The Pegg-Barnett phase operator and the discrete Fourier transform

• Published in: Physica scripta Vol. 91; no. 4; pp. 43008 - 43011
• Main Authors: Perez-Leija, Armando, Andrade-Morales, Luis A, Soto-Eguibar, Francisco, Szameit, Alexander, Moya-Cessa, Héctor M
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01-04-2016
• Subjects: Arrays; discrete Fourier transform; Fourier transforms; Hilbert space; Logarithms; Operators; optical lattices; phase operator; Phase transformations; Photonics; Quantum mechanics
• ISSN: 0031-8949; 1402-4896
• DOI: 10.1088/0031-8949/91/4/043008

In quantum mechanics the position and momentum operators are related to each other via the Fourier transform. In the same way, here we show that the so-called Pegg-Barnett phase operator can be obtained by the application of the discrete Fourier transform to the number operators defined in a finite-dimensional Hilbert space. Furthermore, we show that the structure of the London-Susskind-Glogower phase operator, whose natural logarithm gives rise to the Pegg-Barnett phase operator, is contained in the Hamiltonian of circular waveguide arrays. Our results may find applications in the development of new finite-dimensional photonic systems with interesting phase-dependent properties.