Collective oscillations of a trapped quantum gas in low dimensions

Year: 2015

Authors: De Rosi G., Stringari S.

Autors Affiliation: Univ Trento, INO CNR BEC Ctr, I-38123 Povo, Italy; Univ Trento, Dipartimento Fis, I-38123 Povo, Italy.

Abstract: 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.

Journal/Review: PHYSICAL REVIEW A

Volume: 92 (5)      Pages from: 53617-1  to: 53617-10

More Information: The authors would like to acknowledge fruitful discussions with L. P. Pitaevskii. G. De Rosi wishes to thank also P.-E. Larre, S. Giorgini, and F. Dalfovo for insightful discussions. This work has been supported by ERC through the QGBE grant, by the QUIC grant of the Horizon2020 FET program, and by Provincia Autonoma di Trento.
KeyWords: Bose-einstein Condensate; Tonks-girardeau Gas; Fermi Gases; Scissors Mode; Excitations; Bosons; Superfluidity; System; Atoms
DOI: 10.1103/PhysRevA.92.053617

Citations: 25
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