Deformed Two-Photon Squeezed States in Noncommutative Space

TL;DR

This paper develops a formalism for two-photon squeezed states in noncommutative space, revealing how spatial noncommutativity introduces correlations between degrees of freedom and affects quantum variances.

Contribution

It introduces a new formalism for deformed two-photon squeezed states in noncommutative space, highlighting correlations induced by noncommutativity.

Findings

Variances of quadratures include contributions from other degrees of freedom.

Correlations reveal new features of spatial noncommutativity.

Enhanced understanding of correlated boson commutators.

Abstract

Recent studies on non-perturbation aspects of noncommutative quantum mechanics explored a new type of boson commutation relations at the deformed level, described by deformed annihilation-creation operators in noncommutative space. This correlated boson commutator correlates different degrees of freedom, and shows an essential influence on dynamics. This paper devotes to the development of formalism of deformed two-photon squeezed states in noncommutative space. General representations of deformed annihilation-creation operators and the consistency condition for the electromagnetic wave with a single mode of frequency in NC space are obtained. Two-photon squeezed states are studied. One finds that variances of the dimensionless hermitian quadratures of the annihilation operator in one degree of freedom include variances in the other degree of freedom. Such correlations show the new feature of spatial noncommutativity and allow a deeper understanding of the correlated boson commutator.