Deformed squeezed states in noncommutative phase space

TL;DR

This paper introduces a deformed boson algebra from noncommutative phase space, constructs coherent and squeezed states, and analyzes their uncertainty properties, revealing restrictions on noncommutative parameters to uphold Heisenberg's principle.

Contribution

It develops a new algebraic framework for quantum states in noncommutative phase space and explores their uncertainty relations, which was not previously addressed.

Findings

Noncommutative coherent and squeezed states are constructed.

Variances of quadrature operators are evaluated on these states.

Restrictions between noncommutative parameters are necessary to satisfy Heisenberg's uncertainty relations.

Abstract

A deformed boson algebra is naturally introduced from studying quantum mechanics on noncommutative phase space in which both positions and momenta are noncommuting each other. Based on this algebra, corresponding intrinsic noncommutative coherent and squeezed state representations are constructed, and variances of single- and two-mode quadrature operators on these states are evaluated. The result indicates that in order to maintain Heisenberg's uncertainty relations, a restriction between the noncommutative parameters is required.