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Chinese Physics Letters

Two-Parameter Correlated Negative Binomial State in Two-Mode Fock Space

Hong-Yi Fan, Xiao‐Yin Pan, Bo-zhan Chen

Published Jul 1, 1998• 4 citations
Publisher

Abstract

A kind of two-parameter correlated negative binomial state is constructed and analysed from the point of view of quantum optics theory in two-mode Fock space. By choosing a suitable two-mode correlated Holstein-Primakoff-analogue transformation, the state can be identified as a type of correlated SU (1, 1) coherent state. The possible physical uses of the state are also pointed out.

DOI
10.1088/0256-307x/15/7/001

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Physical Review A•Aug 1, 1994•29 citations
A kind of two-parameter correlated negative binomial state is constructed and analysed from the point of view of quantum optics theory in two-mode Fock space. By choosing a suitable two-mode correlated Holstein-Primakoff-analogue transformation, the state can be identified as a type of correlated SU (1, 1) coherent state. The possible physical uses of the state are also pointed out.
We have constructed a new kind of two-mode bosonic realization of SU (1,1) Lie algebra, on the basis of which the SU (1,1) generalized coherent states in the two-mode Fock space are derived. These two-mode SU (1,1) coherent states, which are called uncorrelated two-mode SU (1,1) coherent states, include three special cases. For these states, we study the mean photon number distribution and their non-classical properties, which are photon anti-bunching, violations of Cauchy-Schwarz inequality and two-mode squeezing.
Using the q analog of the Holstein-Primakoff boson realization of the su(2) generators, we show that a type of q-deformed binomial state that corresponds to the Heine distribution can be identified as an su(2)q{)}_{\mathit{q}})q​ coherent state. This fact is a q extension of the fact that the ordinary binomial state is a particular su(2) coherent state when the Holstein-Primakoff transformation is employed.