Quantum corrections to the semiclassical collective dynamics in the Tavis-Cummings model

TL;DR

This paper investigates how quantum dynamics in the Tavis-Cummings model approaches semiclassical behavior as the number of two-level systems increases, revealing slow convergence and significant effects of detuning.

Contribution

It provides a detailed analysis of the slow convergence of quantum eigenvalues to their semiclassical limits and the impact of detuning on quantum corrections in large systems.

Findings

Eigenvalues approach semiclassical limit slowly, scaling with the logarithm of system size.

Quantum effects of detuning decay slowly, often exceeding classical effects at fixed detuning.

Quantum corrections remain significant even for large system sizes.

Abstract

The Tavis-Cummings model (the Dicke model treated in the rotating wave approximation) describing many two-level systems coupled to a single bosonic mode, has been long known to show collective semiclassical oscillations when prepared in an inverted state, with all two-level systems excited, and the bosonic mode empty. This paper discusses how the quantum dynamics approaches this semiclassical result for large numbers of two-level systems, focussing on how the eigenvalues approach their semiclassical limit. The approach to the semiclassical result is found to be slow, scaling like a power of the logarithm of the system size. Considering also the effect of weak detuning between the two-level system and the bosonic field, quantum corrections are again found to decay slowly with system size, such that for a fixed detuning, the quantum effects of detuning are greater than the classical effect.