Comparison of the semiclassical and quantum optical field dynamics in a pulse-excited optical cavity with a finite number of quantum emitters

TL;DR

This paper compares the quantum and semiclassical dynamics of a set of quantum emitters in a cavity after pulsed excitation, revealing how quantum effects like collapse, revival, and Schrödinger cat states emerge as the number of emitters varies.

Contribution

It provides a detailed comparison between the full quantum Tavis-Cummings model and its semiclassical approximation for different emitter numbers and pulse amplitudes.

Findings

Quantum spectra approach semiclassical results as emitter number increases.

Good agreement in temporal dynamics for low photon numbers.

Quantum states show deviations from coherence, including Schrödinger cat states at higher pulse amplitudes.

Abstract

The spectral and temporal response of a set of $N$ quantum emitters embedded in a photonic cavity is studied. Quantum mechanically, such systems can be described by the Tavis-Cummings (TC) model of $N$ two-level systems coupled to a single light mode. Here we compare the full quantum solution of the TC model for different numbers of quantum emitters with its semiclassical limit after a pulsed excitation of the cavity mode. Considering different pulse amplitudes, we find that the spectra obtained from the TC model approach the semiclassical one for an increasing number of emitters $N$. Furthermore they match very well for small pulse amplitudes. While we observe a very good agreement in the temporal dynamics for photon numbers much smaller than $N$, considerable deviations occur in the regime of photon numbers similar to or larger than $N$, which are linked to collapse and revival phenomena. Wigner functions of the light mode are calculated for different scenarios to analyze the quantum state of the light field. We find strong deviations from a coherent state even if the dynamics of the expectation values are still well described by the semiclassical limit. For higher pulse amplitudes Wigner functions similar to those of Schr\"odinger cat states between two or more quasi-coherent contributions build up.