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/0702318 · Physical Review A

Breathing modes of a fast rotating Fermi gas

Mauro Antezza, Marco Cozzini, S. Stringari

Published May 23, 2007• 13 citations
arXivHTMLPDF

Abstract

We derive the frequency spectrum of the lowest compressional oscillations of a three-dimensional harmonically trapped Fermi superfluid in the presence of a vortex lattice, treated in the diffused vorticity approximation within a hydrodynamic approach. We consider the general case of a superfluid at $T=0$ characterized by a polytropic equation of state $(\ensuremath{\sim}{n}^{\ensuremath{\gamma}})$, which includes both the Bose-Einstein condensed regime of dimers $(\ensuremath{\gamma}=1)$ and the unitary limit of infinite scattering length $(\ensuremath{\gamma}=2∕3)$. Important limiting cases are considered, including the centrifugal limit, the isotropic trapping, and the cigar geometry. The conditions required to enter the lowest Landau level and quantum Hall regimes at unitarity are also discussed.

DOI
10.1103/physreva.75.053609

Related papers

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

Tkachenko modes in a superfluid Fermi gas at unitarity

Gentaro Watanabe A, Marco Cozzini, S. Stringari

We calculate the frequencies of the Tkachenko oscillations of a vortex lattice in a harmonically trapped superfluid Fermi gas. We use the elastohydrodynamic theory and properly account for the elastic constants, the Thomas-Fermi density profile of the atomic cloud, and the boundary conditions. Thanks to the Fermi pressure, which is responsible for larger cloud radii with respect to the case of dilute Bose-Einstein condensed gases, large vortex lattices are achievable in the unitary limit of infinite scattering length, even at relatively small angular velocities. This opens the possibility of experimentally observing vortex oscillations in the regime where the dispersion relation approaches the Tkachenko law for incompressible fluids and the mode frequency is almost comparable to the trapping frequencies.

arXiv:0709.2757•Physical Review A•Feb 7, 2008•3 citations

Collective oscillations of a trapped superfluid Fermi gas near a Feshbach resonance

S. Stringari

The frequencies of the collective oscillations of a harmonically trapped Fermi gas interacting with large scattering lengths are calculated at zero temperature using hydrodynamic theory. Different regimes are considered, including the molecular Bose-Einstein condensate and the unitarity limit for collisions. We show that the frequency of the radial compressional mode in an elongated trap exhibits a pronounced non-monotonous dependence on the scattering length, reflecting the role of the interactions in the equation of state.

arXiv:cond-mat/0312614•Europhysics Letters (EPL)•Mar 1, 2004•116 citations

Collective oscillations of a trapped quantum gas in low dimensions

Giulia De Rosi, S. Stringari

We present a comprehensive study of the discretized modes of an atomic gas in different conditions of confinement. Starting from the equations of hydrodynamics we derive a closed equation for the velocity field, depending on the adiabatic and isothermal compressibilities and applicable to different dimensions and quantum statistics. At zero temperature the equation reproduces the irrotational behavior of superfluid hydrodynamics. It is also applicable above the critical temperature in the collisional regime, where the appearance of rotational components in the velocity field is caused by the external potential. In the presence of harmonic trapping, a general class of analytic solutions is obtained for systems exhibiting a polytropic equation of state, characterized by a power law isoentropic dependence of the pressure on the density. Explicit results for the compressional modes are derived for both Bose and Fermi gases in the pancake and cigar as well as in the deep two- and one-dimensional regimes. Our results agree with the analytical predictions available in the literature in some limiting cases. They are particularly relevant in one-dimensional configurations, where the study of the collective frequencies could provide a unique test of the achievement of the collisional regime at finite temperature.

arXiv:1507.07821•Physical Review A•Nov 18, 2015•37 citations

Breathing mode of rapidly rotating Bose-Einstein condensates

Gentaro Watanabe A

We show that the breathing mode of a rapidly rotating, harmonically trapped Bose-Einstein condensate may be described by a generalized lowest Landau level (LLL) wave function, in which the oscillator length is treated as a variable. Using this wave function in a variational Lagrangian formalism, we show that the frequency of the breathing mode for a two-dimensional cloud is $2{\ensuremath{\omega}}_{\ensuremath{\perp}}$, where ${\ensuremath{\omega}}_{\ensuremath{\perp}}$ is the trap frequency. We also study large-amplitude oscillations and confirm that the above result is not limited to linear oscillations. The resulting mode frequency can be understood in terms of orbits of a single particle in a harmonic trap. The mode frequency is also calculated for a cloud in three dimensions and the result for the axial breathing mode frequency agrees with recent experimental data in the rapid rotation regime.

