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Physical Review A

Exactly solvable model for Landau-Zener-Stückelberg-Majorana interferometry

Qiongtao Xie

Published Feb 21, 2018• 7 citations
Publisher

Abstract

A periodically driven multiple-parametric two-level model is introduced. Under certain special parameter conditions, an exact analytical solution to this model can be obtained in an explicit form. This gives an exact analytical demonstration of the well-known Landau-Zener-St"uckelberg-Majorana resonances.
DOI
10.1103/physreva.97.022113

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Since the pioneering works by Landau, Zener, Stückelberg, and Majorana (LZSM), it has been known that driving a quantum two-level system results in tunneling between its states. Even though the interference between these transitions is known to be important, it is only recently that it became both accessible, controllable, and useful for manipulating a growing number of quantum systems. Here, we systematically study various aspects of LZSM physics and review the relevant literature, significantly expanding the review article in Ref. [504].
Recent experiments have shown that Landau-Majorana-Stückelberg-Zener (LMSZ) interferometry is a powerful tool for demonstrating and exploiting quantum coherence not only in atomic systems but also in a variety of solid state quantum systems such as spins in quantum dots, superconducting qubits, and nitrogen vacancy centers in diamond. In this Letter, we propose and develop a general (and, in principle, exact) theoretical formalism to identify and characterize the interference resonances that are the hallmark of LMSZ interferometry. Unlike earlier approaches, our scheme does not require any approximations, allowing us to uncover important and previously unknown features of the resonance structure. We also discuss the experimental observability of our results.
A simple algorithm is presented based on a type of partial reverse engineering that generates an unlimited number of exact analytical solutions to the Schr\"odinger equation for a general time-dependent two-level Hamiltonian. I demonstrate this method by deriving 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 nonadiabatic rapid passage and Landau-Zener interferometry near the quantum speed limit. A general, exact formula for Landau-Zener interference patterns is derived.