Generalized Localized Matter Wavepackets

Abstract

Studying the system of the non-Hermitian (NH) generalized parametric oscillator, we use the Wei–Norman factorization method, as well as the biorthonormal basis formalism, in order to initiate a complex probability density. Generalizing the usual Yuen procedure for the calculation of the variances Δq, Δp in terms of the complex probability density, we obtain a reduction in the position and an increase in the momentum uncertainty, in discrete time intervals. In the framework of the macroscopic quantum tunneling (MQT) effect, such a suppression of the matter wavepacket spreading provides a mechanism to localize a quantum particle, and is responsible for its behavior as a macroscopic state, inhibiting the tunneling process. Applications of squeezed matter wavepackets can be found in the control of excited-state chemical reactions, in MQT for Josephson junctions, and in the tunneling of trapped atoms in optical crystals.