Quantum Mechanics in Technicolor; Analytic Expressions for a Spin-Half Particle Driven by Polychromatic Light

TL;DR

This paper introduces a novel analytical method for solving the multi-frequency Rabi model, enabling precise description of spin-half particle dynamics driven by polychromatic light, which was previously unsolvable analytically.

Contribution

The authors develop the first general analytic solution for the multi-frequency Rabi model, extending the dressed atom approach to polychromatic fields.

Findings

Analytic expressions accurately describe multi-frequency driven spin dynamics.

Solutions are valid even in strong interaction regimes.

Results have broad applications in quantum information and nonlinear optics.

Abstract

A vast collection of light-matter interactions are described by the single-frequency Rabi model. However, the physical world is polychromatic, and until now there is no general method to find analytic solutions to the multi-frequency Rabi model. We present the first general method to solve the Rabi model with N frequency modes. Analytic expressions are derived for a spin-half particle in a multi-frequency coherent field, and accurately describe the time evolution even when the interactions are strong. The dynamics are solved in an extended dressed atom picture whereby the spin is progressively dressed by each frequency mode. For weak fields, the closed form expressions for the time evolution of atoms or their analogues take a particularly simple form. These results analytically solve problems in a wide range of fields including quantum information processing, coherent control and resonant nonlinear optics.