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Journal of Physics B Atomic Molecular and Optical Physics

Modulational instability in a one-dimensional spin–orbit coupled Bose–Bose mixture

Dheerendra Singh, Mithilesh K. Parit, Thokala Soloman Raju, Prasanta Kumar Panigrahi

Published Oct 22, 2020• 17 citations
Publisher

Abstract

Abstract We establish the condition of modulational instability (MI) in one-dimensional effective one-component self-bound quantum droplets and Bose–Bose (BB) mixture, coupled through spin–orbit and Rabi couplings. For the self-bound quantum droplets of effective one-component BB mixture, MI occurs for the atom density: P < g 3 / 2 δ g 2 m 2 π 2 ℏ 2 , where δg = g + g 12 with g indicate intra-atomic and g 12 inter-atomic interaction strengths. The MI growth rate of BB mixture in the presence of spin–orbit and Rabi couplings shows distinct signatures of the couplings, in the form of multiple domains of instability. In particular, we demonstrate the explicit difference in MI, between the effective one-component self-bound quantum droplets and BB mixture.

DOI
10.1088/1361-6455/abc3d2

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Abstract We establish the condition of modulational instability (MI) in one-dimensional effective one-component self-bound quantum droplets and Bose–Bose (BB) mixture, coupled through spin–orbit and Rabi couplings. For the self-bound quantum droplets of effective one-component BB mixture, MI occurs for the atom density: P < g 3 / 2 δ g 2 m 2 π 2 ℏ 2 , where δg = g + g 12 with g indicate intra-atomic and g 12 inter-atomic interaction strengths. The MI growth rate of BB mixture in the presence of spin–orbit and Rabi couplings shows distinct signatures of the couplings, in the form of multiple domains of instability. In particular, we demonstrate the explicit difference in MI, between the effective one-component self-bound quantum droplets and BB mixture.
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 investigate modulational instability(MI) of a coupled two-component Bose–Einstein condensates in a rotating ring trap. The excitation spectrum and the MI condition of the system are presented analytically. We find that the coupling between the two components strongly modifies the MI condition, and the MI condition is phase-dependent.Furthermore, we discuss the effect of MI on both density excitation and spin excitation. If the inter- and intra-component interaction strengths are all equal, the MI causes density excitation but not spin excitation, and if the inter- and intracomponent interaction strengths are different, the MI causes both density excitation and spin excitation. Our results provide a promising approach for controlling the stability and excitation of a rotating two-component Bose–Einstein condensates by modulating its coupling strength and interaction strength.
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 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.
Recent experimental and theoretical results show that weakly interacting atomic Bose-Bose mixtures with attractive interspecies interaction are stabilized by beyond-mean-field effects. Here we consider the peculiar properties of these systems in a strictly one-dimensional configuration, taking also into account the nontrivial role of spin-orbit and Rabi couplings. We show that when the value of inter- and intraspecies interaction strengths are such that mean-field contributions to the energy cancel, a self-bound bright soliton fully governed by quantum fluctuations exists. We derive the phase diagram of the phase transition between a single-peak soliton and a multipeak (striped) soliton, produced by the interplay between spin-orbit, Rabi couplings and beyond-mean-field effects, which also affect the breathing mode frequency of the atomic cloud. Finally, we prove that a phase imprinting of the single-peak soliton leads to a self-confined propagating solitary wave even in the presence of spin-orbit coupling.
Abstract We investigate modulational instability (MI) of a coupled two-component Bose–Einstein condensates in a rotating ring trap. The excitation spectrum and the MI condition of the system are presented analytically. We find that the coupling between the two components strongly modifies the MI condition, and the MI condition is phase-dependent. Furthermore, we discuss the effect of MI on both density excitation and spin excitation. If the inter- and intra-component interaction strengths are all equal, the MI causes density excitation but not spin excitation, and if the inter- and intra-component interaction strengths are different, the MI causes both density excitation and spin excitation. Our results provide a promising approach for controlling the stability and excitation of a rotating two-component Bose–Einstein condensates by modulating its coupling strength and interaction strength.