Unitary quantum phase operators for bosons and fermions: A model study on quantum phases of interacting particles in a symmetric double-well potential

TL;DR

This paper develops and compares unitary and non-unitary quantum phase operators for bosons and fermions in a double-well potential, revealing significant differences especially for low particle numbers and exploring quantum phase fluctuations.

Contribution

It introduces unitary quantum phase operators for both bosons and fermions and applies them to analyze quantum phases in a double-well system, highlighting their advantages over non-unitary operators.

Findings

Unitary phase operators differ notably from non-unitary ones at low boson numbers.

Fermionic phase operators are successfully defined for two-component fermions.

Quantum phase and number fluctuations reveal uncertainty relations in the system.

Abstract

We introduce unitary quantum phase operators for material particles. We carry out a model study on quantum phases of interacting bosons in a symmetric double-well potential in terms of unitary and commonly-used non-unitary phase operators and compare the results for different number of bosons. We find that the results for unitary quantum phase operators are significantly different from those for non-unitary ones especially in the case of low number of bosons. We introduce unitary operators corresponding to the quantum phase-difference between two single-particle states of fermions. As an application of fermionic phase operators, we study a simple model of a pair of interacting two-component fermions in a symmetric double-well potential. We also investigate quantum phase and number fluctuations to ascertain number-phase uncertainty in terms of unitary phase operators.