Contributor info: Prof. Joachim Brand

Ulrich Ebling, Ulrich Zülicke, Joachim Brand

SciPost Phys. 12, 167 (2022) · published 19 May 2022 | Toggle abstract · pdf

We theoretically study spin-$1/2$ fermions confined to two spatial dimensions and experiencing isotropic short-range attraction in the presence of both spin-orbit coupling and Zeeman spin splitting - a prototypical system for developing topological superfluidity in the many-body sector. Exact solutions for two-particle bound states are found to have a triplet contribution that dominates over the singlet part in an extended region of parameter space where the combined Zeeman- and center-of-mass-motion-induced spin-splitting energy is large. The triplet character of dimers is purest in the regime of weak $s$-wave interaction strength. Center-of-mass momentum is one of the parameters determining the existence of bound states, which we map out for both two- and one-dimensional types of spin-orbit coupling. Distinctive features emerging in the orbital part of the bound-state wave function, including but not limited to its $p$-wave character, provide observable signatures of unconventional pairing.

Joachim Brand, Lauri A. Toikka, Ulrich Zuelicke

SciPost Phys. 5, 016 (2018) · published 15 August 2018 | Toggle abstract · pdf

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.

Sophie S. Shamailov, Joachim Brand

SciPost Phys. 4, 018 (2018) · published 31 March 2018 | Toggle abstract · pdf

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.