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Physical Review A

Intense-field renormalization of cavity-induced spontaneous emission

G. S. Agarwal, W. Lange, HERBERT WALTHER

Published Dec 1, 1993• 79 citations
Publisher

Abstract

We examine theoretically the recent experiments of Lange and Walther on the dynamical interaction of Rydberg atoms in a microwave cavity in the presence of a strong driving field. In particular, we study how the intense field renormalizes the cavity-induced spontaneous emission. For this purpose we derive the master equation for the atomic dynamics by adiabatically eliminating the cavity-field variables, while treating the intense driving field nonperturbatively. We present analytical and numerical solutions of the master equation, taking into account the turn on and turn off of the atom-field coupling in the rest frame of the atoms, as well as the velocity distribution of the atomic beam. We obtain good agreement between theoretical results and experiments.

DOI
10.1103/physreva.48.4555

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We examine theoretically the recent experiments of Lange and Walther on the dynamical interaction of Rydberg atoms in a microwave cavity in the presence of a strong driving field. In particular, we study how the intense field renormalizes the cavity-induced spontaneous emission. For this purpose we derive the master equation for the atomic dynamics by adiabatically eliminating the cavity-field variables, while treating the intense driving field nonperturbatively. We present analytical and numerical solutions of the master equation, taking into account the turn on and turn off of the atom-field coupling in the rest frame of the atoms, as well as the velocity distribution of the atomic beam. We obtain good agreement between theoretical results and experiments.
We present a theoretical treatment of the problem of a Rydberg atom near-resonantly coupled to a mode in a microwave cavity. We analyze the properties of cavity-induced spontaneous emission in the case of the cavity being driven by one or two near-resonant microwave fields. We find that the spontaneous emission of the atom can be turned off by one strong field (dynamical suppression) and that the addition of a second strong field can break this dynamical suppression and allow the atom to fluoresce in the presence of both fields. The analysis is cast both in a full master-equation treatment and in a Floquet treatment of an atom driven bichromatically in vacuum, the latter allowing for an interpretation of the full calculation. The calculations are performed in the intermediately strong coupling limit, in which both atomic and cavity dynamics must be considered.
A theoretical study of the dynamics of Rydberg atoms in a microwave cavity driven by a strong bichromatic field is presented. The resonator is assumed to operate in the low-Q regime. As a consequence, photons emitted by the atoms are dissipated in the cavity walls during the interaction time of the atoms inside the resonator. In this situation the cavity field follows the atomic dynamics adiabatically. The transient behavior of the system is analyzed in terms of Floquet states, and cavity-induced transition rates between these states are calculated for a large range of parameters of the bichromatic field. Narrow resonances are found in the transition rates, in agreement with recent experimental investigations of cavity Rydberg atoms subjected to strong bichromatic driving. We explain in detail the structure of the resonances, which is determined by the frequency-dependent cavity-mode density as well as the Rabi frequencies of the applied fields. The intensity-dependent shifts of the resonance frequencies are also calculated and found to be largely insensitive to inhomogeneous broadening. Finally, the numerical results are compared with experimental observations.
We solve the spontaneous-emission problem for an atom coupled to a standing-wave cavity mode. The interaction between the atom and the cavity mode is treated nonperturbatively with the quantized motion of the atom along the cavity axis included. Results are presented for the spontaneous-emission spectrum and the final momentum distribution of the atom. For equal atomic and cavity linewidths analytical results are obtained using a Bloch-state basis (eigenstates of the coupled atom and cavity mode); these are compared with results calculated in the Raman-Nath approximation. The case of unequal linewidths may be solved numerically using the eigenstates of the uncoupled atom and cavity mode as a basis, or analytically by making a secular approximation in the Bloch-state basis. The distribution of final atomic momentum shows that under strong-coupling conditions the atom is diffracted by its radiation reaction field. We compare the spontaneous emission spectra with spectra calculated by treating the motion of the atom classically. Generally there is good agreement when the classical results are averaged over the quantum-mechanical uncertainty in the initial position of the atom. The agreement is lost for sufficiently strong dipole coupling or sufficiently light atoms. Then, spectra that are symmetric in the classical treatment are asymmetric in the quantum treatment due to energy exchange between the internal degrees of freedom and center-of-mass degrees of freedom of the atom.
We report a Rydberg-atom experiment, demonstrating the dynamic suppression of spontaneous emission in a resonant microwave cavity driven by a resonant external field. If the Rabi frequency of the injected field is larger than the atomic and cavity line widths, the atoms almost completely decouple from the cavity mode due to suppressed field fluctuations at the sideband frequencies of the Mollow triplet. This was achieved with about 100 microwave photons in the cavity. The reduced decay rate is a consequence of non-Markovian dynamics induced by the finite cavity-response time.
Experimental and theoretical studies of Rydberg masers-quantum-electronic devices which produce and employ microwave radiation from highly excited atoms in a cavity-are reviewed. The experimental results are based mainly on studies performed by S. Haroche's group in Paris and H. Walther's group in Munich. In contradistinction to the usual quantum generators the quantum properties of the electromagnetic field itself play an important role in the analysis of the behavioral dynamics of Rydberg masers. The most striking results obtained in this field are the discovery of quantum revival and the achievement of maser generation on two-photon transitions and Fok states of the electromagnetic field.
The decay characteristics of two-state Rydberg atoms are investigated in a microwave cavity driven simultaneously by two strong rf fields. Tuning one of the driving fields leads to sharp resonances in the decay rate of the upper atomic level. Their width may become smaller than the cavity linewidth and transit time broadening. We present a theoretical model, interpreting the resonances as cavity-induced decay of Floquet states of the composite atom-field system. The observed phenomena arise from the interplay of cavity-modified Bloch-Siegert shifts and dynamic enhancement of spontaneous emission at single-photon and multiphoton resonances.