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Journal of Physics B Atomic Molecular and Optical Physics

Modulation instability of a spin-1 Bose–Einstein condensate with spin–orbit coupling

Guan-Qiang Li, Guangde Chen, Ping Peng, Zhi Li, Xiaodong Bai

Published Oct 11, 2017• 9 citations
Publisher

Abstract

Abstract We investigate the modulation instability (MI) of plane-wave states in a spin–orbit-coupled spin-1 Bose–Einstein condensate (BEC). The MI of the system can be adjusted by the intensities of the spin–orbit coupling (SOC), Raman coupling and atom–atom interactions. Our analysis shows that the MI of a system without the SOC and Raman coupling mainly occurs for repulsive density–density and spin–exchange interactions due to the combined effects coming from both of them. But when considering the SOC, a multi-peak structure appears in the momentum distribution for the instability, which may be thought of as a precursor to the generation of the stripe-type nonlinear excitations in such systems. The MI becomes more remarkable with increasing intensity of Raman coupling. In addition, the SOC inevitably contributes to the instability for the ternary superfluid regardless of the nature of the density–density and spin–exchange interactions.

DOI
10.1088/1361-6455/aa92b7

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Abstract We investigate the modulation instability (MI) of plane-wave states in a spin–orbit-coupled spin-1 Bose–Einstein condensate (BEC). The MI of the system can be adjusted by the intensities of the spin–orbit coupling (SOC), Raman coupling and atom–atom interactions. Our analysis shows that the MI of a system without the SOC and Raman coupling mainly occurs for repulsive density–density and spin–exchange interactions due to the combined effects coming from both of them. But when considering the SOC, a multi-peak structure appears in the momentum distribution for the instability, which may be thought of as a precursor to the generation of the stripe-type nonlinear excitations in such systems. The MI becomes more remarkable with increasing intensity of Raman coupling. In addition, the SOC inevitably contributes to the instability for the ternary superfluid regardless of the nature of the density–density and spin–exchange interactions.
We theoretically investigate the dynamics of modulation instability (MI) in two-dimensional spin–orbit coupled Bose–Einstein condensates (BECs) with Rabi coupling. The analysis is performed for equal densities of pseudo-spin components. Different combination of the signs of intra- and intercomponent interaction strengths are considered, with a particular emphasis on repulsive interactions. We observe that the unstable modulation builds from originally miscible condensates, depending on the combination of the signs of the intra- and intercomponent interaction strengths. The repulsive intra- and intercomponent interactions admit instability and the MI immiscibility condition is no longer significant. The influence of interaction parameters such as spin–orbit and Rabi coupling on MI are also investigated. The spin–orbit coupling (SOC) inevitably contributes to instability regardless of the nature of the interaction. In the case of attractive interaction, SOC manifests in enhancing the MI. Thus, a comprehensive study of MI in two-dimensional spin–orbit coupled BECs of pseudo-spin components is presented.
We study modulation instability (MI) of flat states in two-component spin-orbit-coupled (SOC) Bose-Einstein condensates (BECs) in the framework of coupled Gross-Pitaevskii equations for two components of the pseudospinor wave function. The analysis is performed for equal densities of the components. Effects of the interaction parameters, Rabi coupling, and SOC on the MI are investigated. In particular, the results demonstrate that the SOC strongly alters the commonly known MI (immiscibility) condition, g122>g1g2{g}_{12}^{2}>{g}_{1}{g}_{2}g122​>g1​g2​, for the binary superfluid with coefficients g1,2{g}_{1,2}g1,2​ and g12{g}_{12}g12​ of the intra- and interspecies repulsive interactions. In fact, the binary BEC is always subject to the MI under the action of the SOC, which implies that the ground state of the system is plausibly represented by a striped phase.
