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.
Highlights
But the protocols found are valid for classical particles
Particle slowers and accelerators are basic tools for fundamental research and applications in different fields covering a huge range of systems, from high-energy physics to atomic and molecular physics
The theory is worked out here for a quantum particle represented by a wave packet, but the resulting protocols apply well to classical particles since, as is well known, harmonic potentials lead to classical equations of motion for the expectation values of position and momentum
Summary
Particle slowers and accelerators are basic tools for fundamental research and applications in different fields covering a huge range of systems, from high-energy physics to atomic and molecular physics. The theory is worked out here for a quantum particle represented by a wave packet, but the resulting protocols apply well to classical particles since, as is well known, harmonic potentials lead to classical equations of motion for the expectation values of position and momentum. We provide expressions for the time dependence of expectation values of position and momentum for a chosen scale factor, as well as expressions for second-order moments for positions and momenta in terms of the initial values This is valuable information to set both practical limits and design details depending on the intended target and resources available. We end the paper by considering related processes, in particular, the scaling of positions, i.e., focusing or antifocusing
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