SciPost Phys. 5, 016 (2018) ·
published 15 August 2018
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The interplay of spin-orbit 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 four-band Bogoliubov-de Gennes formalism for the combined spin-1/2 and particle-hole degrees of freedom. Here we present a simpler, yet accurate, two-band description based on a well-controlled projection technique that provides a new platform for exploring analogies with chiral p-wave superfluidity and detailed future studies of spatially non-uniform situations.
SciPost Phys. 4, 018 (2018) ·
published 31 March 2018
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Superconducting Josephson vortices have direct analogues in ultracold-atom
physics as solitary-wave excitations of two-component superfluid Bose gases
with linear coupling. Here we numerically extend the zero-velocity Josephson
vortex solutions of the coupled Gross-Pitaevskii equations to non-zero
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
low-velocity quasiparticles with negative inertial mass emerge at finite
momentum that are reminiscent of a dark soliton in one component with
counter-flow in the other. In the limit of small linear coupling we compare the
Josephson vortex solutions to sine-Gordon 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 non-zero
self- and cross-component nonlinearities, we find a new solitary-wave
excitation branch. In its presence, both dark solitons and Josephson vortices
are dynamically stable while the new excitations are unstable.
