Time-dependent harmonic potentials for momentum or position scaling

TL;DR

This paper introduces a generic method using time-dependent harmonic potentials to scale particle momentum or position, applicable to quantum and classical systems, with potential uses in cooling, slowing, and accelerating particles.

Contribution

It presents a novel protocol based on inverse techniques and shortcuts to adiabaticity for controlled momentum and position scaling in particles.

Findings

Protocol effectively scales particle momentum and position.

Applicable to both quantum and classical particles.

Timing control influences system evolution and final state.

Abstract

Cooling methods and particle slowers as well as accelerators are basic tools for fundamental research and applications in different fields and systems. We put forward a generic mechanism to scale the momentum of a particle, regardless of its initial position and momentum, by means of a transient harmonic potential. The design of the time-dependent frequency makes use of a linear invariant and inverse techniques drawn from ''shortcuts to adiabaticity''. The timing of the process may be decided beforehand and its influence on the system evolution and final features is analyzed. We address quantum systems but the protocols found are also valid for classical particles. Similar processes are possible as well for position scaling.