Experimental test of nonclassicality criteria for phase-diffused squeezed states

We experimentally examine the nonclassical character of a class of non-Gaussian states known as phase-diffused squeezed states. These states may show no squeezing effect at all and therefore provide an interesting example to test nonclassicality criteria. The characteristic function of the Glauber-Sudarshan representation ($P$ function) proves to be a powerful tool to detect nonclassicality. Using this criterion we find that phase-diffused squeezed states are always nonclassical, even if the squeezing effect vanishes. Testing other criteria of nonclassicality based on higher-order squeezing and the positive semidefiniteness of special matrices of normally ordered moments, it is found that these criteria fail to reveal the nonclassicality for some of the prepared phase-diffused squeezed states.

Figure 1

(Color online) Simplified sketch of the experimental setup. MC: spatial mode cleaner, LO: local oscillator, OPA: squeezed light source, BHD: balanced homodyne detector, and PZT: piezoelectrically actuated mirror. PZT1 was used to control the average phase and PZT2 applied the phase noise.

Figure 2

(Color online) Characteristic functions of different phase-diffused squeezed vacuum states. The shaded area corresponds to one standard deviation; it is added to the nonclassical boundary ${\Phi }_{\text{vac}}\equiv 1$. Take note of the logarithmic scale.