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

TL;DR

This paper explores a one-dimensional Rabi-Hubbard model with three-level quantum dots, revealing entangled phases, symmetry-breaking transitions, and connections to lattice gauge theories, advancing understanding of quantum many-body phenomena.

Contribution

It introduces a novel Rabi-Hubbard model with three-level qdots, demonstrating complex phase transitions, entanglement structures, and a link to lattice gauge theories, which were not previously studied in this context.

Findings

Identification of two entangled incompressible phases separated by a quantum phase transition.

Discovery of a superradiant phase with broken $ ext{Z}_2$ symmetry and Ising universality.

Interpretation of a model limit as a $ ext{Z}_2$ lattice gauge theory.

Abstract

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 $\Lambda$ 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.