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

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<g3/2δg2m2π2ℏ2 , 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.