arXiv:cond-mat/0506331•Physical Review A•Jan 19, 2006•10 citations

Collective Modes in a Unitary Fermi Gas across the Superfluid Phase Transition

Meng Khoon Tey, Leonid A. Sidorenkov, Edmundo R. Sánchez Guajardo +6 more

We provide a joint theoretical and experimental investigation of the temperature dependence of the collective oscillations of first sound nature exhibited by a highly elongated harmonically trapped Fermi gas at unitarity, including the region below the critical temperature for superfluidity. Differently from the lowest axial breathing mode, the hydrodynamic frequencies of the higher-nodal excitations show a temperature dependence, which is calculated starting from Landau two-fluid theory and using the available experimental knowledge of the equation of state. The experimental results agree with high accuracy with the predictions of theory and provide the first evidence for the temperature dependence of the collective frequencies near the superfluid phase transition.

arXiv:1211.2659•Physical Review Letters•Jan 29, 2013•67 citations
We derive the frequency spectrum of the lowest compressional oscillations of a three-dimensional harmonically trapped Fermi superfluid in the presence of a vortex lattice, treated in the diffused vorticity approximation within a hydrodynamic approach. We consider the general case of a superfluid at T=0T=0T=0 characterized by a polytropic equation of state (\ensuremath∼n\ensuremathγ)(\ensuremath{\sim}{n}^{\ensuremath{\gamma}})(\ensuremath∼n\ensuremathγ), which includes both the Bose-Einstein condensed regime of dimers (\ensuremathγ=1)(\ensuremath{\gamma}=1)(\ensuremathγ=1) and the unitary limit of infinite scattering length (\ensuremathγ=2∕3)(\ensuremath{\gamma}=2∕3)(\ensuremathγ=2∕3). Important limiting cases are considered, including the centrifugal limit, the isotropic trapping, and the cigar geometry. The conditions required to enter the lowest Landau level and quantum Hall regimes at unitarity are also discussed.
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 calculate the frequencies of the Tkachenko oscillations of a vortex lattice in a harmonically trapped superfluid Fermi gas. We use the elastohydrodynamic theory and properly account for the elastic constants, the Thomas-Fermi density profile of the atomic cloud, and the boundary conditions. Thanks to the Fermi pressure, which is responsible for larger cloud radii with respect to the case of dilute Bose-Einstein condensed gases, large vortex lattices are achievable in the unitary limit of infinite scattering length, even at relatively small angular velocities. This opens the possibility of experimentally observing vortex oscillations in the regime where the dispersion relation approaches the Tkachenko law for incompressible fluids and the mode frequency is almost comparable to the trapping frequencies.
The frequencies of the collective oscillations of a harmonically trapped Fermi gas interacting with large scattering lengths are calculated at zero temperature using hydrodynamic theory. Different regimes are considered, including the molecular Bose-Einstein condensate and the unitarity limit for collisions. We show that the frequency of the radial compressional mode in an elongated trap exhibits a pronounced non-monotonous dependence on the scattering length, reflecting the role of the interactions in the equation of state.
We present a comprehensive study of the discretized modes of an atomic gas in different conditions of confinement. Starting from the equations of hydrodynamics we derive a closed equation for the velocity field, depending on the adiabatic and isothermal compressibilities and applicable to different dimensions and quantum statistics. At zero temperature the equation reproduces the irrotational behavior of superfluid hydrodynamics. It is also applicable above the critical temperature in the collisional regime, where the appearance of rotational components in the velocity field is caused by the external potential. In the presence of harmonic trapping, a general class of analytic solutions is obtained for systems exhibiting a polytropic equation of state, characterized by a power law isoentropic dependence of the pressure on the density. Explicit results for the compressional modes are derived for both Bose and Fermi gases in the pancake and cigar as well as in the deep two- and one-dimensional regimes. Our results agree with the analytical predictions available in the literature in some limiting cases. They are particularly relevant in one-dimensional configurations, where the study of the collective frequencies could provide a unique test of the achievement of the collisional regime at finite temperature.
We show that the breathing mode of a rapidly rotating, harmonically trapped Bose-Einstein condensate may be described by a generalized lowest Landau level (LLL) wave function, in which the oscillator length is treated as a variable. Using this wave function in a variational Lagrangian formalism, we show that the frequency of the breathing mode for a two-dimensional cloud is $2{\ensuremath{\omega}}_{\ensuremath{\perp}}$, where ${\ensuremath{\omega}}_{\ensuremath{\perp}}$ is the trap frequency. We also study large-amplitude oscillations and confirm that the above result is not limited to linear oscillations. The resulting mode frequency can be understood in terms of orbits of a single particle in a harmonic trap. The mode frequency is also calculated for a cloud in three dimensions and the result for the axial breathing mode frequency agrees with recent experimental data in the rapid rotation regime.
We provide a joint theoretical and experimental investigation of the temperature dependence of the collective oscillations of first sound nature exhibited by a highly elongated harmonically trapped Fermi gas at unitarity, including the region below the critical temperature for superfluidity. Differently from the lowest axial breathing mode, the hydrodynamic frequencies of the higher-nodal excitations show a temperature dependence, which is calculated starting from Landau two-fluid theory and using the available experimental knowledge of the equation of state. The experimental results agree with high accuracy with the predictions of theory and provide the first evidence for the temperature dependence of the collective frequencies near the superfluid phase transition.