Microscopic theory of nonlinear phase space filling in polaritonic lattices

Abstract

We develop a full microscopic theory for a nonlinear phase space filling (NPSF) in strongly coupled two-dimensional polaritonic lattices. Ubiquitous in polaritonic experiments, the theoretical description of NPSF, also known as nonlinear optical saturation, remains limited to perturbative treatment and homogeneous samples. In this study, we go beyond the existing theoretical description and discover the broad scope of regimes where NPSF crucially modifies the optical response. Studying the quantum effects of non-bosonicity, cooperative light-matter coupling, and Coulomb blockade, we reveal several regimes for observing the nonlinear Rabi splitting quench due to the phase space filling. Unlike prior studies, we derive nonlinear Rabi frequency scaling all the way to the saturation limit and show that the presence of a lattice potential leads to qualitatively distinct nonlinearity. We concentrate on the three regimes of NPSF: (1) planar; (2) fractured; and (3) ultralocalized. For the planar saturation, the Rabi frequency decreases exponentially as a function of exciton density. For the fractured case, where excitons form a lattice with sites exceeding the exciton size, we discover fast NPSF at low occupations. This is followed by slower NPSF as the medium becomes fully saturated. This behavior is particularly pronounced in the presence of Coulomb (or Rydberg) blockade, where regions of fast and slow NPSF depend on the strength of repulsion. For the ultralocalized NPSF, we observe the square-root saturation typical to the collection of two-level systems. Our findings shed light on recent observations of strong nonlinearity in heterobilayers of transition metal dichalcogenides where moiré lattices emerge naturally [Nature (London) 591, 61 (2021)10.1038/s41586-021-03228-5]. Finally, the developed theory opens the prospects for engineering strongly nonlinear responses of polaritonic lattices with patterned samples, driving polaritonics into the quantum regime.