Spinor-induced instability of kinks, holes and quantum droplets

Abstract

We address the existence and stability of one-dimensional (1D) holes and kinks andtwo-dimensional (2D) vortex-holes nested in extended binary Bose mixtures, which emerge in thepresence of Lee–Huang–Yang (LHY) quantum corrections to the mean-field energy, along withself-bound quantum droplets. We consider boththe symmetric system with equal intra-speciesscattering lengths and atomic masses, modeled by a single (scalar) LHY-corrected Gross–Pitaevskiiequation (GPE), and the general asymmetric case with different intra-species scattering lengths,described by two coupled (spinor) GPEs. We found that in the symmetric setting, 1D and 2D holescan exist in a stable form within a range of chemical potentials that overlaps with that ofself-bound quantum droplets, but that extendsfar beyond it. In this case, holes are found to bealways stable in 1D and they transform into pairs of stable out-of-phase kinks at the criticalchemical potential at which localized droplets turn into flat-top states, thereby revealing theconnection between localized and extended nonlinear states. In contrast, we found that the spinornature of the asymmetric systems may lead to instability of 1D holes, which tend to break into twogray states moving in the opposite directions. Remarkably, such instability arises due to spinornature of the system and it affects only holesnested in extended modulationally-stablebackgrounds, while localized quantum dropletfamilies remain completely stable, even in theasymmetric case, while 1D holes remain stable only close to the point where they transform intopairs of kinks. We also found that symmetric systems allow fully stable 2D vortex-carryingsingle-charge states at moderate amplitudes, whileunconventional instabilities appear also at highamplitudes. Symmetry also strongly inhibits instabilities for double-charge vortex-holes, whichthus exhibit unexpectedly robust evolutions at low amplitudes.