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European Quantum Electronics Conference (EQEC)

From super-poissonian to sub-poissonian through non-poissionian statistics within squeezed states

Alfred Wünsche

Published Aug 24, 2005• 0 citations
Publisher
DOI
10.1109/eqec.1994.698255

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After developing the concept of displaced squeezed vacuum states in the nonunitary approach and establishing the connection to the unitary approach we calculate their quasiprobabilities and expectation values † k a a in general form.Then we consider the displacement of the squeezed vacuum states and calculate their photon statistics and their quasiprobabilities.The expectation values of the displaced states are related to the expectation values of the undisplaced states and are calculated for some simplest cases which are sufficient to discuss their categorization as sub-Poissonian and super-Poissonian statistics.A large set of these states do not belong to sub-or to super-Poissonian states but are also not Poissonian states.We illustrate in examples their photon distributions.This shows that the notions of sub-and of super-Poissonian statistics and their use for the definition of nonclassicality of states are problematic.In Appendix A we present the most important relations for ( ) 1,1 SU treatment of squeezing and the disentanglement of their operators.Some initial members of sequences of expectation values for squeezed vacuum states are collected in Appendix E.
A systematic study of squeezing obtained from k-photon anharmonic oscillator (with interaction hamiltonian of the form (a†)kak, k ≥ 2) interacting with light whose statistics can be varied from sub-Poissonian to poissonian via binomial state of field and super-Poissonian to poissonian via negative binomial state of field is presented. We predict that for all values of k there is a tendency increase in squeezing with increased sub-Poissonian character of the field while the reverse is true with super-Poissonian field. We also present non-classical behavior of the first order coherence function explicitly for k = 2 case (i.e., for two-photon anharmonic oscillator model used for a Kerr-like medium) with variation in the statistics of the input light.
We study the conditions for sub-poissonian photon statistics and squeezed states in the field of resonance fluorescence of a two-state atom. These conditions as a function of the detuning from resonance, the linewidth and the Rabi frequency have some overlap, but they are largely complementary. Super-poissonian statistics arise for small linewidths and large detunings, irrespective of the Rabi frequency. Squeezed states require small linewidths and either low or moderate Rabi frequencies, or large detunings from resonance.