Variational approach to light-matter interaction: Bridging quantum and semiclassical limits

TL;DR

This paper introduces a variational method using the multiple Davydov D2 trial state to simulate light-matter interactions across quantum and semiclassical regimes, capturing dynamics accurately for various models.

Contribution

It develops a unified variational framework that bridges quantum and semiclassical descriptions of light-matter systems, applicable to multiple models and multimode fields.

Findings

Variational dynamics agree with semiclassical models at high photon numbers.

Quantum corrections cause collapse of oscillations in the quantum regime.

The approach effectively models the crossover between quantum and semiclassical limits.

Abstract

We present a time-dependent variational approach with the multiple Davydov $D_2$ trial state to simulate the dynamics of light-matter systems when the field is in a coherent state with an arbitrary finite mean photon number. The variational approach captures not only the system dynamics but also the field dynamics and is applicable to a variety of quantum models of light-matter interaction such as the Jaynes-Cummings model, Rabi model, and Dicke model, and is feasible to tackle the multimode quantized fields. By comparison of the variational and semiclassical dynamics of both the system and field, we illustrate that the variational dynamics from the quantum models agrees with those from the corresponding semiclassical models as long as the mean number of photons is sufficiently large. Moreover, we illustrate that in the crossover between the quantum and semiclassical limits, the quantum corrections lead to the collapse of the oscillations in dynamics, which is absent in the semiclassical models. The variational approach provides a unified treatment of light-matter interaction from the quantum to the semiclassical limit.