We consider the phase-transition-like behaviour in the Rabi model containing a single two-level system, or qubit, and a single harmonic oscillator. The system experiences a sudden transition from an uncorrelated state to an increasingly correlated one as the qubit-oscillator coupling strength is varied and increased past a critical point. This singular behaviour occurs in the limit where the oscillator's frequency is much lower than the qubit's frequency; away from this limit one obtains a finite-width transition region. By analyzing the energy-level structure, the value of the oscillator field and its squeezing and the qubit-oscillator correlation, we gain insight into the nature of the transition and the associated critical behaviour.
@article{arxiv.1312.6938,
title = {Superradiance transition in a system with a single qubit and a single oscillator},
author = {S. Ashhab},
journal= {arXiv preprint arXiv:1312.6938},
year = {2013}
}