Stripe and junction-vortex phases in linearly coupled Bose-Einstein condensates

TL;DR

This paper reveals that stripe phases in linearly coupled Bose-Einstein condensates are caused by Josephson vortex arrays, providing analytical solutions and linking superfluid phenomena to superconducting Josephson junction behavior.

Contribution

It demonstrates that stripe phases result from Josephson vortices in coupled BECs and offers closed-form solutions for these vortex arrays, connecting superfluid and superconducting physics.

Findings

Stripe phases are induced by Josephson vortex arrays.

Analytical solutions for vortex arrays are provided.

The system's behavior parallels superconducting Josephson junctions.

Abstract

Soon after its theoretical prediction, striped-density states in the presence of synthetic spin-orbit coupling were realized in Bose-Einstein condensates of ultracold neutral atoms [J.-R. Li et al., Nature \textbf{543}, 91 (2017)]. The achievement opens avenues to explore the interplay of superfluidity and crystalline order in the search for supersolid features and materials. The system considered is essentially made of two linearly coupled Bose-Einstein condensates, that is a pseudo-spin-$1/2$ system, subject to a spin-dependent gauge field $\sigma_z \hbar k_\ell$. Under these conditions the stripe phase is achieved when the linear coupling $\hbar\Omega/2$ is small against the gauge energy $m\Omega/\hbar k_\ell^2<1$ . The resulting density stripes have been interpreted as a standing-wave, interference pattern with approximate wavenumber $2k_\ell$. Here, we show that the emergence of the stripe phase is induced by an array of Josephson vortices living in the junction defined by the linear coupling. As happens in superconducting junctions subject to external magnetic fields, a vortex array is the natural response of the superfluid system to the presence of a gauge field. Also similar to superconductors, the Josephson currents and their associated vortices can be present as a metastable state in the absence of gauge field. We provide closed-form solutions to the 1D mean field equations that account for such vortex arrays. The underlying Josephson currents coincide with the analytical solutions to the sine-Gordon equation for the relative phase of superconducting junctions [C. Owen and D. Scalapino, Phys. Rev. \textbf{164}, 538 (1967)].