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arXiv:0805.3870 · Physical Review A

Stability of the density-wave state of a dipolar condensate in a pancake-shaped trap

Omjyoti Dutta, Rina Kanamoto, Pierre Meystre

Published Oct 13, 2008• 6 citations
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Abstract

We study a dipolar boson-fermion mixture in a pancake-shaped geometry at absolute zero temperature, generalizing our previous work on the stability of polar condensates and the formation of a density-wave state in cylindrical traps. After examining the dependence of the polar condensate stability on the strength of the fermion-induced interaction, we determine the transition point from a ground-state Gaussian to a hexagonal density-wave state. We use a variational principle to analyze the stability properties of those density-wave state.

DOI
10.1103/physreva.78.043608

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We study a dipolar boson-fermion mixture in a pancake-shaped geometry at absolute zero temperature, generalizing our previous work on the stability of polar condensates and the formation of a density-wave state in cylindrical traps. After examining the dependence of the polar condensate stability on the strength of the fermion-induced interaction, we determine the transition point from a ground-state Gaussian to a hexagonal density-wave state. We use a variational principle to analyze the stability properties of those density-wave state.
Using mean-field theory, we study the equilibrium properties of boson-fermion mixtures confined in a harmonic pancake-shaped trap at zero temperature. When the modulus of the sss-wave scattering lengths are comparable to the mixture thickness, two-dimensional scattering events introduce a logarithmic dependence on density in the coupling constants, greatly modifying the density profiles themselves. We show that, for the case of a negative boson-fermion three-dimensional sss-wave scattering length, the dimensional crossover stabilizes the mixture against collapse and drives it toward spatial demixing.
Trapped degenerate dipolar Bose and Fermi gases of the cylindrical symmetry with the polarization vector along the symmetry axis are only stable for the strength of dipolar interaction below a critical value. In the case of bosons, the stability of such a dipolar Bose–Einstein condensate (BEC) is investigated for different strengths of contact and dipolar interactions using a variational approximation and a numerical solution of a mean-field model. In the disc shape, with the polarization vector perpendicular to the plane of the disc, the atoms experience an overall dipolar repulsion and this fact should contribute to the stability. However, a complete numerical solution of the dynamics leads to the collapse of a strongly disc-shaped dipolar BEC due to the long-range anisotropic dipolar interaction. In the case of fermions, the stability of a trapped single-component degenerate dipolar Fermi gas is studied including the Hartree–Fock exchange and Brueckner–Goldstone correlation energies in the local-density approximation valid for a large number of atoms. Estimates for the maximum allowed number of polar Bose and Fermi molecules in the BEC and degenerate Fermi gas are given.
We evaluate in a mean-field model the equilibrium stability conditions of a gaseous mixture of bosonic and spin-polarized fermionic atoms inside a pancake-shaped or a cigar-shaped harmonic trap, under conditions such that the trap thickness approaches the magnitude of the s -wave scattering lengths but the atoms still experience collisions in three dimensions. With decreasing dimensionality, the Fermi pressure plays an increasingly dominant role. Full demixing in the case of repulsive boson-fermion interactions can be induced by squeezing the thickness of the clouds in a pancake-shaped trap or by lowering the number of trapped fermions in a cigar-shaped trap. Collapse under attractive interspecies interaction in quasi-one-dimensional confinement is inhibited within the range of validity of a mean-field model.