Multiple Schr\"odinger pictures and dynamics in shortcuts to adiabaticity

TL;DR

This paper explores how different interaction pictures in quantum mechanics can be used to design alternative experimental routes and improve shortcuts to adiabaticity by engineering Hamiltonians.

Contribution

It introduces novel relations between Schr"odinger equations and interaction pictures, enabling new methods for quantum control and Hamiltonian engineering.

Findings

Multiple Schr"odinger pictures can be used to design feasible shortcuts to adiabaticity.

Engineered Hamiltonians improve the performance of quantum operations.

New experimental routes are proposed for complex quantum processes.

Abstract

A Schr\"odinger equation may be transformed by unitary operators into dynamical equations in different interaction pictures which share with it a common physical frame, i.e., the same underlying interactions, processes and dynamics. In contrast to this standard scenario, other relations are also possible, such as a common interaction-picture dynamical equation corresponding to several Schr\"odinger equations that represent different physics. This may enable us to design alternative and feasible experimental routes for operations that are a priori difficult or impossible to perform. The power of this concept is exemplified by engineering Hamiltonians that improve the performance or make realizable several shortcuts to adiabaticity.