Bound states in a superfluid vortex: A detailed study along the BCS-BEC crossover

Abstract

The bound states that can occur in a superfluid vortex have recently called for attention owing to the capability of detecting them experimentally. However, a detailed theoretical account for the presence of these vortex bound states is still lacking, for all temperatures in the superfluid phase and couplings along the BCS-BEC crossover. Here, we fill this gap and present a systematic theoretical study based on the Bogoliubov-de Gennes equations for the bound states that occur over the two characteristic (inner and outer) spatial ranges in which the extension of a superfluid vortex can be partitioned. It is found that the total number of bound states decreases from the BCS (weak-coupling) side of the crossover toward the intermediate-coupling region where they are still present, whereas the bound states disappear upon entering the BEC (strong-coupling) side. A scaling relation is also obtained that connects the number of bound states in the inner spatial range of the vortex to the depth and width of the vortex itself. A criterion is finally provided in terms of the local density of states, to distinguish where a given fermionic superfluid is located in the coupling-temperature phase diagram of the BCS-BEC crossover.arXiv:1904.03883v1 [cond-mat.supr-con]

Dissipative dynamics of quantum vortices in fermionic superfluid

“…This formula works reasonably well in the entire BCS-UFG range, taking that ∆/ε F ≈ 8 e 2 exp(−π/2|a s k F |) for the BCS and ∆/ε F ≈ 0.5 for the UFG regimes [18]. The number of Andreev states (below the energy gap) scales as N A ∼ |∆|/E mg , and clearly it increases exponentially as we move towards deep BCS limit, see also [33]. Thus the vortices in the BCS regime host more matter inside as compared to UFG limit, compare vortex profiles presented in Fig.…”

Vortex lattice in spin-imbalanced unitary Fermi gas

“…Similar argumentation also applies to particles trapped in the vicinity of nodal lines associated with the FFLO state. In the case of slow ramps from the resonance to the molecular limit, it can be assumed that the process is adiabatic and then the results of static calculations as presented in [66] may be applicable. In such a case information about the initial vortex structure will be also lost.…”