Theory versus experiment for vacuum Rabi oscillations in lossy cavities

TL;DR

This paper analyzes vacuum Rabi oscillations in lossy cavities, showing that open cavity effects and thermal fluctuations significantly influence the observed dynamics and decoherence, challenging previous assumptions about cavity quality and coherence.

Contribution

It introduces an alternative model using dressed-state basis jump operators and accounts for thermal fluctuations, providing a better match to experimental data.

Findings

Agreement with experimental Rabi oscillation data when including thermal fluctuations

Decoherence rate is dominated by fluctuations within dressed states, not cavity Q factor

Improving Q does not necessarily enhance coherence properties

Abstract

The 1996 Brune {\it et al.} experiment on vacuum Rabi oscillation is analyzed by means of alternative models of atom-reservoir interaction. Agreement with experimental Rabi oscillation data can be obtained if one defines jump operators in the dressed-state basis, and takes into account thermal fluctuations between dressed states belonging to the same manifold. Such low-frequency transitions could be ignored in a closed cavity, but the cavity employed in the experiment was open, which justifies our assumption. The cavity quality factor corresponding to the data is $Q=3.31\cdot 10^{10}$, whereas $Q$ reported in the experiment was $Q=7\cdot 10^7$. The rate of decoherence arising from opening of the cavity can be of the same order as an analogous correction coming from finite time resolution $\Delta t$ (formally equivalent to collisional decoherence). Peres-Horodecki separability criterion shows that the rate at which the atom-field state approaches a separable state is controlled by fluctuations between dressed states from the same manifold, and not by the rate of transitions towards the ground state. In consequence, improving the $Q$ factor we do not improve the coherence properties of the cavity.