© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:0805.1641 · Physical Review A

Breathing mode frequencies of a rotating Fermi gas in the BCS-BEC crossover region

Theja N. De Silva

Published Aug 19, 2008• 7 citations

Abstract

We study the breathing mode frequencies of a rotating Fermi gas trapped in a harmonic plus radial quartic potential. We find that as the radial anharmonicity increases, the lowest order radial mode frequency increases while the next lowest order radial mode frequency decreases. Then at a critical anharmonicity, these two modes merge and beyond this merge the cloud is unstable against the oscillations. The critical anharmonicity depends on both rotational frequency and the chemical potential. As a result of the large chemical potential in the BCS regime, even with a weak anharmonicity the lowest order mode frequency increases with decreasing the attractive interaction. For large enough anharmonicities in the weak-coupling BCS limit, we find that the excitation of the breathing mode frequencies make the atomic cloud unstable.

DOI: 10.1103/physreva.78.023623

Related papers

Critical rotation of an anharmonically trapped Bose–Einstein condensate

Juan Ma, Zhi Li, Xue Ju-Kui

We consider rotational motion of an interacting atomic Bose–Einstein condensate (BEC) with both two- and three-body interactions in a quadratic-plus-quartic and harmonic-plus-Gaussian trap. By using the variational method, the influence of the three-body interaction and the anharmonicity of the trap on the lowest energy surface mode excitation and the spontaneous shape deformation (responsible for the vortex formation) in a rotating BEC is discussed in detail. It is found that the repulsive three-body interaction helps the formation of the vortex and reduces the lowest energy surface mode frequency and the critical rotational frequency of the system. Moreover, the critical rotational frequency for the vortex formation in the harmonic-plus-Gaussian potential is lower than that in the quadratic-plus-quartic potential.

Chinese Physics B•Sep 29, 2009•7 citations

Collective modes of a Fermi superfluid containing vortices along the BEC-BCS crossover

Tarun Kanti Ghosh, Kazushige Machida

Using the coarse-grain averaged hydrodynamic approach, we calculate all low energy transverse excitation spectrum of a rotating Fermi superfluid containing vortex lattices for all regimes along the Bose-Einstein condensate--Bardeen-Cooper-Schrieffer (BEC-BCS) crossover. In the fast rotating regime, the molecular BEC enters into the lowest Landau level, but the superfluid in the unitarity and the BCS regimes occupies many low-lying Landau levels. The difference between the breathing mode frequencies at the BEC and unitarity limit shrinks to zero as the rotation speed approaches the radial trap frequency, in contrast to the finite difference in the nonrotating systems.

arXiv:cond-mat/0510721•Physical Review A•Feb 6, 2006•8 citations

First- and second-sound-like modes at finite temperature in trapped Fermi gases from BCS to BEC

Yan He, Qijin Chen, Chih-Chun Chien +1 more

We determine the temperature $(T)$ dependence of first- and second-sound-like mode frequencies for trapped Fermi gases undergoing the BCS to Bose--Einstein condensation (BEC) crossover. Our results are based on numerical solution of the two-fluid equations in conjunction with a microscopic calculation of thermodynamical variables. As in experiment and at unitarity, we show that the lowest radial breathing mode is $T$ independent. At finite $T$, higher-order breathing modes strongly mix with second sound. Their complex $T$ dependence should provide an alternative way of measuring the transition temperature ${T}_{c}$.

arXiv:0704.1889•Physical Review A•Nov 8, 2007•22 citations

Pairing gaps in atomic gases at the BCS–BEC crossover

H. Heiselberg

Strong evidence for pairing and superfluidity has recently been found in atomic Fermi gases at the BCS–BEC crossover both in collective modes and radio frequency (RF) excitation energies. It is argued that the scale for the effective pairing gaps measured in RF experiments is set by the lowest quasiparticle in-gap excitation energies. These are calculated at the BCS–BEC crossover from semiclassical solutions to the Bogoliubov–deGennes equations. The strong damping of the radial breathing mode observed in the BCS limit occurs when the lowest quasiparticle excitation energies coincide with the radial frequency, which indicates that a coupling between them takes place.

arXiv:cond-mat/0406714•New Journal of Physics•Oct 22, 2004•7 citations

Collective modes as a probe of the equation of state for partially polarized Fermi gases

Theja N. De Silva, Erich J. Mueller

We calculate the collective modes of a partially polarized Fermi gas trapped in a spherically symmetric harmonic potential. We show that the breathing mode frequency exhibits non-monotonic dependence on polarization in the entire BCS-BEC crossover region. Moreover, we find that the breathing mode can be used to distinguish between two commonly used unitary gas equations of state.

