Inverse operator representations of quantum phase

TL;DR

This paper introduces a novel inverse operator approach to defining quantum phase, linking it to existing phase operators and exploring its implications for quantum optics, especially in squeezed states.

Contribution

It presents a new inverse operator framework for quantum phase, extending the definitions of phase operators and including negative energy states in the Hilbert space.

Findings

Inverse operators can define quantum phase similarly to existing operators.

The Hilbert space for the unitary phase operator includes negative energy states.

Potential applications in quantum optics, particularly in squeezed states.

Abstract

We define quantum phase in terms of inverses of annihilation and creation operators. We show that like Susskind - Glogower phase operators, the measured phase operators and the unitary phase operators can be defined in terms of the inverse operators. However, for the unitary phase operator the Hilbert space includes the negative energy states. The quantum phase in inverse operator representation may find the applications in the field of quantum optics particularly in the squeezed states.