Quantum collapses and revivals of a matter wave in the dynamics of symmetry breaking

TL;DR

This paper explores how the Wigner distribution visualizes quantum trajectories during symmetry breaking, revealing a sequence of revivals and collapses that connect quantum and classical states.

Contribution

It demonstrates the evolution of the Wigner distribution during symmetry breaking, highlighting the process of revivals and collapses in quantum systems far from equilibrium.

Findings

Wigner distribution reflects full quantum state during symmetry breaking

Quantum system undergoes revivals into unbroken symmetry state

Collapse leads to a delocalized quasi-classical state

Abstract

Using the remarkable mathematical construct of Eugene Wigner to visualize quantum trajectories in phase space, quantum processes can be described in terms of a quasi-probability distribution analogous to the phase space probability distribution of the classical realm. In contrast to the incomplete glimpse of the wave function that is achievable in a single shot experiment, the Wigner distribution, accessible by quantum state tomography, reflects the full quantum state. We show that during the fundamental symmetry-breaking process of a generic quantum system - with a symmetry breaking field driving the quantum system far from equilibrium - the Wigner distribution evolves continuously with the system undergoing a sequence of revivals into the symmetry unbroken state, followed by collapses onto a quasi-classical state akin the one realised in infinite size systems. We show that generically this state is completely delocalised both in momentum and in real space.