Abstract
We prove that the observable telegraph signal accompanying the bistability in the photon-blockade-breakdown regime of the driven and lossy Jaynes–Cummings model is the finite-size precursor of what in the thermodynamic limit is a genuine first-order phase transition. We construct a finite-size scaling of the system parameters to a well-defined thermodynamic limit, in which the system remains the same microscopic system, but the telegraph signal becomes macroscopic both in its timescale and intensity. The existence of such a finite-size scaling completes and justifies the classification of the photon-blockade-breakdown effect as a first-order dissipative quantum phase transition.
Highlights
A number of recent theoretical proposals and experiments refer to a new type of dissipative phase transition in a quantum system, that is said to be of first order
If such a finite size scaling is possible – and here we show that this is the case for the photon-blockade breakdown effect, the bistability that can be observed in a given experimental realization of the system with its finite parameters not in the thermodynamic limit, can be considered the finite-size approximation of what is a genuine first-order phase transition in the thermodynamic limit
The two-level system can be an atom or artificial atom, whereas the oscillator can represent a single lossy mode of the radiation field or a longitudinal mode of a stripline resonator. We describe this interaction within the driven JaynesCummings model, i.e., using the electric-dipole coupling and the rotating-wave approximation (RWA): H = ωM a†a + ωA σ† σ + ig a† σ − σ† a + iη a† e−iωt − a eiωt, (1)
Summary
A number of recent theoretical proposals and experiments refer to a new type of dissipative phase transition in a quantum system, that is said to be of first order. This paper is devoted to complete and justify the interpretation of the photon-blockade-breakdown effect as a first-order dissipative quantum phase transition To this end, one needs to introduce the concepts of thermodynamic limit and finite-size scaling for the microscopic system of a driven dissipative Jaynes-Cummings model. The blinking telegraph-like signal vanishes completely and the state of the system is determined by the initial condition, to the usual hysteresis behaviour in classical critical systems If such a finite size scaling is possible – and here we show that this is the case for the photon-blockade breakdown effect –, the bistability that can be observed in a given experimental realization of the system with its finite parameters not in the thermodynamic limit, can be considered the finite-size approximation of what is a genuine first-order phase transition in the thermodynamic limit.
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