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Register a new userFinite temperature effective field theory for dark solitons in superfluid Fermi gases
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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 accross 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. In the strong-coupling regime and/or for sufficiently high temperatures, the obtained analytic solutions match well the numeric results obtained using the Bogoliubov - de Gennes equations.
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In this work dark soliton collisions in a one-dimensional superfluid Fermi gas are studied across the BEC-BCS crossover by means of a recently developed finite-temperature effective field theory [S. N. Klimin, J. Tempere, G. Lombardi, J. T. Devreese, Eur. Phys. J. B 88, 122 (2015)] . The evolution of two counter-propagating solitons is simulated numerically based on the theorys nonlinear equation of motion for the pair field. The resulting collisions are observed to introduce a spatial shift into the trajectories of the solitons. The magnitude of this shift is calculated and studied in different conditions of temperature and spin-imbalance. When moving away from the BEC-regime, the collisions are found to become inelastic, emitting the lost energy in the form of small-amplitude density oscillations. This inelasticity is quantified and its behavior analyzed and compared to the results of other works. The dispersion relation of the density oscillations is calculated and is demonstrated to show a good agreement with the spectrum of collective excitations of the superfluid.
Dark solitons in superfluid Bose gases decay through the snake instability mechanism, unless they are strongly confined. Recent experiments in superfluid Fermi gases have also interpreted soliton decay via this mechanism. However, we show using both an effective field numerical simulation and a perturbative analysis that there is a qualitative difference between soliton decay in the BEC- and BCS-regimes. On the BEC-side of the interaction domain, the characteristic snaking deformations are induced by fluctuations of the amplitude of the order parameter, while on the BCS-side, fluctuations of the phase destroy the soliton core through the formation of local Josephson currents. The latter mechanism is qualitatively different from the snaking instability and this difference should be experimentally detectable.
We use the time-dependent Bogoliubov de Gennes equations to study dark solitons in three-dimensional spin-imbalanced superfluid Fermi gases. We explore how the shape and dynamics of dark solitons are altered by the presence of excess unpaired spins which fill their low-density core. The unpaired particles broaden the solitons and suppress the transverse snake instability. We discuss ways of observing these phenomena in cold atom experiments.
The recent experimental realization of Bose-Fermi superfluid mixtures of dilute ultracold atomic gases has opened new perspectives in the study of quantum many-body systems. Depending on the values of the scattering lengths and the amount of bosons and fermions, a uniform Bose-Fermi mixture is predicted to exhibit a fully mixed phase, a fully separated phase or, in addition, a purely fermionic phase coexisting with a mixed phase. The occurrence of this intermediate configuration has interesting consequences when the system is nonuniform. In this work we theoretically investigate the case of solitonic solutions of coupled Bogoliubov-de Gennes and Gross-Pitaevskii equations for the fermionic and bosonic components, respectively. We show that, in the partially separated phase, a dark soliton in Fermi superfluid is accompanied by a broad bosonic component in the soliton, forming a dark-bright soliton which keeps full spatial coherence.
Studying the collective pairing phenomena in a two-component Fermi gas, we predict the appearance near the transition temperature $T_c$ of a well-resolved collective mode of quadratic dispersion. The mode is visible both above and below $T_c$ in the systems response to a driving pairing field. When approaching $T_c$ from below, the phononic and pair-breaking branches, characteristic of the zero temperature behavior, reduce to a very low energy-momentum region when the pair correlation length reaches its critical divergent behavior $xi_{rm pair}propto|T_c-T|^{-1/2}$; elsewhere, they are replaced by the quadratically-dispersed pairing resonance, which thus acts as a precursor of the phase transition. In the strong-coupling and Bose-Einstein Condensate regime, this mode is a weakly-damped propagating mode associated to a Lorentzian resonance. Conversely, in the BCS limit it is a relaxation mode of pure imaginary eigenenergy. At large momenta, the resonance disappears when it is reabsorbed by the lower-edge of the pairing continuum. At intermediate temperatures between 0 and $T_c$, we unify the newly found collective phenomena near $T_c$ with the phononic and pair-breaking branches predicted from previous studies, and we exhaustively classify the roots of the analytically continued dispersion equation, and show that they provided a very good summary of the pair spectral functions.
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