Classical Weyl–Wigner correspondence of optical field's phase operator

展德会 ZHAN De-hui, 卢道明 Lu Daoming, 范洪义 FAN Hong-yi

M. Davidović

Abstract Coherent states, in Wigner representation of quantum mechanics which is classical in structure with Wigner function playing the role of classical phase space probability distribution, and standard quantum mechanical expression for average values of corresponding Weyl quantum operators, general expression for matrix elements of the operator corresponding to phase of the oscillator by Weyl procedure, are obtained in the |n〉 basis. The general expression for matrix elements in the same basis of any other operator is also obtained. As the only mathematical technique necessary in the proposed procedure is a simple change of variables to polar coordinates in the corresponding integrals, this way to introduce Weyl phase operator, and some other operators in Weyl quantization, greatly simplifies necessary derivations and calculations.

K. Kakazu, Eijiro Sakai

It is shown that the number-phase (or rotational) Wigner function is obtained from the Weyl symmetrization rule for the correspondence between classical functions and quantum operators. In spite of the complicated form of the commutator for the number and phase operators, the Weyl symmetrization rule is similar to that in the case of the position and momentum operators. In addition, it is found that the ordering of the number and phase operators also has the same structure as that for the position-momentum pair.

Masashi Ban

V. N. Popov, Vladimir Sergeevich Yarunin, L. Siurakshina

Xuechao Li, Yang Yang, Fan Hong‐Yi

Using the technique of integration within an ordered product of operators, we derive Weyl ordered expansion for optical field phase operator and inverse of creation and annhilation operators. The results are used to obtain the classical correspondence, new generation function formula of some special functions and new integration formulas. In particular, for the first time we derive complex Gaussian integral formula when the integrand has negative power function.