Towards a quantum time mirror for nonrelativistic wave packets

TL;DR

This paper introduces a quantum time mirror technique that uses a short-time nonlinear perturbation to reverse the evolution of nonrelativistic wave packets, enabling time-reversal echoes in quantum systems.

Contribution

The paper proposes a novel quantum time mirror method based on a nonlinear time-dependent perturbation to achieve partial time-reversal of nonrelativistic wave packets.

Findings

Numerical simulations confirm effective time-reversal echoes in 1D and 2D.

The method is supported by analytical calculations.

Potential experimental implementations are discussed.

Abstract

We propose a method -- a quantum time mirror (QTM) -- for simulating a partial time-reversal of the free-space motion of a nonrelativistic quantum wave packet. The method is based on a short-time spatially-homogeneous perturbation to the wave packet dynamics, achieved by adding a nonlinear time-dependent term to the underlying Schr\"odinger equation. Numerical calculations, supporting our analytical considerations, demonstrate the effectiveness of the proposed QTM for generating a time-reversed echo image of initially localized matter-wave packets in one and two spatial dimensions. We also discuss possible experimental realizations of the proposed QTM.