Advances and Applications in Statistics
Volume 30, Issue 2, Pages 135 - 149
(October 2012)
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THE GENERALIZED Q MANDEL’S PARAMETER CANNOT REVEAL THE NONCLASSICALITY OF THE SQUEEZED COHERENT STATES
J. S. Sales and N. G. de Almeida
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Abstract: 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 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 is a sufficient, but not a necessary condition for the nonclassicality of a quantum state, in [2], a generalized parameter recovering the original Q for was introduced. We show that whenever 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 what is corroborated by the examples analyzed by us. Here we carry out a detailed study of the evolving under a thermal reservoir and show, by an explicit counter-example, that the nonclassicality of squeezed coherent states is not revealed by regardless of its order. |
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