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We investigate the ground state and dynamics of one-dimensional spin-orbitcoupled (SOC) quantum droplets within the extended Gross-Pitaevskii approach.As the SOC wavenumber increases, stripe droplet patterns emerge, with aflat-top background, for larger particle numbers. The surface energy decaysfollowing a power-law with respect to the interactions. At small SOCwavenumbers, a transition from Gaussian to flat-top droplets occurs for eithera larger number of atoms or reduced intercomponent attraction. The excitationspectrum shows that droplets for relatively small SOC wavenumbers are stable,otherwise stripe droplets feature instabilities as a function of the particlenumber or the interactions. We also witness rich droplet dynamical featuresusing velocity imprinting and abrupt changes in the intercomponent interactionor the SOC parameters. Characteristic responses include breathing oscillations,expansion, symmetric and asymmetric droplet fragmentation, admixtures of singleand stripe droplet branches, and erratic spatial distributions suggesting thetriggering of relevant instabilities. Our results reveal the controlleddynamical generation and stability properties of stripe droplets that should bedetectable in current cold-atom experiments.

Spectrum and quench-induced dynamics of spin-orbit coupled quantum droplets