Properties of a Polarization based Phase Operator

TL;DR

This paper introduces a Hermitian phase operator for photons that incorporates polarization, providing a unitary operator satisfying canonical relations and applicable to various quantum states.

Contribution

It defines a polarization-based phase operator for photons that is Hermitian, unitary, and acts as a ladder operator across all polarization states, advancing quantum phase theory.

Findings

The phase operator is unitary and satisfies canonical commutation relations.

The operator effectively describes phase properties of coherent, squeezed, and thermal states.

Density matrices and phase distributions were successfully calculated for different states.

Abstract

We define a Hermitian phase operator for zero mass spin one particles (photons) by taking account polarization. The Hilbert space includes the positive helicity states and negative helicity states with opposite circular polarization. We define an operator which corresponds to the physical process of reversing the sense of polarization and acts as a bridge between positive helicity states and negative helicity states. The exponential phase operator obtained using the entire set is unitary and acts as ladder operator over all the states. The phase operator derived from this exponential operator satisfies the canonical commutation relations with the number operator. We have calculated the density matrix and the phase probability distribution of various states like coherent states, squeezed states and thermal states, to illustrate the utility of our operator.