Quantum droplet phases in multimode optical cavities

Multimode optical cavities is a rapidly developing experimental platform for studying strongly coupled light-matter systems. While in single-mode cavities the interactions are of infinite range and all phase transitions are expected to be of the mean-field type, the multimode cavities feature tunable short- to long-range interactions and give an opportunity for observing transitions where the quantum fluctuations play a significant role.

We study the system of bosonic atoms in a multimode optical cavity, which can be modeled by an extended Bose-Hubbard model with competing on-site repulsive and finite-range (cavity-mediated) attractive interactions. We use the canonical worm Quantum Monte Carlo algorithm to explore the phase diagram of the model. Our approach is numerically exact and goes beyond the standard Gross-Pitaevskii analysis allowing us to study both superfluid and Mott phases. Moreover, since we explicitly work in the canonical ensemble, we don't have to fine-tune the chemical potential and can deal with arbitrary occupation numbers (up to the total number of particles in the system). 

I will show that in addition to the previously studied density-wave and supersolid self-organized superradiant phases, the finite-range cavity-mediated attraction can lead to the formation of quantum self-bound droplets. The droplet phases dominate the phase diagram and can include both compressible superfluid/supersolid as well as incompressible Mott and density-wave droplets.