On the Weyl Correspondence of the Photon Phase Operator

Weifeng Wu, Hong-Yi Fan

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.

T.B. Smith, Daniel A. Dubin, Mark A. Hennings

We suggest a candidate for a non-canonical Hermitian operator corresponding to phase angle, based on the Weyl correspondence rule. The matrix elements of this operator, for harmonic oscillator number states, coincide, in the correspondence limit, with those of a phase operator proposed by Barnett and Pegg, when the dimension of their defining space becomes infinite.

Kazuo Fujikawa

A.S. Shumovsky

The quantum polarization and phase properties of an electric dipole radiation are examined. It is shown that, unlike the classical picture, the quantum description of polarization needs nine independent Stokes operators, forming a representation of SU (3) sub-algebra in the Weyl-Heisenberg algebra of photons. A corresponding Cartan algebra determines the cosine and sine of the radiation phase operators. A new representation of dipole photons is proposed. The generators of the Cartan algebra are diagonal in this representation so that the corresponding number states describe the number of photons with given radiation phase. The eigenstates of the radiation phase are determined. They have a discrete spectrum and natural behaviour in the classical limit. The relation between the radiation phase, operational phases and the Pegg-Barnett approach is discussed.

Helman Le Pas de Sécheval, C. Bendjaballah