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Amplitude-squared squeezing in superposed coherent states

Authors:	H Prakash P Kumar

Institution:	(1) Department of Physics, University of Allahabad, Allahabad, 211002, India;(2) M.N. Saha Centre of Space Studies, Institute of Interdisciplinary Studies, University of Allahabad, Allahabad, 211002, India;(3) Bhavan's Mehta Mahavidyalaya (V.S. Mehta College of Science), Bharwari, Kaushambi, 212201, India

Abstract:	We study amplitude-squared squeezing of the Hermitian operator Z_θ=Z₁ cosθ+Z₂ sin θ, in the most general superposition state $\left\| \psi \right\rangle =C_1 \left\| \alpha \right\rangle +C_2 \left\| \beta \right\rangle$ , of two coherent states $\left\| \alpha \right\rangle$ and $\left\| \beta \right\rangle$ . Here operators Z_1,2 are defined by $Z_{1 }+ i Z_{2 }=a-\left\langle \psi \right\|a\left\| \psi \right\rangle ]^2$ , a is annihilation operator, θ is angle, and complex numbers C_1,2, α, β are arbitrary and only restriction on these is the normalization condition of the state $\left\| \psi \right\rangle$ . We define the condition for a state $\left\| \psi \right\rangle$ to be amplitude-squared squeezed for the operator Z_θ if squeezing parameter $S\equiv \left\langle \psi \right\|(\Delta Z_\theta )^{2}\left\| \psi \right\rangle -\left\langle \psi \right\|N\left\| \psi \right\rangle +\left\langle \psi \right\|a\left\| \psi \right\rangle \left\langle \psi \right\|a^+\left\| \psi \right\rangle ]<\frac{1}{2}$ , where N=a⁺a and $\Delta Z_\theta =Z_\theta -\left\langle \psi \right\|Z_\theta \left\| \psi \right\rangle$ . We find maximum amplitude-squared squeezing of Z_θ in the superposed coherent state $\left\| \psi \right\rangle$ with minimum value 0.3268 of the parameter S for an infinite combinations with α- β= 2.16 exp ±i(π/4) + iθ/2], $C_2 /C_1 =0.3 \exp \frac{1}{2}(\alpha \beta ^\ast -\alpha ^\ast \beta )]$ and with arbitrary values of (α+β) and θ. For this minimum value of squeezing parameter S, the expectation value of photon number can vary from the minimum value 1.0481 to infinity. Variations of the parameter S with different variables at maximum amplitude-squared squeezing are also discussed.

Keywords:	42 50 Dv Nonclassical states of the electromagnetic field including entangled photon states quantum state engineering and measurements
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