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arXiv:1710.03644

One dimensional phase transition problem modelling striped spin orbit coupled Bose-Einstein condensates

Amandine Aftalion, Rémy Rodiac

Published Oct 10, 2017• 1 citation
arXivHTMLPDF

Abstract

We study the behaviour of a Modica-Mortola phase transition type problem with a non-homogeneous Neumann boundary condition. According to the parameters of the problem, this leads to the existence of either one component occupying most of the condensate with an outer boundary layer containing the other component, or to many interfaces, on a periodic pattern. This is related to the striped behaviour of a two component Bose-Einstein condensate with spin orbit coupling in one dimension. We prove that minimizers of the full Gross-Pitaevskii energy in 1D converge, in the Thomas-Fermi limit of strong intra-component interaction, to those of the simplified Modica-Mortola problem we have studied in the first part.

DOI
10.48550/arxiv.1710.03644

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We study the role of coupling parameters on the ground state phases of spin-orbit coupled Bose-Einstein condensates with an equal combination of Rashba and Dresselhaus coupling strength with Rabi mixing using quasi-one-dimensional coupled Gross-Pitaevskii equations. By considering weak repulsive inter- and intra-species interactions between the condensate atoms, we investigate the contribution of spin-orbit and Rabi coupling parameters on the phases. We find that for a finite Rabi coupling strength, the system undergoes a phase transition from double plane-wave phase to stripe wave phase at a critical spin-orbit coupling strength.
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Abstract We consider an effective two-dimensional Bose–Einstein condensate with some spin–orbit coupling (SOC) and a rotation term in an external harmonic potential. We find the striped state, and analyze the effects of SOC, the external potential, and the rotation frequency/direction on the profile and the stability of the striped state. Without the rotation term, the two spinor components exhibit striped pattern, and the numbers of stripes in the two components are always an odd–even or an even–odd. With the increase of the SOC strength, the number of stripes in both components increases, while the difference of the striped numbers is always one. After adding the rotation term, the profiles of the spinor components change qualitatively, and the change regulation of the striped numbers differs, while the difference of the striped numbers is still one. In addition, we find that the rotation direction only makes the striped state of the two spinor components exchange each other, though the clockwise and counterclockwise rotation directions are inequivalent with the presence of SOC. Such regulation is different from the previous study. And the rotation frequency gives rise to the transition from the striped state to a mixture of the striped state and vortex state. Furthermore, we prove the stability of these states by the evolution and linear stability analysis.