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Journal of Shangluo University

Quantum Phase Density Distribution of Amplitude Coherent States

Ying Li

Published Jan 1, 2008• 0 citations
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Abstract

Pegg-Barnett Quantum phase density distribution properties of amplitude coherent states are studied.It is find that:1.the Quantum phase density distribution of amplitude coherent states p(θ,m) is influenced by superposition angle φ which is the vacuum state |o〉superposed by coherent state|α〉,average photon number and θ-γ that is the quantum phase θ minus displace angle of coherent state γ.2.the quantum phase density distribution changes with φ and θ-γ periodically;it becomes large with increase of average photon numbers.Under certain conditions,extremums of quantum phase density distribution are restricted by φ and θ-γ.

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Chinese Physics Letters•Sep 1, 2006•11 citations
Pegg-Barnett Quantum phase density distribution properties of amplitude coherent states are studied.It is find that:1.the Quantum phase density distribution of amplitude coherent states p(θ,m) is influenced by superposition angle φ which is the vacuum state |o〉superposed by coherent state|α〉,average photon number and θ-γ that is the quantum phase θ minus displace angle of coherent state γ.2.the quantum phase density distribution changes with φ and θ-γ periodically;it becomes large with increase of average photon numbers.Under certain conditions,extremums of quantum phase density distribution are restricted by φ and θ-γ.
Quantum-statistical properties of the phase of electromagnetic field in the case of phase superpositions of coherent states of the type Nα,β,ξneiϕα+eiξneiϕβ have been studied. Formulas for the average values and fluctuations (variances) of Hermitian phase operator ϕˆθ of the electromagnetic field (so-called Pegg–Barnett optical phase operator) in the case of general superposition of coherent states are obtained and analysed. The states of phase superpositions of the ‘Schrödinger cat’ type Nα,−α,ξ(|α⟩+eiξ|−α⟩),ϕβ=ϕα+π, and superpositions of coherent states of the type Nα,α∗,ξ(|α⟩+eiξ|α∗⟩),ϕβ=−ϕα, are considered separately.
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.
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 .