Finite-temperature effective field theory for dark solitons in superfluid Fermi gases

Abstract

We use a finite-temperature effective field theory recently developed for superfluid Fermi gases to investigate the properties of dark solitons in these superfluids. Our approach provides an analytic solution for the dip in the order parameter and the phase profile across the soliton, which can be compared with results obtained in the framework of the Bogoliubov-de Gennes equations. We present results in the whole range of the BCS-BEC crossover, for arbitrary temperatures and taking into account Gaussian fluctuations about the saddle point. The obtained analytic solutions yield an exact energy-momentum relation for a dark soliton showing that the soliton in a Fermi gas behaves like a classical particle even at nonzero temperatures. The spatial profile of the pair field and for the parameters of state for the soliton are analytically studied.

Dark soliton collisions in superfluid Fermi gases

“…The functions f j (β, ò, ζ) in the above expressions are defined by is the dispersion relation for a free fermion, x = + Y ( | | ) E k k 2 1 2 is the Bogoliubov excitation energy, and a s is the s-wave scattering length that determines the strength and the sign of the contact interaction. It is important to note that, while both the coefficients C and E in the action functional are kept constant and equal to the value they assume in the uniform system case, the coefficient D and the thermodynamic potential Ω s fully depend upon the order parameter [25]. The regularized real-time Lagrangian density that follows from (1) reads…”

“…The consequent limitations and validity of the EFT are discussed in section 2.2. The theory has already been successfully employed in the description of both stable dark solitons and the snake instability mechanism in different regimes of temperature and population imbalance [25][26][27]. In this work, we use the EFT equation of motion that governs the dynamics of the order parameter to numerically simulate the collision of two solitons in a 1D Fermi superfluid and study the properties of the re-emerging solitons across the BEC-BCS crossover.…”

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

“…The present work for the first time systematically describes the derivation of the finite temperature EFT formalism, which is only briefly represented in Ref. [31], and applies the theory to describe vortex structure in the BCS-BEC crossover.…”

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

“…Consequently, the effective KTD theory [21][22][23] is used in the present work. The effective KTD theory corresponds nicely with the numerical BdG results, except in the deep BCS regime for temperatures far below T C 24 .…”

“…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.…”