Transient particle energies in shortcuts to adiabatic expansions of harmonic traps

TL;DR

This paper investigates the energetic aspects of shortcuts to adiabaticity in harmonic traps, establishing bounds and virial relations for finite-time protocols and their realizability.

Contribution

It introduces a virial theorem for STA processes and sets minimal energy bounds for finite-time expansions of harmonic traps.

Findings

Proves a virial theorem for STA processes.

Establishes minimal energy bounds for specific process durations.

Discusses realizability of protocols via Dirac impulses.

Abstract

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, non-adiabatic) and of the instantaneous power in characterizing or selecting different protocols.Specifically, we prove a virial theorem for STA processes, set minimal energies for specific times or viceversa, and discuss their realizability by means of Dirac impulses or otherwise.