Fermionization and collective excitations of one-dimensional polariton lattices

We theoretically demonstrate that the hallmarks of correlation and fermionization in a one-dimensional exciton-polariton gas can be observed with state-of-the-art technology. Our system consists of a chain of excitonic quantum dots coupled to a photonic waveguide, with a low filling of polaritons. We analytically identify the Tonks-Girardeau, Tavis-Cummings, and mean-field limits and relate them to different regimes of excitonic anharmonicity and photonic bandwidth. Using matrix-product states, we numerically calculate the ground-state energies, correlation functions, and dynamic structure factor of the system. In particular, the latter has a finite weight in the Lieb-Liniger hole branch, and the density-density correlator displays Friedel-like oscillations for realistic parameters, which reveal the onset of fermionization close to the Tonks-Girardeau regime. Our work encourages future experiments aimed at observing, for the first time and in spite of the moderate excitonic anharmonicity, strongly correlated exciton-polariton physics.