Non-classicality and coherence of squeezed states

After having set up a concise frame for pure and mixed all-order coherent states, we let them undergo a rather general squeezing transformation. These squeezed states are always non-classical, but some—apparently experimentally preparable—of them are still second-order coherent. They combine peculiar properties of their quantum fluctuations with the ordering features of coherence, and deserve special attention. Quite generally, several criteria for non-classicality are discussed and applied to the considered class of squeezed states. The connection between non-classicality and anti-bunching resp. sub-Poissonian photon statistics is shown to be more subtle than quantum optical usage suggests.