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Journal of Mathematical Physics

The q-phase-difference operator and two-mode q-coherent states

Yaping Yang, Weiguo Feng, Xiang Xia Wu

Published Dec 1, 1997• 3 citations
Publisher

Abstract

In this paper, we introduce unitary and Hermitian phase-difference operators for the two modes of the electromagnetic field in the q-deformed case. The q-creation and annihilation operators of phase-difference quanta are given, and the algebraic properties of some operators in phase space are discussed. The phase-difference properties of two-mode q-coherent states are investigated.

DOI
10.1063/1.532215

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In this paper, we introduce unitary and Hermitian phase-difference operators for the two modes of the electromagnetic field in the q-deformed case. The q-creation and annihilation operators of phase-difference quanta are given, and the algebraic properties of some operators in phase space are discussed. The phase-difference properties of two-mode q-coherent states are investigated.
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Quantum-mechanical operators of phase difference between two electromagnetic fields are proposed and their properties are analyzed. The Hermitian phase-difference operators are determined using the operators of interference of the two fields, which appears upon their mixing on a beam splitter. The results of calculations for the measured mean values and dispersions (fluctuations) of the trigonometric functions of the phase-difference operators, which follow from the Pegg–Barnett theory, are compared with the corresponding values for the proposed operators. Calculations and comparison are carried out for the Fock, coherent, and squeezed quantum states of electromagnetic fields. Analysis is performed for quantum microscopic fields with mean values n^\hat {n}n^ ~ 1 of the number of photons, which are currently used in quantum technologies. The quantitative agreement between two different theories is demonstrated for the Fock and squeezed states of the fields; in the case of coherent states, an appreciable quantitative difference in the predictions of the theories is observed.
Based on our previous work, the phase state and phase operator introduced by Pegg and Barnett are generalized to two-mode q-deformed circumstances. With the aid of numerical method, the phase probability distributions of q-deformed pair coherent state are investigated. It is shown that these probability distributions of the state are regulated by the parameters of phase, the q-number and the magnitude of |ξ|. Therefore, the q-deformed pair coherent state exhibits different quantum interference properties.
We introduce a unitary operator representing the exponential of the phase difference between two modes of the electromagnetic field. The eigenvalue spectrum has a discrete character that is fully analyzed. We relate this operator with a suitable polar decomposition of the Stokes parameters of the field, obtaining a natural classical limit. The cases of weakly and highly excited states are considered, discussing to what extent it is possible to talk about the phase for a single-mode field. This operator is applied to some interesting two-mode fields.