Atom in a $q$-Analog Harmonic Oscillator Trap

We study the population inversion and Q-function of a two-level atom, interacting with single-mode laser light field, in a $q$-analog harmonic oscillator trap for increasing $q$. For $\tau=.003(q=e^{\tau})$ the collapses and revivals of population inversion become well defined facilitating experimental observation but for large $\tau \sim 0.1$ the time dependence of population inversion is completely wiped out.