Antibunching and unconventional photon blockade with Gaussian squeezed states

There is considerable interest in both the circuit QED\footnote{D. Bozyigit, \textit{et al.}, Nat. Phys. \textbf{7}, 154-158 (2011).} and optomechanics,\footnote{J. D. Cohen, \textit{et al.} arXiv:1410.1047.} experiments in using the measured intensity fluctuations of a bosonic field as a direct signature of a nonclassical state. Although these nonclassical signatures, such as antibunching, are usually observed in strongly nonlinear systems, they also have been reported with Gaussian states in linear systems.\footnote{N. B. Grosse, \textit{et al.}, Phys. Rev. Lett. \textbf{98}, 153603 (2007).} To clarify the significance of the intensity correlations, we derive a sufficient condition for deducing if a field is non-Gaussian based on intensity correlations measurement.\footnote{M.-A. Lemonde, N. Didier, A. A. Clerk, arXiv:1410.6510.} With these results in hands, we shed light on the so-called \textit{unconventional photon blockade} effect predicted in a driven two-cavity setup with surprisingly weak Kerr nonlinearities, stressing that it is a particular realization of optimized Gaussian amplitude squeezing.