Abstract
Arrays of coupled QED cavities have been proposed as promising candidates to study hybrid many-body states of light and matter in a controlled way. The rich scenario emerging in these systems stems from the interplay between intra-cavity light-matter interaction and inter-cavity photon hopping. Coherent light-matter interaction generates polaritonic excitations with physical properties resembling those of bosonic particles in a lattice. We review the most salient features of the zero-temperature equilibrium phase diagram of a polaritonic lattice model, focusing on a quantitative analysis for the one-dimensional case. A judicious analysis of the system, however, cannot neglect the effect of losses and decoherence of both light and matter components of the polaritonic excitation. External driving is typically needed to counteract such losses. In this case, the knowledge of the equilibrium phase diagram is not sufficient to describe the state of the system during its time-evolution, and its possible approach to the steady state. For this reason, we also discuss the nonequilibrium dynamics resulting from the interplay between losses and external driving in some relevant cases.
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Notes
- 1.
This procedure is formally equivalent to finding the critical hopping \(J^\star \) at which, in the grand canonical ensemble, the critical chemical potentials \(\mu _\mathrm{c}^\pm (\rho , J)\) of Eq. (1.14) coincide.
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Acknowledgements
We acknowledge the EU (through IP-SIQS and STREP-TermiQ) and the Italian MIUR through FIRB (Project RBFR12NLNA) and PRIN (Project 2010LLKJBX), for financial support. We would also acknowledge a fruitful collaboration on the topics discussed in this chapter with I. Carusotto, S. Diehl, D. Gerace, V. Giovannetti, A. Imamoğlu, D. Marcos, P. Rabl, G. Santoro, and H. Türeci.
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Tomadin, A., Rossini, D., Fazio, R. (2017). Strongly Correlated Polaritons in Nonlinear Cavity Arrays. In: Angelakis, D. (eds) Quantum Simulations with Photons and Polaritons. Quantum Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-52025-4_1
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