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

We study the time dependent transitions of quantum forced harmonic oscillator (QFHO) in noncommutative $\text{mathds}{R}^{1,1}$ 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.