Theory versus experiment for vacuum Rabi oscillations in lossy cavities

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.Comment: typo in eq. (60) corrected; (older comments: 14 figures (1 added), value of Q improved, a section on the Peres-Horodecki test of separability added, various small improvements; v3 includes discussion of finite time resolution, v4 includes microscopic derivation of the master equation