SciPost Phys. 5, 016 (2018) ·
published 15 August 2018

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The interplay of spinorbit coupling and Zeeman splitting in ultracold Fermi gases gives rise to a topological superfluid phase in two spatial dimensions that can host exotic Majorana excitations. Theoretical models have so far been based on a fourband Bogoliubovde Gennes formalism for the combined spin1/2 and particlehole degrees of freedom. Here we present a simpler, yet accurate, twoband description based on a wellcontrolled projection technique that provides a new platform for exploring analogies with chiral pwave superfluidity and detailed future studies of spatially nonuniform situations.
SciPost Phys. 4, 018 (2018) ·
published 31 March 2018

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Superconducting Josephson vortices have direct analogues in ultracoldatom
physics as solitarywave excitations of twocomponent superfluid Bose gases
with linear coupling. Here we numerically extend the zerovelocity Josephson
vortex solutions of the coupled GrossPitaevskii equations to nonzero
velocities, thus obtaining the full dispersion relation. The inertial mass of
the Josephson vortex obtained from the dispersion relation depends on the
strength of linear coupling and has a simple pole divergence at a critical
value where it changes sign while assuming large absolute values. Additional
lowvelocity quasiparticles with negative inertial mass emerge at finite
momentum that are reminiscent of a dark soliton in one component with
counterflow in the other. In the limit of small linear coupling we compare the
Josephson vortex solutions to sineGordon solitons and show that the
correspondence between them is asymptotic, but significant differences appear
at finite values of the coupling constant. Finally, for unequal and nonzero
self and crosscomponent nonlinearities, we find a new solitarywave
excitation branch. In its presence, both dark solitons and Josephson vortices
are dynamically stable while the new excitations are unstable.