One- and two-dimensional reductions of the mean-field description of degenerate Fermi gases

Abstract

We study collective behavior of Fermi gases trapped in various external potentials, including optical lattices (OLs), in the framework of the mean-field (hydrodynamic) description. Using the variational method, we derive effective dynamical equations for the one- and two-dimensional (1D and 2D) settings from the general 3D mean-field equation. The respective confinement is provided by trapping potentials with the cylindrical and planar symmetry, respectively. The resulting equations are nonpolynomial Schr% ödinger equations (NPSEs) coupled to equations for the local transverse size of the trapped states. Numerical simulations demonstrate close agreement of results produced by the underlying 3D equation and the effective low-dimensional ones. We consider the ground state in these settings. In particular, analytical solutions are obtained for the effectively 2D non-interacting Fermi gas. Differences between the 1D and 2D configurations are highlighted. Finally, we analyze the dependence of the 1D and 2D density patterns of the trapped gas, in the presence of the OL, on the strengths of the confining and OL potentials, and on the scattering length which determines the strength of interactions between non-identical fermions.

Journal of Physics B, in press

References in corpus (18)

• Many-Body Physics with Ultracold Gases
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Theory of ultracold Fermi gases
• Phase diagram of a strongly interacting polarized Fermi gas in one dimension
• Radiofrequency spectroscopy of a strongly interacting two-dimensional Fermi gas
• An exactly solvable model of the BCS-BEC crossover
• Double-degenerate Bose-Fermi mixture of strontium
• Highly polarized Fermi gases: One-dimensional case
• Tightly bound gap solitons in a Fermi gas
• One-dimensional superfluid Bose-Fermi mixture: mixing, demixing and bright solitons
• Superfluid Fermi-Fermi mixture: phase diagram, stability, and soliton formation
• Effect of interactions on harmonically confined Bose-Fermi mixtures in optical lattices
• Faraday waves in elongated superfluid fermionic clouds
• Mixing-demixing in a trapped degenerate fermion-fermion mixture
• Miscibility in a degenerate fermionic mixture induced by linear coupling
• Canted Antiferromagnetic Order of Imbalanced Fermi-Fermi mixtures in Optical Lattices by Dynamical Mean-Field Theory
• Density profiles of polarized Fermi gases confined in harmonic traps
• Effects of periodic potentials on the critical velocity of superfluid Fermi gases in the BCS-BEC crossover

Cited by in corpus (1)

• Correlations and synchronization in a Bose-Fermi mixture