Abstract Parity-time ( P T ) symmetry has drawn great research interest in non-Hermitian physics. Recently, there is an emerging model of P T -symmetric spin–orbit coupling (SOC) which could be realized with spin-1/2 atomic Bose–Einstein condensates (BECs) when the two spin components are respectively subjected to momentum-dependent gain and loss (Qin et al 2022 New J. Phys. 24 063025). In this model, inter-atom interaction has no influence on the P T -symmetric plane waves. Thus, collective excitation playing the role of fingerprint of inter-atom interaction is investigated in this paper. For the phonon excitation, it is shown that the repulsive interaction between atoms in different spin states, which tends to drive the atoms to populate in only one spin component, can break the P T -symmetry, and leads to a phonon instability. Whereas, for the case of the phonon-maxon-roton collective excitation spectrum, the repulsive interaction between atoms in different spin states can lead to a maxon instability, which does not occur in Hermitian BEC systems (dipolar BECs or BECs with Raman induced SOC). Simulation of the time evolution of the plane wave solution against small noise shows that the maxon instability can result in the formation of a supersolid-like stripe pattern at the initial stage, but the non-Hermitian nature of the system finally destroys the pattern. The phase diagram of stability shows that the Rabi coupling and repulsive interaction between the atoms in the same spin state can stabilize the system.
Abstract We analytically and numerically study three-component rogue waves (RWs) in spin-1 Bose–Einstein condensates with Raman-induced spin–orbit coupling (SOC). Using the multiscale perturbative method, we obtain approximate analytical solutions for RWs with positive and negative effective masses, determined by the effective dispersion of the system. The solutions include RWs with smooth and striped shapes, as well as higher-order RWs. The analytical solutions demonstrate that the RWs in the three components of the system exhibit different velocities and their maximum peaks appear at the same spatiotemporal position, which is caused by SOC and interactions. The accuracy of the approximate analytical solutions is corroborated by comparison with direct numerical simulations of the underlying system. Additionally, we systematically explore existence domains for the RWs determined by the baseband modulational instability (BMI). Numerical simulations corroborate that, under the action of BMI, plane waves with random initial perturbations excite RWs, as predicted by the approximate analytical solutions.
The nonlinear dynamics induced by the modulation instability (MI) of a binary mixture in an atomic Bose-Einstein condensate (BEC) is investigated theoretically under the joint effects of higher-order residual nonlinearities and helicoidal spin-orbit (SO) coupling in a regime of unbalanced chemical potential. The analysis relies on a system of modified coupled Gross-Pitaevskii equations on which the linear stability analysis of plane-wave solutions is performed, from which an expression of the MI gain is obtained. A parametric analysis of regions of instability is carried out, where effects originating from the higher-order interactions and the helicoidal spin-orbit coupling are confronted under different combinations of the signs of the intra- and intercomponent interaction strengths. Direct numerical calculations on the generic model support our analytical predictions and show that the higher-order interspecies interaction and the SO coupling can balance each other suitably for stability to take place. Mainly, it is found that the residual nonlinearity preserves and reinforces the stability of miscible pairs of condensates with SO coupling. Additionally, when a miscible binary mixture of condensates with SO coupling is modulationally unstable, the presence of residual nonlinearity may help soften such instability. Our results finally suggest that MI-induced formation of stable solitons in mixtures of BECs with two-body attraction may be preserved by the residual nonlinearity even though the latter enhances the instability.
Abstract We study pattern-forming nonlinear dynamics starting from a continuous wave state of quasi-one-dimensional two-component Bose–Einstein condensates with synthetic spin–orbit coupling induced by Raman lasers. Modulation instability (MI) can occur even when the miscibility condition due to the interatomic interactions is satisfied. We find that the initial stage of the nonlinear development is consistent with the prediction of MI, where the two primary and secondary instability bands lead to the spontaneous growth of the modulation and the subsequent complicated dynamics of pattern formation. At later stages of the evolution, the wave functions undergo clear separation in the momentum space, reflected in the dispersion of the single particle Hamiltonian.