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arXiv:1311.5387 · Europhysics Letters (EPL)

Wave patterns generated by a flow of a two-component Bose-Einstein condensate with spin-orbit interaction past a localized obstacle

Yaroslav V. Kartashov, A. M. Kamchatnov

Published Jul 1, 2014• 3 citations
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Abstract

It is shown that a spin-orbit interaction leads to drastic changes in wave patterns generated by a flow of a two-component Bose-Einstein condensate (BEC) past an obstacle. The combined Rashba and Dresselhaus spin-orbit interaction affects in different ways two types of excitations —density and polarization waves— which can propagate in a two-component BEC. We show that the density and polarization "ship wave" patterns rotate in opposite directions around the axis located at the obstacle position and the angle of rotation depends on the strength of the spin-orbit interaction. This rotation is accompanied by a narrowing of the Mach cone. The influence of the spin-orbit coupling on density solitons and polarization breathers is studied numerically.

DOI
10.1209/0295-5075/107/10008

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It is shown that a spin-orbit interaction leads to drastic changes in wave patterns generated by a flow of a two-component Bose-Einstein condensate (BEC) past an obstacle. The combined Rashba and Dresselhaus spin-orbit interaction affects in different ways two types of excitations —density and polarization waves— which can propagate in a two-component BEC. We show that the density and polarization "ship wave" patterns rotate in opposite directions around the axis located at the obstacle position and the angle of rotation depends on the strength of the spin-orbit interaction. This rotation is accompanied by a narrowing of the Mach cone. The influence of the spin-orbit coupling on density solitons and polarization breathers is studied numerically.
We predict that oblique breathers can be generated by a flow of two-component Bose-Einstein condensates past a polarized obstacle that attracts one component of the condensate and repels the other one. The breather exists if intraspecies interaction constants differ from the interspecies interaction constant, and it corresponds to the nonlinear excitation of the so-called polarization mode with domination of the relative motion of the components. Analytical theory is developed for the case of small-amplitude breathers that is in reasonable agreement with the numerical results.
Generation of wave structures by a two-dimensional (2D) object (laser beam) moving in a 2D two-component Bose-Einstein condensate with a velocity greater than the two sound velocities of the mixture is studied by means of analytical methods and systematic simulations of the coupled Gross-Pitaevskii equations. The wave pattern features three regions separated by two Mach cones. Two branches of linear patterns similar to the so-called ``ship waves'' are located outside the corresponding Mach cones, and oblique dark solitons are found inside the wider cone. An analytical theory is developed for the linear patterns. A particular dark-soliton solution is also obtained, its stability is investigated, and two unstable modes of transverse perturbations are identified. It is shown that for a sufficiently large flow velocity, this instability has a convective character in the reference frame attached to the moving body, which makes the dark soliton effectively stable. The analytical findings are corroborated by numerical simulations.
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We investigate the dynamics around an obstacle potential moving in the plane-wave state of a pseudospin-1/21/21/2 Bose-Einstein condensate with Rashba spin-orbit coupling. We numerically investigate the dynamics of the system and find that it depends not only on the velocity of the obstacle but also significantly on the direction of obstacle motion, both of which are verified by the Bogoliubov analysis. The excitation diagram with respect to the velocity and direction is obtained. The dependence of the critical velocity on the strength of the spin-orbit coupling and the size of the obstacle is also investigated.
We study the Faraday patterns generated by spin-orbit-coupling induced parametric resonance in a spinor Bose-Einstein condensate with repulsive interaction. The collective elementary excitations of the Bose-Einstein condensate, including density waves and spin waves, are coupled as the result of the Raman-induced spin-orbit coupling and a quench of the relative phase of two Raman lasers without the modulation of any of the system's parameters. We observed several higher parametric resonance tongues at integer multiples of the driving frequency and investigated the interplay between Faraday instabilities and modulation instabilities when we quench the spin-orbit-coupled Bose-Einstein condensate from zero-momentum phase to plane-wave phase. If the detuning is equal to zero, the wave number of combination resonance barely changes as the strength of spin-orbit coupling increases. If the detuning is not equal to zero after a quench, a single combination resonance tongue will split into two parts.
We analytically and numerically discuss the dynamics of two pseudospin components Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) in deep optical lattices. Rich localized phenomena, such as breathers, solitons, self-trapping, and diffusion, are revealed and strongly depend on the strength of the atomic interaction, SOC, Raman detuning, and the spin polarization (i.e., the initial population difference of atoms between the two pseudospin components of BECs). The critical conditions for the transition of localized states are derived analytically. Based on the critical conditions, the detailed dynamical phase diagram describing the different dynamical regimes is derived. When the Raman detuning satisfies a critical condition, localized states with a fixed initial spin polarization can be observed. When the critical condition is not satisfied, we use two quenching methods, i.e., suddenly and linearly quenching Raman detuning from the soliton or breather state, to discuss the spin dynamics, phase transition, and wave packet dynamics by numerical simulation. The sudden quenching results in a damped oscillation of spin polarization and transforms the system to a new polarized state. Interestingly, the linear quenching of Raman detuning induces a controllable phase transition from an unpolarized phase to an expected polarized phase, while the soliton or breather dynamics is maintained.