https://doi.org/10.1140/epjd/e20020086
Splitting between quadrupole modes of dilute quantum gas in a two-dimensional anisotropic trap
1
The Institute of Mathematical Sciences, C.I.T. Campus, Chennai 600 113, India
2
Laboratorie Kastler-Brossel, 24 rue Lhomond, 75005 Paris, France
Corresponding author: a tkghosh@imsc.ernet.in
Received:
21
September
2001
Revised:
9
December
2001
Published online: 15 June 2002
We consider quadrupole excitations of quasi-two-dimensional interacting quantum gas in an anisotropic harmonic oscillator potential at zero temperature. Using the time-dependent variational approach, we calculate a few low-lying collective excitation frequencies of a two-dimensional anisotropic Bose gas. Within the energy weighted sum-rule approach, we derive a general dispersion relation of two quadrupole excitations of a two-dimensional deformed trapped quantum gas. This dispersion relation is valid for both statistics. We show that the quadrupole excitation frequencies obtained from both methods are exactly the same. Using this general dispersion relation, we also calculate the quadrupole frequencies of a two-dimensional unpolarized Fermi gas in an anisotropic trap. For both cases, we obtain analytic expressions for the quadrupole frequencies and the splitting between them for arbitrary value of trap deformation. This splitting decreases with increasing interaction strength for both statistics. For a two-dimensional anisotropic Fermi gas, the two quadrupole frequencies and the splitting between them become independent of the particle number within the Thomas-Fermi approach.
PACS: 03.75.Fi – Phase coherent atomic ensembles; quantum condensation phenomena / 05.30.Jp – Boson systems
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002