THE GENERALIZED Q MANDEL'S PARAMETER CANNOT REVEAL THE NONCLASSICALITY OF THE SQUEEZED COHERENT STATES

The Q parameter was introduced by Mandel [1] to characterize the photon number distribution of a given state, such that an arbitrary distribution is defined to be sub- or super-Poissonian depending on Q < 0, Q > 0, respectively. While a sub- Poissonian distribution implies photon antibunching, which is a manifestation of the non-classical characteristic of the radiation, super-Poissonian distribution does not require a complete quantum treatment to its explanation. Also, it is generally spoken of states whose Q Mandel's parameter is null as being "Poissonian" states, from which coherent states are the most popular example. Since Q < 0 is a sufficient, but not a necessary condition for the nonclassicality of a quantum state, in [2], a generalized Q(k) parameter recovering the original Q for k = 1 was introduced. We show that whenever Q(k) is negative for some k, it implies that the radiation is non-classical, such that, in principle, nonclassicality could be revealed by resorting to higher orders of Q(k), what is corroborated by the examples analyzed by us. Here we carry out a detailed study of the Q(k) evolving under a thermal reservoir and show, by an explicit counter-example, that the nonclassicality of squeezed coherent states is not revealed by Q(k) regardless of its order.