We study the full field and frequency filtered output photon statistics of a resonator in thermal equilibrium with a bath and containing an arbitrarily large quartic nonlinearity. According to the general theory of photodetection, we derive general i
nput-output relations valid for the ultra-anharmonic regime, where the nonlinearity becomes comparable to the energy of the resonator, and show how the emission properties are modified as compared to the generally assumed simple anharmonic regime. We analyse the impact of the nonlinearity on the full statistics of the emission and its spectral properties. In particular we derive a semi-analytical expression for the frequency resolved two-photon correlations or two-photon spectrum of the system in terms of the master equation coefficients and density matrix. This provides a very clear insight into the level structure and emission possibilities of the system.
Thermal or chaotic light sources emit radiation characterized by a slightly enhanced probability of emitting photons in bunches, described by a zero-delay second-order correlation function $g^{(2)}(0) = 2$. Here we explore photon-coincidence counting
statistics of thermal cavities in the ultrastrong coupling regime, where the atom-cavity coupling rate becomes comparable to the cavity resonance frequency. We find that, depending on the system temperature and coupling rate, thermal photons escaping the cavity can display very different statistical behaviors, characterised by second-order correlation functions approaching zero or greatly exceeding two.
We explore photon coincidence counting statistics in the ultrastrong-coupling regime where the atom-cavity coupling rate becomes comparable to the cavity resonance frequency. In this regime usual normal order correlation functions fail to describe th
e output photon statistics. By expressing the electric-field operator in the cavity-emitter dressed basis we are able to propose correlation functions that are valid for arbitrary degrees of light-matter interaction. Our results show that the standard photon blockade scenario is significantly modified for ultrastrong coupling. We observe parametric processes even for two-level emitters and temporal oscillations of intensity correlation functions at a frequency given by the ultrastrong photon emitter coupling. These effects can be traced back to the presence of two-photon cascade decays induced by counter-rotating interaction terms.
We study the all-optical time-control of the strong coupling between a single cascade three-level quantum emitter and a microcavity. We find that only specific arrival-times of the control pulses succeed in switching-off the Rabi oscillations. Depend
ing on the arrival times of control pulses, a variety of exotic non-adiabatic cavity quantum electrodynamics effects can be observed. We show that only control pulses with specific arrival times are able to suddenly switch-off and -on first-order coherence of cavity photons, without affecting their strong coupling population dynamics. Such behavior may be understood as a manifestation of quantum complementarity.
