Phase Transition of Light in Cavity QED Lattices

Abstract

Systems of strongly interacting atoms and photons, that can be realized wiring up individual cavity QED systems into lattices, are perceived as a new platform for quantum simulation. While sharing important properties with other systems of interacting quantum particles here we argue that the nature of light-matter interaction gives rise to unique features with no analogs in condensed matter or atomic physics setups. By discussing the physics of a lattice model of delocalized photons coupled locally with two-level systems through the elementary light-matter interaction described by the Rabi model, we argue that the inclusion of counter rotating terms, so far neglected, is crucial to stabilize finite-density quantum phases of correlated photons out of the vacuum, with no need for an artificially engineered chemical potential. We show that the competition between photon delocalization and Rabi non-linearity drives the system across a novel Z2 parity symmetry-breaking quantum criticality between two gapped phases which shares similarities with the Dicke transition of quantum optics and the Ising critical point of quantum magnetism. We discuss the phase diagram as well as the low-energy excitation spectrum and present analytic estimates for critical quantities. Introduction -Interaction between light and matter is one of the most basic processes in nature and represents a cornerstone in our understanding of a broad range of physical phenomena. In the study of strongly correlated systems and collective phenomena, light has traditionally assumed the role of a spectroscopic probe. The increasing level of control over light-matter interactions with atomic and solid-state systems [1-3] has brought forth a new class of quantum many body systems where light and matter play equally important roles in emergent phenomena: photon lattices [4][5][6][7][8][9][10][11][12][13][14][15]. The basic building block of such systems is the elementary Cavity QED (CQED) system formed by a two-level system (TLS) interacting with a single mode of an electromagnetic resonator. When CQED systems are coupled to form a lattice, the interplay between photon blockade [17][18][19] and inter-cavity photon tunnelling leads to phenomenology akin to those of Hubbard models of massive bosons as realized e.g. by ultracold atoms in optical lattices [20]. The possibility of quantum phase transitions of light between Mott-like insulating and superfluid phases has stimulated a great deal of discussion recently [4][5][6][7][8][9][11][12][13][14]. The excitement about these systems stems from their potential as dissipative quantum simulators that provide full access to individual sites through continuous weak measurements [16].

Lattice mapping for many-body open quantum systems and its application to atoms in photonic crystals

“…The nonlinearities in this system lead to an on-site repulsion, which combined with the hopping term between the cavity modes b n leads to a Bose-Hubbard-like dynamics where quantum phase transitions of light can be described in the ground state between a Mott-like phase (i.e., the photon blockade regime) and a superfluid phase [33][34][35]41]. In addition, strong signatures of photon blockade have also been observed in the nonequilibrium dynamics of weakly coupled cavity arrays [42].…”

Large-scale maximal entanglement and Majorana bound states in coupled circuit quantum electrodynamic systems

“…Finishing this work, we have noticed a closely related preprint [34]. While they focus on the phase transition of the circuit-QED chain, we are mainly concerned about the quantum properties of the nearly degenerated ground states on one side of the phase transition.…”

Keldysh field theory for driven open quantum systems

“…In cirquit QED, strong non-linearities can be generated, e.g., by coupling to adjacent qubits made of Cooper pair boxes [132,133]. This gives rise to many-body variants of the Rabi model [134], whose phase diagrams have been studied recently [135][136][137]. Furthermore, for the implementation of lattice Dicke models with large collective spins, the use of hybrid quantum systems consisting of superconducting cavity arrays coupled to solid-state spin ensembles have been proposed [138].…”