Regular phase operator and SU(1,1) coherent states of the harmonic oscillator

TL;DR

This paper introduces a new regular phase operator for the quantum harmonic oscillator using an exponential operator approach, linking it to SU(1,1) coherent states and providing a consistent phase representation.

Contribution

It presents a novel regular phase operator based on a polar decomposition, with eigenstates as SU(1,1) coherent states, addressing longstanding issues in quantum phase description.

Findings

Constructed a strongly convergent power series for the phase operator

Eigenstates form SU(1,1) coherent states in the Holstein-Primakoff realization

Derived phase densities and spectral resolution compatible with classical intuition

Abstract

A new solution is proposed to the long-standing problem of describing the quantum phase of a harmonic oscillator. In terms of an'exponential phase operator', defined by a new 'polar decomposition' of the quantized amplitude of the oscillator, a regular phase operator is constructed in the Hilbert-Fock space as a strongly convergent power series. It is shown that the eigenstates of the new 'exponential operators are SU(1,1) coherent states in the Holstein-Primakoff realization. In terms of these eigenstates, the diagonal representation of phase densities and a generalized spectal resolution of the regular phase operator are derived, which suit very well to our intuitive pictures on classical phase-related quantities