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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Nonclassicality of two-mode states of the quantized radiation field

Adrian Alexandrescu, Diethard H. Schiller

Published Oct 1, 2003• 0 citations
Publisher

Abstract

The second-order coherence (correlation) functions are used to investigate the classicality (nonclassicality) of quantum states, as defined by the existence (nonexistence) of a positive definite (Glauber-Sudarshan) P-representation. We study nonclassical behavior as revealed by sub-Poissonian statistics and/or violation of the classical Cauchy-Schwarz inequality. The two-mode states considered include Bell-like superpositions of Fock states, Schrödinger cat states and the ideal squeezed states.

DOI
10.1117/12.519807

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The second-order coherence (correlation) functions are used to investigate the classicality (nonclassicality) of quantum states, as defined by the existence (nonexistence) of a positive definite (Glauber-Sudarshan) P-representation. We study nonclassical behavior as revealed by sub-Poissonian statistics and/or violation of the classical Cauchy-Schwarz inequality. The two-mode states considered include Bell-like superpositions of Fock states, Schrödinger cat states and the ideal squeezed states.
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.
We examine the nonclassical properties of the pair coherent states defined as the simultaneous eigenstates of the operator that annihilates photons in pairs and of the operator that gives the relative occupation number in the two modes. We show that fields in such states have remarkable quantum features such as sub-Poissonian statistics correlations in the number fluctuations, squeezing, and violations of Cauchy–Schwarz inequalities. We show how such pair coherent states can be generated by the competition of different nonlinear processes in a two-photon medium. The quantam features occur not only in the transient domain but also survive in the steady state because of the balance between nonlinear processes.
The two-mode photon-added state defined by |?, q; m>?=?a+mb+m|?, q> up to a normalization constant is introduced, where |?, q> is a pair coherent state and m an integer. It is shown that the fields in such a state have remarkable quantum features such as sub-Poissonian statistics, violations of Cauch-Schwarz inequalities, correlations in the number fluctuations and squeezing. We examine the influence of photon-adding on the properties of pair coherent state, and propose a method of generating two-mode photon-added states in the context of cavity quantum electrodynamics.
We examine the non-classical properties of two-mode coherent states based on different unitary irreducible representations of SU(1, 1). Such states are generated by the action of the two-mode squeezing operator on initial states of the field containing arbitrary numbers of photons in each of the two modes. If the initial state of the field is a two-mode vacuum state, the final state is of course the two-mode squeezed vacuum. An initial occupation generalizes the idea of a squeezed vacuum to the SU(1, 1) coherent states. We show that fields in such states have remarkable quantum properties such as sub-Poissonian statistics, violations of the Cauchy-Schwarz inequality, strong correlations in the photon number fluctuations and squeezing. Using information theory formalism, we show that these coherent states are less correlated than the usual two-mode squeezed vacuum. Moreover, we show that an initial coherent amplitude contribution, in a large amplitude limit, can result in the reduction of correlations between modes.