Unconventional criticality in the driven Jaynes-Cummings model

We study the single-atom Jaynes-Cummings model in the presence of cavity damping and coherent cavity drive. The undamped version of this model is known to exhibit an eigenstate transition, closely related to “spontaneous dressed-state polarization”, when the cavity driving strength exceeds the atom-cavity coupling. We investigate the consequence of this transition for the steady state at small cavity damping rates. Numerical and analytical evidence suggests the existence of a critical exponent (the so-called photon flux exponent) that is intermediate to the case of either a quantum or a thermal phase transition with respect to the underlying Hamiltonian. We contrast this finding to the well-studied (large-N) limit of many atoms, showing new evidence that the critical behavior for a single atom is of a fundamentally different nature.