Exact real-time dynamics of the quantum Rabi model

TL;DR

This paper provides an exact analytical solution for the quantum Rabi model, enabling precise calculation of time evolution of key observables across all coupling regimes without Hilbert space truncation.

Contribution

It introduces absolutely convergent series expressions for eigenstates and scalar products, allowing for numerically exact dynamics computation in the quantum Rabi model.

Findings

Different behaviors of <σ_x(t)> and <σ_z(t)> linked to parity subspaces

Exact solutions valid for all coupling strengths

No Hilbert space truncation needed for calculations

Abstract

We use the analytical solution of the quantum Rabi model to obtain absolutely convergent series expressions of the exact eigenstates and their scalar products with Fock states. This enables us to calculate the numerically exact time evolution of <\sigma_x(t)> and <\sigma_z(t)> for all regimes of the coupling strength, without truncation of the Hilbert space. We find a qualitatively different behavior of both observables which can be related to their representations in the invariant parity subspaces.