Solution to the Landau-Zener problem via Susskind-Glogower operators

TL;DR

This paper presents a method to solve the fully quantized Landau-Zener problem across different coupling regimes using unitary transformations, enabling analytical and numerical solutions.

Contribution

It introduces a novel approach employing Susskind-Glogower operators and transformations to solve the quantized Landau-Zener Hamiltonian in both weak and strong coupling regimes.

Findings

Analytical solutions in the weak-coupling regime using known Landau-Zener solutions.

Diagonalization in the atomic basis for strong-coupling regime.

Numerical solutions feasible for few-photon scenarios.

Abstract

We show that, by means of a right-unitary transformation, the fully quantized Landau-Zener Hamiltonian in the weak-coupling regime may be solved by using known solutions from the standard Landau-Zener problem. In the strong-coupling regime, where the rotating wave approximation is not valid, we show that the quantized Landau-Zener Hamiltonian may be diagonalized in the atomic basis by means of a unitary transformation; hence allowing numerical solutions for the few photons regime via truncation.