Abstract
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.
Highlights
The concept of inertial mass [1] is commonly used in condensed matter physics: it captures the response of a quasiparticle in an interacting system to an applied force, encapsulating the emergent Newton’s equations of quasiparticle dynamics
We show that there is a critical value of the linear coupling at which the Josephson vortex dispersion relation changes from having a single maximum to having three extrema: a maximum, minimum and another maximum
Analytical expressions are available for dark solitons, zero-velocity Josephson vortices, and the Manakov solutions for γ = 0
Summary
The concept of inertial (or effective) mass [1] is commonly used in condensed matter physics: it captures the response of a quasiparticle in an interacting system to an applied force, encapsulating the emergent Newton’s equations of quasiparticle dynamics. After the work presented in this paper was completed we became aware of the related recent work by Qu et al [42], which considers Josephson vortices (called magnetic solitons in [42]) in a regime of weak tunneling and almost equal self- and cross-nonlinearities, where the particle number density is approximately constant.. After the work presented in this paper was completed we became aware of the related recent work by Qu et al [42], which considers Josephson vortices (called magnetic solitons in [42]) in a regime of weak tunneling and almost equal self- and cross-nonlinearities, where the particle number density is approximately constant.1 They find analytical and numerical results for solitary wave solutions, their dispersion relations and their dynamics under harmonic trapping. Appendix A presents details of how we perform the stability calculation and appendix B derives the sine-Gordon equation from the Gross-Pitaevskii model, enabling a direct comparison of the two
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
