Spin-orbit-coupling-induced quantum droplet in ultracold Bose-Fermi mixtures

Quantum droplets have aroused much attention recently in view of their successful observations in ultracold homonuclear atoms. In this paper, we demonstrate an alternative mechanism for the formation of quantum droplets in heteronuclear atomic systems, i.e., by applying synthetic spin-orbit coupling (SOC). Taking the Bose-Fermi mixture, for example, we show that by imposing a Rashba SOC between the spin states of fermions such that all fermions occupy the lower helicity branch, the greatly suppressed Fermi pressure can enable the formation of Bose-Fermi droplets even for very weak boson-fermion attractions, which are insufficient to bound a droplet if without SOC. In such SOC-induced quantum droplets, the boson-fermion density ratio universally depends on the SOC strength, and they occur in the mean-field collapsing regime but with a negative fluctuation energy, distinct from the interaction-induced droplets found in literature. The accessibility of these Bose-Fermi droplets in ultracold Cs-Li and Rb-K mixtures is also discussed. Our results shed light on the droplet formation in a vast class of heteronuclear atomic systems through the manipulation of single-particle physics.