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Journal of Physics B Atomic Molecular and Optical Physics

Higher order sub-Poissonian photon statistics and their use in detection of Hong and Mandel squeezing and amplitude-squared squeezing

Hari Prakash, Devendra Kumar Mishra

Published Apr 24, 2006• 51 citations
Publisher

Abstract

We study higher order sub-Poissonian photon statistics conditions for non-classicality in the form of general inequalities for expectation values of products of arbitrary powers of photon number and of photon-number fluctuation. We discuss their use for the detection of (i) Hong and Mandel's squeezing of arbitrary order and (ii) amplitude-squared squeezing. Also, we discuss examples of states that exhibit some higher order sub-Poissonian photon statistics but not others.

DOI
10.1088/0953-4075/39/9/014

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We study higher order sub-Poissonian photon statistics conditions for non-classicality in the form of general inequalities for expectation values of products of arbitrary powers of photon number and of photon-number fluctuation. We discuss their use for the detection of (i) Hong and Mandel's squeezing of arbitrary order and (ii) amplitude-squared squeezing. Also, we discuss examples of states that exhibit some higher order sub-Poissonian photon statistics but not others.
It is pointed out that, although squeezing and sub-Poissonian photon statistics need not go together, in the sense that an electromagnetic field may exhibit one but not the other, the method that is normally used to detect a squeezed state automatically generates sub-Poissonian photon statistics. However, when these considerations are applied to the fluorescence from a coherently driven atom, which exhibits both squeezing and sub-Poisson fluctuations, one finds that the statistics of the emitted photons show even larger departures from classical field theory than the squeezing.
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.
The statistical fluctuations of light can, under certain circumstances, exhibit a number of interesting nonclassical features. These include photon antibunching, sub-Poissonian statistics, and squeezing, all of which exist only in a quantum field. The three effects are distinct, and do not necessarily go together, although the first two are sometimes mistakenly treated as interchangeable. Both photon antibunching and sub-Poissonian statistics have been observed in experiments on resonance fluorescence from single atoms, which is described. Squeezing has not yet been seen experimentally, although many nonlinear processes are expected to give rise to it. The squeezed state can be recognized in heterodyne or homodyne experiments, where the squeezing becomes manifest as sub-Poissonian photon fluctuations.
A parameteric study was performed of the sub-Poissonian photon statistics and higher-order squeezing characteristics of Bernouilli states undergoing a linear amplification process. The necessary and sufficient conditions on the amplifier gain under which the output light exhibits sub-Poissonian photon statistics or squeezing were compared with exact numerical results, and good agreement was obtained. On the other hand, it was shown that Bernouilli states exhibit higher-order squeezing for some parameter ranges. The degree of higher-order squeezing decreases, and its duration becomes shorter, as the phase of the Bernouilli state increases.
We examine the influence of thermal noise on several non-classical properties of squeezed number states. In order to evaluate arbitrary-order moments of both amplitude and quadrature operators of the superposition, we use a normal-ordering technique based on McCoy's theorem. Our analytical results are compact formulae involving Gauss hypergeometric functions. We find that the thermal mean occupancy sufficient to destroy squeezing to any order is less than . Other non-classical features of a squeezed number state, such as pairwise oscillations in the photon number distribution, sub-Poissonian statistics and amplitude-squared squeezing disappear completely above this threshold.