Including temperature in a wavefunction description of the dynamics of the quantum Rabi model

TL;DR

This paper introduces a wavefunction method incorporating temperature effects into the quantum Rabi model, improving accuracy over traditional thermal Hamiltonian approaches, especially for moderate coupling and single oscillator systems.

Contribution

The authors develop a Davydov-Ansatz based approach with statistical sampling to include finite temperature initial conditions in the quantum Rabi model.

Findings

The new method outperforms the thermal Hamiltonian approach in accuracy.

Boltzmann weighting of eigenstates yields the best agreement with full quantum results.

Stochastic sampling approaches are computationally favorable for many oscillators.

Abstract

We present a wavefunction methodology to account for finite temperature initial conditions in the quantum Rabi model. The approach is based on the Davydov-Ansatz together with a statistical sampling of the canonical harmonic oscillator initial density matrix. Equations of motion are gained from a variational principle and numerical results are compared to those of the thermal Hamiltonian approach. For a system consisting of a single spin and a single oscillator and for moderate coupling strength, we compare our new results with full quantum ones as well as with other Davydov-type results based on alternative sampling/summation strategies. All of these perform better than the ones based on the thermal Hamiltonian approach. The best agreement is shown by a Boltzmann weighting of individual eigenstate propagations. Extending this to a bath of many oscillators will, however, be very demanding numerically. The use of any one of the investigated stochastic sampling approaches will then be favorable.