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Acta Sinica Quantum Optica

Quantum Statistical Properties of Minimum Correlation States

Yun‐Jie Xia

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

In this paper we study the quantum statistical properties of minimum correlation states in different coefficients.We find out that the minimum correlation states disobey with the classical Cauchy-Schwartz inequality and exhibit non-classical correlations.We also study the non-classical properties about squeezing and sub-Poissonian statistics of minimum correlation states.

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In this paper we study the quantum statistical properties of minimum correlation states in different coefficients.We find out that the minimum correlation states disobey with the classical Cauchy-Schwartz inequality and exhibit non-classical correlations.We also study the non-classical properties about squeezing and sub-Poissonian statistics of minimum correlation states.
We discuss some mathematical aspects of photon antibunching and sub-Poisson photon statistics. It is known that Bell's inequalities for entangled states can be reduced to the Cauchy-Bunyakovsky inequalities. In this note some rigorous results on impossibility of classical hidden variables representations of certain quantum correlation functions are proved which are also based on the Cauchy-Bunyakovsky inequalities. The difference K between the variance and the mean as a measure of non-classicality of a state is discussed. For the classical case K is nonnegative while for the n-particle state it is negative and moreover it equals -n. The non-classicality of quantum states discussed here for the sub-Poisson statistics is different from another non-classicality called entanglement though both can be traced to the violation of the Cauchy-Bunyakovsky inequality.
We have studied quantum statistical properties in a zero-temperature two-species Bose–Einstein condensate system in the presence of the nonlinear self-interaction of each species, the interspecies nonlinear interaction, and the Josephson-like tunneling interaction. It is found that the two condensates may periodically exhibit sub-Poissonian distribution. It is revealed that the correlation between the two condensates can be nonclassical, which means that there exists a violation of Cauchy–Schwartz inequality. The nonclassical effect about the correlation between the two condensates can be realized experimentally by properly preparing the total number of atoms in the two condensates.
The properties of states generated by the application of the two-mode squeeze operator to the pair coherent states are studied. These states are the two-mode analogues of the single-mode squeezed states generated by the application of the single-mode squeeze operator to an ordinary coherent state. In the present case there are correlations between the modes and strong non-classical properties are to be expected. We study the statistical properties of the photon number distributions, squeezing, violations of the Cauchy-Schwartz inequality, quasiprobability distributions and the phase distributions.
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.