Transitionless quantum drivings for the harmonic oscillator

TL;DR

This paper compares two methods for changing a quantum harmonic oscillator's frequency rapidly without inducing unwanted transitions, one using a transitionless-tracking algorithm and the other based on invariant engineering.

Contribution

It introduces and compares two novel techniques for transitionless quantum control of harmonic oscillators, one utilizing non-local potentials and the other maintaining local potentials.

Findings

Both methods successfully achieve transitionless frequency changes.

The invariant-based method maintains locality of the potential.

The transitionless algorithm employs a generalized oscillator with non-local potential.

Abstract

Two methods to change a quantum harmonic oscillator frequency without transitions in a finite time are described and compared. The first method, a transitionless-tracking algorithm, makes use of a generalized harmonic oscillator and a non-local potential. The second method, based on engineering an invariant of motion, only modifies the harmonic frequency in time, keeping the potential local at all times.