arXiv:cond-mat/0607491•Jul 19, 2006•0 citations

Superfluid Fermi Gases in a Rotating Anharmonic Trap

Juan Ma, Ju-Kui Xue

The quadrupole mode frequency, the monopole mode frequency, and the critical rotational frequency for stirring a single vortex nucleation along the BEC-BCS crossover are obtained. The results show that, in a rotating anisotropic anharmonic trap, the quadrupole mode frequency and the critical rotational frequency for stirring a single vortex nucleation are modified significantly when the system crosses from the BEC side to the BCS side: the anisotropy of the trap induces a downshift of the quadrupole mode frequency and the critical rotational frequency and helps the vortex formation in the system, while an anharmonic trap induces an upshift of the quadrupole mode frequency and the critical rotational frequency and suppresses the vortex formation in the system.

Communications in Theoretical Physics•Mar 1, 2011•5 citations

We study the breathing mode frequencies of a rotating Fermi gas trapped in a harmonic plus radial quartic potential. We find that as the radial anharmonicity increases, the lowest order radial mode frequency increases while the next lowest order radial mode frequency decreases. Then at a critical anharmonicity, these two modes merge and beyond this merge the cloud is unstable against the oscillations. The critical anharmonicity depends on both rotational frequency and the chemical potential. As a result of the large chemical potential in the BCS regime, even with a weak anharmonicity the lowest order mode frequency increases with decreasing the attractive interaction. For large enough anharmonicities in the weak-coupling BCS limit, we find that the excitation of the breathing mode frequencies make the atomic cloud unstable.

We consider rotational motion of an interacting atomic Bose–Einstein condensate (BEC) with both two- and three-body interactions in a quadratic-plus-quartic and harmonic-plus-Gaussian trap. By using the variational method, the influence of the three-body interaction and the anharmonicity of the trap on the lowest energy surface mode excitation and the spontaneous shape deformation (responsible for the vortex formation) in a rotating BEC is discussed in detail. It is found that the repulsive three-body interaction helps the formation of the vortex and reduces the lowest energy surface mode frequency and the critical rotational frequency of the system. Moreover, the critical rotational frequency for the vortex formation in the harmonic-plus-Gaussian potential is lower than that in the quadratic-plus-quartic potential.

Using the coarse-grain averaged hydrodynamic approach, we calculate all low energy transverse excitation spectrum of a rotating Fermi superfluid containing vortex lattices for all regimes along the Bose-Einstein condensate--Bardeen-Cooper-Schrieffer (BEC-BCS) crossover. In the fast rotating regime, the molecular BEC enters into the lowest Landau level, but the superfluid in the unitarity and the BCS regimes occupies many low-lying Landau levels. The difference between the breathing mode frequencies at the BEC and unitarity limit shrinks to zero as the rotation speed approaches the radial trap frequency, in contrast to the finite difference in the nonrotating systems.

We determine the temperature

(T)

dependence of first- and second-sound-like mode frequencies for trapped Fermi gases undergoing the BCS to Bose--Einstein condensation (BEC) crossover. Our results are based on numerical solution of the two-fluid equations in conjunction with a microscopic calculation of thermodynamical variables. As in experiment and at unitarity, we show that the lowest radial breathing mode is

T

independent. At finite

T

, higher-order breathing modes strongly mix with second sound. Their complex

T

dependence should provide an alternative way of measuring the transition temperature

{T}_{c}

.

Strong evidence for pairing and superfluidity has recently been found in atomic Fermi gases at the BCS–BEC crossover both in collective modes and radio frequency (RF) excitation energies. It is argued that the scale for the effective pairing gaps measured in RF experiments is set by the lowest quasiparticle in-gap excitation energies. These are calculated at the BCS–BEC crossover from semiclassical solutions to the Bogoliubov–deGennes equations. The strong damping of the radial breathing mode observed in the BCS limit occurs when the lowest quasiparticle excitation energies coincide with the radial frequency, which indicates that a coupling between them takes place.

The quadrupole mode frequency, the monopole mode frequency, and the critical rotational frequency for stirring a single vortex nucleation along the BEC-BCS crossover are obtained. The results show that, in a rotating anisotropic anharmonic trap, the quadrupole mode frequency and the critical rotational frequency for stirring a single vortex nucleation are modified significantly when the system crosses from the BEC side to the BCS side: the anisotropy of the trap induces a downshift of the quadrupole mode frequency and the critical rotational frequency and helps the vortex formation in the system, while an anharmonic trap induces an upshift of the quadrupole mode frequency and the critical rotational frequency and suppresses the vortex formation in the system.