Quantum phase transitions in an array of coupled nanocavity quantum dots

We investigate exciton-photon quantum phase transitions in a planar lattice of one-mode cavities containing one quantum dot. The quantum dot can be occupied by up to two excitons with opposite spin. We adopt the well-established mean-field approximation comprising an exciton order parameter and a photon coherence parameter. Calculating exciton- and photon-phase diagrams it is demonstrated that by controlling exciton- and photon-hopping energies a very rich scenario of coupled fermionic-bosonic quantum phase transitions, including, e.g., quantum phase transitions of the Hubbard model or quantum phase transitions of the light, is revealed. Moreover, our results support the interpretation of polariton Bose-Einstein condensation as only (polariton) laser coherence.