Quantum droplets are self-bound low density configurations which may appear in ultracold gases with competing interactions. Since the first predictions and experimental observations in dilute bosonic mixtures, where the attractive mean-field energy is balanced by the repulsive correction stemming from quantum fluctuations, the study of quantum droplets in cold-atomic settings has recently become a very active research field.
In this talk I will show how a similar scenario arises also in solid-state systems, specifically atomically thin semiconductor layers. When these materials are embedded in an optical microcavity, exciton-polariton quasiparticles (polaritons) result from the strong coupling between semiconductor excitons and cavity photon modes.
Polaritons carry a spin degree of freedom inherited from both their matter and light components, thus resulting in the possibility of interactions between these quasiparticles.
The competition between the spin-singlet and spin-triplet channels of the interaction opens the way to the formation of a quantum droplet in a spin mixture of polaritons.
Motivated by the success of variational approaches to the polaron problem, I will present a suitable variational ansatz which includes bosonic pairing of excitons, in analogy with Cooper pairs of fermions in the conventional Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity. The resulting analysis of the free energy of the polariton mixture provides a general criterion to characterize the emergence of this novel self-bound droplet phase.