Superradiance, charge density waves and lattice gauge theory in a generalized Rabi-Hubbard chain

We investigate a one-dimensional Rabi-Hubbard type of model, arranged such that a qdot is sandwiched between every cavity. The role of the qdot is to transmit photons between neighboring cavities, while simultaneously acting as a photon non-linearity. We consider three-level qdots in the $Λ$ configuration, where the left and right leg couples exclusively to the left or right cavity. This non-commuting interaction leads to two highly entangled incompressible phases, separated by a second order quantum phase transition: the qdot degrees-of-freedom act as a dynamical lattice for the photons and a Peierls instability breaks a second $\mathbb{Z}_2$ symmetry which leads to a dimerization in entanglement and photon number. We also find a normal insulating phase and a superfluid phase that acts as a quantum many-body superradiant phase. In the superradiant phase, a $\mathbb{Z}_2$ symmetry is broken and the phase transition falls within the transverse field Ising model universality class. Finally, we show that a limit of the model can be interpreted as a $\mathbb{Z}_2$ lattice gauge theory.

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