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TURKISH JOURNAL OF PHYSICS

Nonlinear Two-Mode Squeezed Vacuum States as Realization of SU(1,1) Lie Algebra

G. M. Abd Al-Kader, A.‐S. F. Obada

Published Jul 7, 2008• 0 citations
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Abstract

Nonlinear extensions of the two-mode squeezed vacuum states (NTMSVS’s) are constructed and special cases of these states are discussed. We have constructed the NTMSVS’s realization of SU(1,1) Lie algebra. Two cases of the definition are considered for unitary and non-unitary deformation operator functions. Some nonclassical properties of these states are discussed.

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Nonlinear extensions of the two-mode squeezed vacuum states (NTMSVS’s) are constructed and special cases of these states are discussed. We have constructed the NTMSVS’s realization of SU(1,1) Lie algebra. Two cases of the definition are considered for unitary and non-unitary deformation operator functions. Some nonclassical properties of these states are discussed.
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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.
We theoretically construct a two-parameter two-mode squeezing operator by combining the two-mode coupled harmonic oscillator Hamiltonian with beam splitter transformations. A novel two-mode squeezed vacuum state (NTMSVS) is generated via the application of this operator to the two-mode vacuum state. Numerical investigations demonstrate that the NTMSVS exhibits intermediate properties between the conventional two-mode squeezed vacuum state (TMSVS) and the product state of two independent single-mode squeezed vacua across multiple quantum metrics, including Wigner distribution characteristics, logarithmic negativity, EPR steering robustness and Bell inequality violation. Notably, the quadrature squeezing and sum squeezing amplitudes are significantly amplified under specific parametric regimes, offering enhanced nonclassicality compared to standard squeezed states.