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Communications in Theoretical Physics

Superfluid Fermi Gases in a Rotating Anharmonic Trap

Juan Ma, Ju-Kui Xue

Published Mar 1, 2011• 5 citations
Publisher

Abstract

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.

DOI
10.1088/0253-6102/55/3/13

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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.
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.
We study a rotating atomic Fermi gas near a narrow sss-wave Feshbach resonance in a uniaxial trap with frequencies ${\ensuremath{\Omega}}_{\ensuremath{\perp}}$, ${\ensuremath{\Omega}}_{z}$. We predict the upper-critical angular velocity, ${\ensuremath{\omega}}_{c2}(\ensuremath{\delta},T)$, as a function of temperature TTT and detuning $\ensuremath{\delta}$ across the BEC-BCS crossover. The suppression of superfluidity at ${\ensuremath{\omega}}_{c2}$ is distinct in the BCS and BEC regimes, with the former controlled by depairing and the latter by the dilution of bosonic molecules. At low TTT and ${\ensuremath{\Omega}}_{z}\ensuremath{\ll}{\ensuremath{\Omega}}_{\ensuremath{\perp}}$, in the BCS and crossover regimes of $0\ensuremath{\lesssim}\ensuremath{\delta}\ensuremath{\lesssim}{\ensuremath{\delta}}_{c}$, ${\ensuremath{\omega}}_{c2}$ is implicitly given by $\ensuremath{\hbar}\sqrt{{\ensuremath{\omega}}_{c2}^{2}+{\ensuremath{\Omega}}_{\ensuremath{\perp}}^{2}}\ensuremath{\approx}2\ensuremath{\Delta}\sqrt{\ensuremath{\hbar}{\ensuremath{\Omega}}_{\ensuremath{\perp}}/{ϵ}_{F}}$, vanishing as ${\ensuremath{\omega}}_{c2}\ensuremath{\sim}{\ensuremath{\Omega}}_{\ensuremath{\perp}}(1\ensuremath{-}\ensuremath{\delta}/{\ensuremath{\delta}}_{c}{)}^{1/2}$ near ${\ensuremath{\delta}}_{c}\ensuremath{\approx}2{ϵ}_{F}+\frac{\ensuremath{\gamma}}{2}{ϵ}_{F}\mathrm{ln}({ϵ}_{F}/\ensuremath{\hbar}{\ensuremath{\Omega}}_{\ensuremath{\perp}})$ (with $\ensuremath{\Delta}$ the BCS gap and $\ensuremath{\gamma}$ the resonance width), and extending the bulk result $\ensuremath{\hbar}{\ensuremath{\omega}}_{c2}\ensuremath{\approx}2{\ensuremath{\Delta}}^{2}/{ϵ}_{F}$ to a trap. In the BEC regime of $\ensuremath{\delta}<0$ we find ${\ensuremath{\omega}}_{c2}\ensuremath{\rightarrow}{\ensuremath{\Omega}}_{\ensuremath{\perp}}^{\ensuremath{-}}$, where molecular superfluidity is destroyed only by large quantum fluctuations associated with comparable boson and vortex densities.
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 report the equilibrium vortex phase diagram of a rotating two-band Fermi gas confined to a cylindrically symmetric parabolic trapping potential, using the recently developed finite-temperature effective field theory (Klimin et al 2016 Phys. Rev. A 94 023620). A non-monotonic resonant dependence of the free energy as a function of the temperature and the rotation frequency is revealed for a two-band superfluid. We particularly focus on novel features that appear as a result of interband interactions and can be experimentally resolved. The resonant dependence of the free energy is directly manifested in vortex phase diagrams, where areas of stability for both integer and fractional vortex states are found. The study embraces the BCS–BEC crossover regime and the entire temperature range below the critical temperature T c . Significantly different behavior of vortex matter as a function of the interband coupling is revealed in the BCS and BEC regimes.
We investigate the ground state and quadrupole excitations of an anisotropically trapped Fermi superfluid gas with arbitrary number of atoms in the BCS–BEC crossover based on a time-dependent variational model. A variational trial wavefunction is used to enable an analytical treatment that covers the whole crossover regime. A correct prefactor is validly considered in the power-law equation of state. Then we focus on three quadrupole modes in different cylindrical symmetric traps which correspond to quasi-one-, quasi-two- and three-dimensional (Q1D, Q2D and 3D) superfluids. We note that the contribution to oscillation frequencies by the quantum pressure cannot be neglected and the excitation frequencies in strong confinement direction are much larger than that in the weak confinement direction both in the Q1D and in Q2D cases. The results are compared with the recent experimental and numerical data. Finally, we discuss the free expansion of the condensate.