Crossover between snake instability and Josephson instability of dark solitons in superfluid Fermi gases

Abstract

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. * wout.vanalphen@uantwerpen.be arXiv:1901.10751v1 [cond-mat.quant-gas]

Signatures of the BCS-BEC crossover in the yrast spectra of Fermi quantum rings

“…This indicates a further change to the properties of the system, likely a transition from a soliton state to a vortex pair. This scenario is closely related to the snaking instability of a planar dark soliton in a two-dimensional superfluid, where the soliton decays into pairs of oppositely charged vortices as the system becomes wide enough [41,68,70]. However, we cannot directly show a potential density depression caused by the soliton.…”

“…We find an increase of the inertial mass by a factor of 2 when the transverse dimension is large enough for the system to be considered truly 2D, which is indica-tive of a transition from dark soliton to a solitonic vortex [67,68]. From mean-field and basic hydrodynamic theory, in the 1D to 2D crossover dark solitons are replaced as stable yrast excitations by solitonic vortices [68,69], or vortex pairs [41,70], which have larger inertial mass [34,71,72]. By looking at the pair densities of these yrast states, we find that fragmented condensation into more than one momentum state takes place, as expected for superfluid yrast states [28].…”

Splitting instability of a doubly quantized vortex in superfluid Fermi gases

“…The fact that the core mode doesn't seem to interact with the phonon modes at all implies that some other kind of mechanism induces the instability here. Analytically, we find that, in the deep BCS-regime, where the coefficients Q and R become large and the coefficient D can be neglected [32], the linear equations ( 5) and ( 6) can be reduced to a Schrödinger-like equation with eigenvalue ω 2 . The core mode then plays the role of a bound state of the potential created by the vortex profile, and the instability is induced solely by the core mode with ω 2 < 0.…”

Vortices in Fermi gases with spin-dependent rotation potentials

“…In this Appendix, a summarized discussion of the EFT is presented. More details on the EFT can be found in [27][28][29][30][31]47] + i D(r)…”

“…For a consistent treatment, some care should be taken as the coefficients C(r), E (r), D(r), and U (r) in front of these terms themselves depend on ω σ and (r). In the coefficients C(r) and E (r), the bosonic field (r) is replaced by the uniform background amplitude solution ∞ , as using (r) would provide a gradient contribution to the kinetic energy beyond second order [47]. Furthermore, the ω σ dependence effectively corresponds to contributions that are at least of the order of ω σ |∇ | 2 , which were explicitly neglected during the derivation.…”