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arXiv:0804.0782 · Annals of Physics

Collective modes in asymmetric ultracold Fermi systems

Elena Gubankova, Massimo Mannarelli, Rishi Sharma

Published May 11, 2010• 8 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2010.05.001

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Abstract We describe the effects of spin–orbit (SO) coupling on the collective properties of a two-dimensional (2D) ultracold Fermi gas with Rashba and Dresselhaus SO couplings of equal strength. We first analyse the thermodynamics of the Fermi gas in the absence of repulsive interaction between the atoms (non-interacting system) showing that SO coupling determines one or more second-order phase transitions in the equation of state of the system; we subsequently suggest an experimental strategy that can make these transitions visible. We then study the interacting system using Feynman’s path integral formulation. The aim of this analysis is to describe the collective properties of the system in the paramagnetic phase and in weak non-equilibrium conditions. Particular emphasis is given to the numerical analysis of the collective modes of the system, in particular to the zero sound mode and to the spin modes.
Low-energy theory of the Nambu-Goldstone modes of an ultracold 6Li−^6Li-6Li− 40K^{40}K40K mixture in an optical lattice
A low-energy theory of the Nambu-Goldstone excitation spectrum and the corresponding speed of sound of an interacting Fermi mixture of Lithium-6 and Potassium-40 atoms in a two-dimensional optical lattice at finite temperatures with the Fulde-Ferrell order parameter has been formulated. It is assumed that the two-species interacting Fermi gas is described by the one-band Hubbard Hamiltonian with an attractive on-site interaction. The discussion is restricted to the BCS side of the Feshbach resonance where the Fermi atoms exhibit superfluidity. The quartic on-site interaction is decoupled via a Hubbard-Stratonovich transformation by introducing a four-component boson field which mediates the Hubbard interaction. A functional integral technique and a Legendre transform are used to give a systematic derivation of the Schwinger-Dyson equations for the generalized single-particle Green's function and the Bethe-Salpeter equation for the two-particle Green's function and the associated collective modes. The numerical solution of the Bethe-Salpeter equation in the generalized random phase approximation shows that there exist two distinct sound velocities in the long-wavelength limit. In addition to the long-wavelength mode (Goldstone mode), the two-species Fermi gas has a superfluid phase revealed by two rotonlike minima in the asymmetric collective-mode energy.