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.
Highlights
At the quantum level of single photons, strongly coupled light and matter can form novel states with no counterparts in other branches in physics [1]; new interacting quantum manybody models arise which may host exotic phases
In 1973, first by Hepp and Lieb [5] and shortly afterwards by Wang and Hioe [6], it was demonstrated that the Dicke model supports a second-order phase transitions (PTs) from a “normal” to a “superradiant” phase as the light-matter coupling is raised above a critical value
The corresponding PT is accompanied by a spontaneous breaking of a Z2 symmetry
Summary
At the quantum level of single photons, strongly coupled light and matter can form novel states with no counterparts in other branches in physics [1]; new interacting quantum manybody models arise which may host exotic phases. Contrary to a traditional Peierls instability for free fermions, the periodicity is not set by the filling but is induced by effective interactions between the photons This is akin to the bosonic Peierls transition recently discussed in an extended Bose-Hubbard model with a similar dynamical lattice as the one considered here [25]. In order to realize the aforementioned many-body normalsuperradiant QPT we assume a static dipolar field driving the |1 ↔ |2 transitions Such a field has a “resetting” effect on the qutrits; e.g., a qutrit undergoing the transitions |1 → |3 → |2 by transferring one photon between two resonators can be reset by the field to its original state |1 without involving further photons from the resonators.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
