Exactly solvable two-level quantum systems and Landau-Zener interferometry

TL;DR

This paper introduces a simple algorithm for generating exact analytical solutions to the Schrödinger equation for two-level quantum systems, enabling precise control protocols and Landau-Zener interferometry near the quantum speed limit.

Contribution

A novel partial reverse-engineering method that produces unlimited exact solutions for time-dependent two-level Hamiltonians, facilitating advanced quantum control and interferometry.

Findings

Derived new exact solutions for fast control pulses with tunable parameters

Developed an exact formula for Landau-Zener interference patterns

Demonstrated control protocols near the quantum speed limit

Abstract

I present a simple algorithm based on a type of partial reverse-engineering that generates an unlimited number of exact analytical solutions to the Schrodinger equation for a general time-dependent two-level Hamiltonian. I demonstrate this method by deriving new exact solutions corresponding to fast control pulses that contain arbitrarily many tunable parameters. It is shown that the formalism is naturally suited to generating analytical control protocols that perform precise non-adiabatic rapid passage and Landau-Zener interferometry near the quantum speed limit. A general, exact formula for Landau-Zener interference patterns is derived.