Abstract
We review the study of the superfluid phase transition in a system of fermions whose interaction can be tuned continuously along the crossover from Bardeen–Cooper–Schrieffer (BCS) superconducting phase to a Bose–Einstein condensate (BEC), also in the presence of a spin–orbit coupling. Below a critical temperature the system is characterized by an order parameter. Generally a mean field approximation cannot reproduce the correct behavior of the critical temperature Tc over the whole crossover. We analyze the crucial role of quantum fluctuations beyond the mean-field approach useful to find Tc along the crossover in the presence of a spin–orbit coupling, within a path integral approach. A formal and detailed derivation for the set of equations useful to derive Tc is performed in the presence of Rashba, Dresselhaus and Zeeman couplings. In particular in the case of only Rashba coupling, for which the spin–orbit effects are more relevant, the two-body bound state exists for any value of the interaction, namely in the full crossover. As a result the effective masses of the emerging bosonic excitations are finite also in the BCS regime.
Highlights
Experimental developments in confining, cooling and controlling the strength of the interaction of alkali atoms brought a lot of attention to the physics of the crossover between two fundamental and paradigmatic many-body systems, the Bose–Einstein condensation (BEC) and the Bardeen–Cooper–Schrieffer (BCS) superconductivity.A system of weakly attracting fermions can be treated in the context of the well-known BCS theory [1], originally formulated to describe superconductivity in some materials where an effective attractive interaction between electrons can arise from electron-phonon interaction
The aim of this paper is to review some basic concepts on the BCS-BEC crossover, whose properties will require taking into account quantum fluctuations in order to get a better theoretical predictions when comparing with experimental results [70]
We reviewed the calculations for the critical temperature along the BCS-BEC crossover with and without spin–orbit couplings in the path integral formalism
Summary
Experimental developments in confining, cooling and controlling the strength of the interaction of alkali atoms brought a lot of attention to the physics of the crossover between two fundamental and paradigmatic many-body systems, the Bose–Einstein condensation (BEC) and the Bardeen–Cooper–Schrieffer (BCS) superconductivity. In particular the mechanism of the so-called Feshbach resonance allows one to control the strength of the interaction between two atoms by a magnetic field, for example, making it sufficiently strong to support a new bound state This phenomenon was first predicted and observed experimentally [9,10] in bosonic systems. Soon after these techniques have been extended to create and manipulate ultracold gases for fermionic systems [11,12,13,14] employing atomic alkali gases with two different components, a mixture of atoms in two different spin or pseudospin states, where the quantum degeneracy is reached when lowering the temperature the energy of the system ceases to depend on the temperature In this system by Feshbach resonance the interaction among the atoms can be made sufficiently strong to allow the formation of a two-body bound state, called. We will show how Tc can be strongly enhanced by the SO couplings in the BCS side, already at the mean-field level, while its increase is softened by the effects of the quantum fluctuations specially in the intermediate region of the crossover and in the strong coupling regime
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