Optimizing adiabaticity in quantum mechanics

TL;DR

This paper derives a condition on the Hamiltonian of a time-dependent quantum system that ensures optimal adiabatic evolution, tested on a solvable spin in magnetic field example.

Contribution

It introduces a new condition for optimal adiabaticity in quantum systems expressed via the Hamiltonian and evolution operator.

Findings

Condition implies optimal adiabaticity when satisfied.

Tested on an exactly-solvable spin problem.

Provides insights into Hamiltonian design for adiabatic processes.

Abstract

A condition on the Hamiltonian of a time-dependent quantum mechanical system is derived which, if satisfied, implies optimal adiabaticity (defined below). The condition is expressed in terms of the Hamiltonian and in terms of the evolution operator related to it. Since the latter depends in a complicated way on the Hamiltonian, it is not yet clear how the condition can be used to extract useful information about the optimal Hamiltonian. The condition is tested on an exactly-soluble time-dependent problem (a spin in a magnetic field), where perfectly adiabatic evolution can be easily identified.