Application of Wavepacket Dynamics: Illuminating Examples

Keith H. Hughes, Róbert E. Wyatt

B. M. Garraway

We examine an extension to the theory of Gaussian wavepacket dynamics in a one-dimensional potential by means of a sequence of time-dependent displacement and squeezing transformations. Exact expressions for the quantum dynamics are found, and relationships are explored between the squeezed system, Gaussian wavepacket dynamics, the time-dependent harmonic oscillator, and wavepacket dynamics in a Gauss-Hermite basis. Expressions are given for the matrix elements of the potential in some simple cases. Several examples are given, including the propagation of a non-Gaussian initial state in a Morse potential.

Paul Hockett

Mordechai Bixon

Keith H. Hughes, Róbert E. Wyatt

A moving grid approach to wavepacket dynamics is described that enables grid points to be used efficiently in regions where high resolution of the wavepacket is required. The grid movement is based on the principle of equidistribution and by using a grid smoothing technique the grid points trace a path that continuously adapt to reflect the dynamics of the wavepacket. The technique is robust and allows accurate computations to be obtained for long wavepacket propagation times. Results are presented for two systems: tunnelling dynamics in a double well potential and scattering of a wavepacket from a repulsive Eckart barrier.

Marco Genovese, Ivano Ruo-Berchera

Quantum illumination represents one of the most interesting examples of quantum technologies. On the one hand, it can find significant applications; on the other hand, it is one of the few quantum protocols robust against noise and losses. Here we present a short summary of the history of this quantum protocol.