Ginzburg-Landau theory of a trapped Fermi gas with a BEC-BCS crossover

Abstract

The Ginzburg-Landau theory of a trapped Fermi gas with a BEC-BCS crossover is derived by the path-integral method. In addition to the standard Ginzburg-Landau equation, a second equation describing the total atom density is obtained. These two coupled equations are necessary to describe both homogeneous and inhomogeneous systems. The Ginzburg-Landau theory is valid near the transition temperature $T_c$ on both sides of the crossover. In the weakly-interacting BEC region, it is also accurate at zero temperature where the Ginzburg-Landau equation can be mapped onto the Gross-Pitaevskii (GP) equation. The applicability of GP equation at finite temperature is discussed. On the BEC side, the fluctuation of the order parameter is studied and the renormalization to the molecule coupling constant is obtained.

16 pages, 2 figures, to be published in PRA

References in corpus (7)

• Vortices and Superfluidity in a Strongly Interacting Fermi Gas
• Observation of the Pairing Gap in a Strongly Interacting Fermi Gas
• Weakly bound dimers of fermionic atoms
• Quantum Fluctuations in the Superfluid State of the BCS-BEC Crossover
• Equation of state of a superfluid Fermi gas in the BCS-BEC crossover
• Broad versus narrow Fano-Feshbach resonances in the BCS-BEC crossover with trapped Fermi atom
• Vortex Properties of a Resonant Superfluid

Cited by in corpus (9)

• Finite temperature effective field theory and two-band superfluidity in Fermi gases
• Finite temperature effective field theory for dark solitons in superfluid Fermi gases
• Snake instability of dark solitons across the BEC-BCS crossover: an effective field theory perspective
• Soliton core filling in superfluid Fermi gases with spin-imbalance
• Time-dependent Ginzburg-Landau theory with floating nucleation kernel; FIR conductivity in the Abrikosov vortex lattice
• Finite temperature vortices in a rotating Fermi gas
• Dynamics of quantum quenching for BCS-BEC systems in the shallow BEC regime
• Nonequilibrium Dynamics of Ultracold Fermi Superfluids
• Reliability of the Ginzburg-Landau Theory in the BCS-BEC Crossover by Including Gaussian Fluctuations for 3D Attractive Fermions