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Laser Physics

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

Published Mar 10, 2010• 6 citations
Publisher

Abstract

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.

DOI
10.1134/s1054660x10070212

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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.
We study theoretically the collective mode spectrum of a strongly imbalanced two-component unitary Fermi gas in a cigar-shaped trap, where the minority species forms a gas of polarons. We describe the collective breathing mode of the gas in terms of the Fermi-liquid kinetic equation taking collisions into account using the method of moments. Our results for the frequency and damping of the longitudinal in-phase breathing mode are in good quantitative agreement with an experiment by Nascimb\`ene et al. [Phys. Rev. Lett. 103, 170402 (2009)] and interpolate between a hydrodynamic and a collisionless regime as the polarization is increased. A separate out-of phase breathing mode, which for a collisionless gas is sensitive to the effective mass of the polaron, however, is strongly damped at finite temperature, whereas the experiment observes a well-defined oscillation.
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.
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.
We have investigated collective breathing modes of a unitary Fermi gas in deformed harmonic traps. The ground state is studied by the superfluid local density approximation (SLDA) and small-amplitude collective modes are studied by the iterative quasiparticle random phase approximation (QRPA). The results illustrate the evolutions of collective modes of a small system in traps from spherical to elongated or pancake-shaped deformations. For small spherical systems, the influences of different SLDA parameters are significant, and, in particular, a large pairing strength can shift up the oscillation frequency of collective modes. The transition currents from QRPA show that the compressional flow patterns are nontrivial and dependent on the deformation. Finally, the finite-size effects are demonstrated to be reasonable when progressing towards larger systems. The hydrodynamical results of collective frequencies can be reproduced by SLDA-QRPA with reduced pairing strengths. Our studies indicate that experiments on small and medium systems are valuable for understanding effective interactions in systems with varying sizes and trap deformations.
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.
Quasi-one-dimensional two-component Fermi gases with effectively attractive and repulsive interactions are characterized for arbitrary interaction strength. The ground-state properties of the gas confined in highly elongated harmonic traps are determined within the local density approximation. For strong attractive effective interactions the existence of a molecular Tonks-Girardeau gas is predicted. The frequency of the lowest breathing mode is calculated as a function of the coupling strength for both attractive and repulsive interactions.