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arXiv:2007.09949 · Physical Review Research

Time-dependent harmonic potentials for momentum or position scaling

J. G. Muga, S. Martínez-Garaot, M. Ll. Pons, M. Palmero, A. Tobalina

Published Oct 30, 2020• 5 citations

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.

DOI: 10.1103/physrevresearch.2.043162

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The expansion of a harmonic potential that holds a quantum particle may be realized without any final particle excitation but much faster than adiabatically via "shortcuts to adiabaticity" (STA). While ideally the process time can be reduced to zero, practical limitations and constraints impose minimal finite times for the externally controlled time-dependent frequency protocols. We examine the role of different time-averaged energies (total, kinetic, potential, nonadiabatic) and of the instantaneous power in characterizing or selecting different protocols. Specifically, we prove a virial theorem for STA processes, set minimal energies (or times) for given times (or energies), and discuss their realizability by means of Dirac impulses or otherwise.

A method is proposed to drive an ultrafast non-adiabatic dynamics of an ultracold gas trapped in a time-dependent box potential. The resulting state is free from spurious excitations associated with the breakdown of adiabaticity, and preserves the quantum correlations of the initial state up to a scaling factor. The process relies on the existence of an adiabatic invariant and the inversion of the dynamical self-similar scaling law dictated by it. Its physical implementation generally requires the use of an auxiliary expulsive potential. The method is extended to a broad family of interacting many-body systems. As illustrative examples we consider the ultrafast expansion of a Tonks-Girardeau gas and of Bose-Einstein condensates in different dimensions, where the method exhibits an excellent robustness against different regimes of interactions and the features of an experimentally realizable box potential.