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.
Cited by 4
I. Morera et al., Dark-dark-soliton dynamics in two density-coupled Bose-Einstein condensates
Phys. Rev. A 97, 043621 (2018) [Crossref]
Christian Baals et al., Nonlinear standing waves in an array of coherently coupled Bose-Einstein condensates
Phys. Rev. A 98, 053603 (2018) [Crossref]
J A Gil Granados et al., Transverse Josephson vortices and localized states in stacked Bose–Einstein condensates
New J. Phys. 21, 043036 (2019) [Crossref]
Sophie S. Shamailov et al., Quantum dark solitons in the one-dimensional Bose gas
Phys. Rev. A 99, 043632 (2019) [Crossref]
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- Marsden Fund (through Organization: Royal Society Te Apārangi / Royal Society of New Zealand)
- Massey University