The Pegg-Barnett phase operator and the discrete Fourier transform

TL;DR

This paper demonstrates that the Pegg-Barnett phase operator can be derived using the discrete Fourier transform applied to the number operator in finite-dimensional quantum systems, linking it to circular waveguide array Hamiltonians.

Contribution

It reveals a novel connection between the Pegg-Barnett phase operator, discrete Fourier transform, and circular waveguide array Hamiltonians in finite-dimensional quantum systems.

Findings

Pegg-Barnett phase operator obtained via discrete Fourier transform.

Structure of London-Susskind-Glogower operator embedded in waveguide Hamiltonian.

Potential applications in finite-dimensional photonic systems.

Abstract

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 operator defined in a finite-dimensional Hilbert space. Furthermore, we show that the structure of the London-Susskind-Glogower phase operator, whose natural logarithm give rise the Pegg-Barnett phase operator, is contained into 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.