Quantum atom-light interfaces enable access to a wealth of quantum phenomena and applications within quantum information science. Despite this, a frontier that remains elusive is the realization and exploration of strongly correlated phenomena, due to two complementary problems. On one hand, such systems still suffer from significant dissipation, particularly at the level of individual quanta. On the other hand, there is a prevailing strategy to improve atom-light interaction efficiencies, by encoding processes into the collective response of many atoms. However, this strategy has the downside that collective spin or mean-field descriptions are typically good starting points to understand the physics, with paradigmatic examples being superradiance or spin squeezing. Such descriptions are incompatible with most known strongly correlated phenomena within physics.

Here, we propose a novel avenue to realize strongly correlated physics using arrays of atoms coupled to a high-finesse cavity. Notably, this approach both evades mean-field behavior despite the infinite-range photon-mediated interactions, and is partially protected from dissipation by exploiting its correlated nature, namely in the form of subradiance. We focus on the realization of topological quantum spin liquids, phases of matter (usually associated with short-range interactions) whose exotic properties include quasi-particle excitations that exhibit fractional or anyonic statistics, emergent gauge fields, and subtle long-range entanglement patterns.

In particular, we consider arrays of atoms featuring short-range and classical Ising (e.g., Rydberg mediated) interactions. We then show how long-range cavity interactions can melt the associated classical states into quantum spin liquids, by effectively projecting the state into highly correlated manifolds in which candidate spin liquid ground states are believed to live. These ground states are further shown to be perfectly dark to cavity-mediated photon emission. We anticipate that this work could open up new opportunities to realize strongly correlated and emergent phenomena with quantum atom-light interfaces, particularly by using the unique combination of long-range interactions and collective dissipation that such platforms naturally offer.