Time dependent transitions with time-space noncommutativity & its implications in Quantum Optics

TL;DR

This paper investigates how time-space noncommutativity affects the dynamics of a quantum forced harmonic oscillator, revealing modifications to the Poisson distribution and the evolution into squeezed states, with implications for quantum optics.

Contribution

It introduces a perturbative analysis of the quantum harmonic oscillator in noncommutative space, highlighting novel effects on state evolution and uncertainties in quantum optics.

Findings

Poisson distribution is modified by noncommutativity.

Vacuum state evolves into a squeezed state.

Uncertainties in position and momentum show interesting time-dependent behavior.

Abstract

We study the time dependent transitions of quantum forced harmonic oscillator (QFHO) in noncommutative $\mathds{R}^{1,1}$ perturbatively to linear order in the noncommutativity $\theta$. We show that the Poisson distribution gets modified, and that the vacuum state evolves into a "squeezed" state rather than a coherent state. The time evolutions of uncertainties in position and momentum in vacuum are also studied and imply interesting consequences for modeling nonlinear phenomena in quantum optics.