Quasiparticles of widely tuneable inertial mass: The dispersion relation of atomic Josephson vortices and related solitary waves

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.

Nonlinear standing waves in an array of coherently coupled Bose-Einstein condensates

“…Let us first consider the case of M = 2 coupled BECs, which has already been studied extensively [11,18,22]. Let us write the stationary coupled GPEs explicitly…”

“…A linear stability analysis reveals that the dark soliton stack (for M = 2) is dynamically stable in the regime where the Josephson vortex solutions do not exist (ν > gn/4) but dynamically unstable for 0 <ν < gn/4, where they are subject to decay into stable Josephson vortices [11,18,22]. In the absence of coherent coupling, atν = 0, and atν = gn/4, dark solitons are marginally stable, i.e.…”

“…The models used to describe coupled 1D BECs start from two linearly coupled Gross-Pitaevskii equations (GPEs) [11], or a coupled Luttinger-liquid model [21]. In the small coupling limit, a sine-Gordon model for the relative phase of the two condensates can be derived where the Josephson vortex becomes a sine-Gordon soliton [11,21,22]. Recently the full dispersion relation of moving Josephson vortices and related solitary excitations in the more general coupled Gross-Pitaevksii model has been found [22].…”

“…In the small coupling limit, a sine-Gordon model for the relative phase of the two condensates can be derived where the Josephson vortex becomes a sine-Gordon soliton [11,21,22]. Recently the full dispersion relation of moving Josephson vortices and related solitary excitations in the more general coupled Gross-Pitaevksii model has been found [22]. Closely related oscillon excitations, which can be understood as long-lived bound states of Josephson vortices were described in Ref.…”

Transverse Josephson vortices and localized states in stacked Bose–Einstein condensates

“…By keeping them, we highlight the correspondence with a sine-Gordon-like equation, where kink solutions can be found [2]. As a limiting case, the kink-type solutions have demonstrated to be useful in the search of solitonic states in the nonlinear dynamics of two-component condensates [13,14,17,18,35].…”