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Optik

Superposition of two coherent states π out of phase with average photon number as relative phase

Muhammad Ashfaq Ahmad, Shutian Liu

Published Sep 19, 2007• 18 citations
Publisher
DOI
10.1016/j.ijleo.2007.02.012

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This paper discusses the amplitude-squared squeezing for the superposition of two coherent states with their phase differences being separately π/2, 3π/2, and π, as well as for the superposition state of two pseudoclassical states. According to the analysis, it is found that the superposition state of two coherent states with their phase differences π/2 and 3π/2, and the superposition state of two pseudoclassical states both do exhibit the amplitude-squared squeezing. Also, some specific states are found to exhibit even stronger squeezing effects when relative phase of the superposition is equal to the average photon number. Amplitude-squared squeezing is dependent on the difference in phase between two coherent states.
We consider the quantum superposition of two coherent states shifted in phase by 3π/2, |α⟩ and |− i α⟩, as well as special states that are characterized solely with respect to amplitude α. According to analysis of nonclassical properties such as oscillatory and sub-Poissonian distribution of photon numbers, photon antibunching, quadrature squeezing, and negativity of Wigner function, it is concluded that the considered superposition state is a nonclassical state. Also, the special state is found to exhibit even stronger nonclassical features when relative phase ϕ of the superposition is equal to the average photon number |α| 2 .
Quantum statistical properties of general superpositions of coherent states of the type Nα,βα+eiξβ have been studied. Formulas for fluctuations (variances) of the coordinate and momentum quadratures and fluctuations of the number of photons in these states are obtained. The amplitude Nα,βnαeiφ+eiξnβeiφ,φ=φα=φβ and phase Nα,βneiφα+eiξneiφβ,n=nα=nβ superpositions of coherent states are considered separately. In the case of amplitude superpositions, a field under certain conditions occurs in a quadrature-squeezed state. At the same time, the photon distribution in the case of amplitude superpositions is always super-Poissonian. In the case of phase superpositions, a field under certain conditions occurs in quadrature-squeezed states for small average numbers of photons. For certain parameters of coherent states, the photon statistics in phase superpositions is sub-Poissonian. Using amplitude superpositions, it is possible to generate a microscopic electromagnetic field with the average photon number below or on the order of unity, as well as mesoscopic and even macroscopic fields with arbitrary large average photon numbers, characterized by significant quadrature squeezing. Using phase superpositions, it is possible to create under certain conditions the electromagnetic field states with sub-Poissonian statistics (squeezed distribution of photon numbers) for an arbitrary large average photon number. Expressions for a ‘strict’ coordinate–momentum uncertainty relation (Cauchy inequality) are obtained and analysed in cases of general, amplitude and phase superpositions of coherent states.