Non-monotonous behavior of the number variance, Mandel factor, invariant uncertainty product and purity for the quantum damped harmonic oscillator

Abstract

We consider the relaxation of the quantum harmonic oscillator in the framework of the standard master equation. Analyzing the known solutions, we have found some new interesting effects. Namely, we show that the evolution of some parameters, such as the energy fluctuations, the Mandel factor, the invariant uncertainty product and quantum purity, can exhibit non-monotonous behavior with big deviations from the initial and final values. Also, we show that highly excited initial Fock states maintain their non-classical nature longer than low excited ones. During the evolution, the quantum purity of these states stays at almost constant low level during a long period, after the fast decrease initially and before the fast return to the final value at the end.