Finite temperature effective field theory and two-band superfluidity in Fermi gases

Abstract

We develop a description of fermionic superfluids in terms of an effective field theory for the pairing order parameter. Our effective field theory improves on the existing Ginzburg -Landau theory for superfluid Fermi gases in that it is not restricted to temperatures close to the critical temperature. This is achieved by taking into account long-range fluctuations to all orders. The results of the present effective field theory compare well with the results obtained in the framework of the Bogoliubov -de Gennes method. The advantage of an effective field theory over Bogoliubov -de Gennes calculations is that much less computation time is required. In the second part of the paper, we extend the effective field theory to the case of a two-band superfluid. The present theory allows us to reveal the presence of two healing lengths in the two-band superfluids, to analyze the finite-temperature vortex structure in the BEC-BCS crossover, and to obtain the ground state parameters and spectra of collective excitations. For the Leggett mode our treatment provides an interpretation of the observation of this mode in two-band superconductors.

Collective modes in a two-band superfluid of ultracold alkaline-earth-metal atoms close to an orbital Feshbach resonance

“…In particular, it is no longer admissible to treat the closed channel state as a single boson without taking into account of its proper internal dynamics. One is thus lead to a situation much the same as a two-band superconductor, where the appropriate picture is that two Fermi surfaces (including both spin) intersect the chemical potential [18][19][20]. We show that this new situation leads to the appearance of new collective modes and in particular, the long-sought Leggett mode in the two-band superconductor.…”

Dark soliton collisions in superfluid Fermi gases

“…Hence, results found in this regime should be treated with additional caution. A second remark that must be made is that in the full version of the EFT, as it was introduced in [21], the action functional (1) contains additional terms that result in terms with second order time derivatives (SOTDs) of the pair field in the equation of motion (9) (with a form similar to the terms for the spatial derivatives). While it would in principle be better to use the full SOTD model, we found that numerical SOTD simulations of soliton-soliton collisions exhibit inherent instabilities in a large area of the parameter domain.…”

“…In order to obtain the corresponding dispersion relation ω(q), we determine the wavelength λ i (measured as the distance between two consecutive peaks) and the velocity v i of each matter wave and apply the relations q i =2π / λ i and ω i =q i v i . The resulting dispersion of the oscillations can then be compared to the spectrum ω s (q) of the collective excitations of the superfluid, which in the context of the present EFT is determined by calculating the poles of the inverse propagator for the bosonic fluctuations [21]. Up to fourth order in q, this leads to the form…”

Verification of an analytic fit for the vortex core profile in superfluid Fermi gases

“…Consequently the use of the BdG theory is mainly limited to the consideration of zero-temperature properties of single-vortex states [10][11][12] . Because of this big computational cost of the BdG theory, there is a recent interest in the development of effective field theories [20][21][22][23][24][25][26] . These effective field theories allow for a description of non-uniform excitations (e.g.…”