Non-Entangling Channels for Multiple Collisions of Quantum Wave Packets

TL;DR

This paper introduces a new analytical method to study multiple collisions of quantum wave packets, showing how entanglement initially increases then decreases, ultimately disappearing as the light particle slows down.

Contribution

The paper presents a novel channel decomposition method that simplifies the quantum collision problem by reducing it to classical calculations, avoiding entanglement.

Findings

Entanglement initially increases then decreases over time.

The method provides a complete analytical solution to the collision problem.

Entanglement disappears when the light particle becomes too slow.

Abstract

We consider multiple collisions of quantum wave packets in one dimension. The system under investigation consists of an impenetrable wall and of two hard-core particles with very different masses. The lighter particle bounces between the heavier one and the wall. Both particles are initially represented by narrow Gaussian wave packets. A complete analytical solution of this problem is presented on the basis of a new method. The idea of the method is to decompose the two-particle wave function into a continuous superposition of terms (channels), such that the multiple collisions within each channel do not lead to subsequent entanglement between the two particles. For each channel, the time evolution of the two-particle wave function is completely determined by the motion of the corresponding classical point-like particles; therefore the whole quantum problem is reduced to a classical calculation. The calculation based on the above method reveals the following unexpected result: The entanglement between the two particles first increases with time due to the collisions, but then it begins to decrease, disappearing completely when the light particle becomes too slow to catch up with the heavy one.