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Modern Physics Letters B

MINIMUM UNCERTAINTY SU(1,1) COHERENT STATES FOR NUMBER DIFFERENCE — TWO-MODE PHASE SQUEEZING

Hong-Yi Fan, Zhihu Sun

Published Feb 28, 2000• 5 citations
Publisher

Abstract

For the two-mode photon number-difference operator D = a†a -b†b and the Noh, Fougers and Mandel (NFM) operational phase operator [Formula: see text], we introduce the concept of number-difference-phase squeezing. We then find a new minimum-uncertainty state for number-difference-phase squeezing, which turns out to be a special combination of generalized SU(1,1) coherent state. As a by-product, a new orthonormal and complete representation in two-mode Fock space made up of R†n|m, m> is found.

DOI
10.1142/s0217984900000239

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For the two-mode photon number-difference operator D = a†a -b†b and the Noh, Fougers and Mandel (NFM) operational phase operator [Formula: see text], we introduce the concept of number-difference-phase squeezing. We then find a new minimum-uncertainty state for number-difference-phase squeezing, which turns out to be a special combination of generalized SU(1,1) coherent state. As a by-product, a new orthonormal and complete representation in two-mode Fock space made up of R†n|m, m> is found.
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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.