Dissipative quantum phase transitions of light in a generalized Jaynes-Cummings-Rabi model

Abstract

The mean-field steady states of a generalized model of N two-state systems interacting with one mode of the radiation field in the presence of external driving and dissipation are surveyed as a function of three control parameters: one governs the interaction strength relative to the resonance frequency, thus accessing the Dicke quantum phase transition, a second the relative strength of counter-rotating to rotating-wave interactions, and a third the amplitude of an external field driving the cavity mode. We unify the dissipative extension of the Dicke quantum phase transition with the recently reported breakdown of photon blockade [H. J. Carmichael, Phys. Rev. X 5, 031028 (2015)]; key to the unification is a previously unreported phase of the Dicke model and a renormalized critical drive strength in the breakdown of photon blockade. For the simplest case of one two-state system, we complement mean-field results with a full quantum treatment: we derive quasi-energies to recover the renormalized critical drive strength, extend the multi-photon resonances of photon blockade to a counter-rotating interaction, and explore quantum fluctuations through quantum trajectory simulations.PACS numbers: PACS numbers go here arXiv:1806.05761v1 [quant-ph]

Introduction to the Dicke Model: From Equilibrium to Nonequilibrium, and Vice Versa

“…When considering the full phase diagram of dissipative Dicke model with , some new features can arise. In particular, there exists a phase where both the normal state and superradiant state are stable, and a multicritical point where this phase vanishes, as was reported a number of times …”

“…The behavior of this model at large driving has also been recently discussed in ref. [], establishing a connection to the breakdown of the photon blockade seen in the single‐atom Jaynes–Cummings model …”

Quasienergy collapse in the driven Jaynes–Cummings–Rabi model: correspondence with a charged Dirac particle in an electromagnetic field

“…The critical behavior persists if the interaction between the two-level system and field mode is extended to include counter-rotating coupling [8]. In this extended model the dynamics in the interaction picture are ruled by the generalized JC-Rabi Hamiltonian…”

“…The interplay between κ, λ and ò determine the maximum photon value, allowing for the definition of a thermodynamical limit in this system where threshold behavior and its relation to a phase transition can be studied. For the generalized model h ¹ ( ) 0 , damping of the cavity mode is considered in [8].…”

“…Previously the quasienergies and eigenstates of the system below the critical amplitude have been obtained through a Bogoliubov transformation [6,8]; this method ceases to be applicable, however, for the continuous spectrum above the critical amplitude. We overcome this problem in the following, where we develop a new method for obtaining the quasienergies and eigenstates, both below and above critical drive, for the driven JC model.…”