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Physical Review Letters

Vacuum-Field Rabi Splittings in Microwave Absorption by Rydberg Atoms in a Cavity

G. S. Agarwal

Published Oct 29, 1984• 404 citations
Publisher

Abstract

The absorption spectrum of a system of $N$ atoms interacting with a single mode of the quantized radiation field is exactly calculated. Such a spectrum shows vacuum-field Rabi splittings, and thus microwave absorption by Rydberg atoms in a cavity should be a useful way to observe these splittings.

DOI
10.1103/physrevlett.53.1732

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The absorption spectrum of a system of NNN atoms interacting with a single mode of the quantized radiation field is exactly calculated. Such a spectrum shows vacuum-field Rabi splittings, and thus microwave absorption by Rydberg atoms in a cavity should be a useful way to observe these splittings.
We present various experiments involving Rydberg atoms interacting with resonant microwave electromagnetic fields inside a cavity, allowing to check different features of the theory presented in the previous paper. We first describe experiments about superradiant emission by Rydberg states in the cavity, also called transient Rydberg atoms maser ; the evolution of the system is detected either on the populations by selective field ionization technique or on the microwave field itself by heterodyne detection. Very low thresholds, down to 100 atoms, for the maser emission have been observed. We then describe various aspects of collective absorption of radiation by very excited atoms including the observation of Rabi nutation in a small applied resonant field, the study of the quantum efficiency of this set-up considered as a microwave photon counter, and finally the unexpected characteristics of the blackbody radiation absorption in the cavity.
The experimental possibility of observing the most basic atom-radiation interactions appears to be much closer than even two years ago. Such experiments are expected to focus on properties of a single Rydberg atom interacting with an ultracold cavity. In the event that the atom is prepared so that it can be approximated as having only two levels, and the cavity is cold enough to be effectively lossless during the interaction time, it is expected to be well described by the Jaynes Cummings (J-C) model1 theory. Rabi oscillations as predicted by J-C theory have already been observed for the N-atom case.2
Quantitative predictions for the quantum electrodynamics of a few atoms interacting with quantized modes of the radiation field are becoming accessible to experimental test—particularly for Rydberg atoms in microwave cavities.1 For these one needs essentially exact predictions in realistic cavities, and these show losses. At microwave frequencies1 the very few thermal photons present even at very low temperatures1 can be significant. We show in this paper that if a single two-level atom is contained in a cavity of high enough Q, interaction with a quantized cavity mode can induce new spectral features.
The vacuum-field Rabi splitting of an optical mode in a cavity interacting with a system of N excitations (atomic or electronic) represented by harmonic oscillators is obtained quantum mechanically both without and with coupling to dissipation. The optical lineshapes and the scaling of the Rabi splitting with the number of oscillators and its dependence on the damping parameters are given. Corresponding results are given for a classical treatment of the oscillators, and it is shown that to the leading order in the dissipation, the quantum mechanical results for absorption are the same as the classical ones.