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

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.