Theory versus experiment for vacuum Rabi oscillations in lossy cavities

Abstract

The 1996 experiment by Brune et al. [Phys. Rev. Lett. 76, 1800 (1996)] 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 approximately $Q=3.31\ifmmode\times\else\texttimes\fi{}{10}^{10}$, whereas $Q$ reported in the experiment was $Q=7\ifmmode\times\else\texttimes\fi{}{10}^{7}$. 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 $\ensuremath{\Delta}t$ (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 toward the ground state. In consequence, improving the $Q$ factor we do not improve the coherence properties of the cavity.