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arXiv:quant-ph/9611014 · Physical Review A

Gaussian-Wigner distributions and hierarchies of nonclassical states in quantum optics: The single-mode case

Arvind, Narasimhaiengar Mukunda, R. Simon

Published Dec 1, 1997• 22 citations
arXivHTMLPDF

Abstract

A recently introduced hierarchy of states of a single-mode quantized radiation field is examined for the case of centered Gaussian-Wigner distributions. It is found that the onset of squeezing among such states signals the transition to the strongly nonclassical regime. Interesting consequences for the photon-number distribution, and explicit representations for them, are presented. The effects of nonideal detection are also carefully analyzed.

DOI
10.1103/physreva.56.5042

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A recently introduced hierarchy of states of a single-mode quantized radiation field is examined for the case of centered Gaussian-Wigner distributions. It is found that the onset of squeezing among such states signals the transition to the strongly nonclassical regime. Interesting consequences for the photon-number distribution, and explicit representations for them, are presented. The effects of nonideal detection are also carefully analyzed.
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We present an analytical framework for the emergence of nonclassical radiation in strongly laser-driven quantum systems, with a focus on high-order harmonic generation (HHG). Starting from a Pauli-Fierz description, we employ a parametric factorization of the coupled light-matter wavefunction that reduces the dynamics to coupled equations for a field-driven electronic state and a quantized light mode. Within this framework, we identify a simple and predictive mechanism for nonclassicality: it originates from the nonlinear dependence of the electronic dipole response on the light-mode coordinate. An approximately constant dipole yields coherent radiation, a linear dependence produces squeezing, and higher-order nonlinearities give rise to Wigner-function negativity. We illustrate this mechanism for atomic and molecular model systems and analyze its scaling in multi-emitter configurations, indicating routes toward high-photon-number nonclassical radiation in HHG. Our results provide a transparent connection between strong-field dynamics and quantum-optical properties of emitted light, offering a basis for engineering nonclassical states in intense laser-matter interactions.
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Nonclassical fields with coherent components generated in a large number of optical processes including losses can be characterized by a Gaussian Wigner function centered around the mean value of the field. The photon-number distributions for such fields are calculated and the numerical results are presented for a range of parameters. As a special case we give the number distributions for photons produced in down-conversion problems. We also give the analytical expression for the photoelectron distributions.
“Hypergeometric states,” which are a one-parameter generalization of binomial states of the single-mode quantized radiation field, are introduced and their nonclassical properties are investigated. Their limits to the binomial states and to the coherent and number states are studied. The ladder operator formulation of the hypergeometric states is found and the algebra involved turns out to be a one-parameter deformation of su(2) algebra. These states exhibit highly nonclassical properties, like sub-Poissonian character, antibunching, and squeezing effects. The quasiprobability distributions in phase space, namely the Q and the Wigner functions are studied in detail. These remarkable properties seem to suggest that the hypergeometric states deserve further attention from theoretical and applicational sides of quantum optics.
A new operator-based condition for distinguishing classical from nonclassical states of quantized radiation is developed. It exploits the fact that the normal ordering rule of correspondence to go from classical to quantum-dynamical variables does not in general maintain positivity. It is shown that the approach naturally leads to distinguishing several layers of increasing nonclassicality, with more layers as the number of modes increases. A generalization of the notion of sub-Poissonian statistics for two-mode radiation fields is achieved by analysing completely all correlations and fluctuations in quadratic combinations of mode annihilation and creation operators conserving the total photon number. This generalization is nontrivial and intrinsically two-mode as it goes beyond all possible single mode projections of the two-mode field. The nonclassicality of pair-coherent states, squeezed vacuum and squeezed thermal states is analysed and contrasted to one another, comparing the generalized sub-Poissonian statistics with extant signatures of nonclassical behaviour.