes of the Bose and Fermi superfluids are all upshifted, and the change speeds of the frequency shifts in the BCS–BEC crossover can characterize the different groundstate phases of the Bose–Fermi superfluid mixtures for different trap geometries.
We investigate the collective modes of a quasi-two-dimensional (Q2D) superfluid Fermi gas in Bardeen–Cooper–Schrieffer Bose–Einstein condensation (BCS-BEC) crossover. For solving a generalized Gross–Pitaevskii equation by using a time-dependent variational method, we take a trial wavefunction with the form of hybrid Gaussian-parabolic type, which not only reflects the Q2D character of the system and also allows an essentially analytical approach of the problem. We present a Q2D criterion that is valid for various superfluid regimes and displays clearly the relation between the maximum condensed particle number and the parameters of trapping potential as well as atom–atom interaction. We show that due to the small particle number in the Q2D condensate, the contribution to oscillating frequencies by the quantum pressure in the strong confinement direction is significant and hence a Thomas–Fermi approximation can not be used.
We investigate collective modes and free expansions of quasi-one- and quasi-two-dimensional (Q1D and Q2D) ultracold Fermi gases in the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC). We solve a superfluid order parameter equation valid for the BCS-BEC crossover by employing a time-dependent variational method. We take a trial wave function of hybrid Gaussian-parabolic type, which not only reflects the low-dimensional character of the system but also allows an essentially analytical approach for the problem. We present Q1D and Q2D criteria that are valid in various superfluid regimes and show clearly the relation between the maximum condensed particle number and the parameters of the trapping potential as well as the atom-atom interaction. We demonstrate that, due to the small particle number in Q1D and Q2D condensates, the contribution to oscillating frequencies of collective modes by the quantum pressure in the strong-confinement direction is significant and hence the Thomas-Fermi approximation cannot be used. We also show that the free expansion of Q1D and Q2D superfluid Fermi gases in the strong-confinement direction is much faster than that in the weak-confinement direction.
We investigate the dynamical behavior of large-amplitude collective modes in a superfluid Fermi gas in the crossover from Bardeen--Cooper--Schrieffer (BCS) superfluid to Bose--Einstein condensate (BEC) based on a hydrodynamic approach. We first solve the superfluid hydrodynamic equations that describe the time evolution of fermionic condensates in the BCS-BEC crossover and calculate explicitly the frequency shifts of the collective modes induced by nonlinear effects using the Lindstedt--Poincar\'e method. The result shows that the frequency shifts display different features in different superfluid regimes. We then study the second-harmonic generation of the collective modes under a phase-matching condition, which can be fulfilled by choosing appropriate parameters of the system. The analytical results obtained are checked by numerical simulations and good agreement is found.
We investigate the properties of a trapped two-component, Fermi gas near the unitary limit regime. The bulk properties are discussed through a quasi-linear approximation with a medium dependent effective interaction. The obtained ground state energy for the unitary fermion system is in good agreement with existing theoretical predictions as well as experimental results. Within the framework of hydrodynamics, the radial and axial frequencies of the breathing modes are analyzed in detail. Applied to the cigar shaped harmonic trap, the theoretical results are reasonably consistent with the experimental measurements.