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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Evolution of the vacuum Rabi peaks in a many-atom system

J. Gripp, Luis A. Orozco

Published Aug 1, 1996• 13 citations
Publisher

Abstract

The two peaks of the vacuum Rabi splitting behave like simple harmonic oscillators for very weak excitation. The transmission spectrum of a cavity filled with two-level atoms shows this doublet at low values of the driving intensity, but only a single peak at high values. The evolution from a doublet to a singlet is governed by the anharmonic response of the system as the driving intensity increases. The anharmonicity can grow to a point where frequency hysteresis appears in the transmission spectrum. This work investigates theoretically with a semiclassical model the transition from the doublet into the singlet. The stability of the different solutions is analysed as the parameters of atomic and cavity detuning vary. The model is extended to include the experimentally relevant transverse profile of the cavity mode as well as the standing wave structure of the field.

DOI
10.1088/1355-5111/8/4/005

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The two peaks of the vacuum Rabi splitting behave like simple harmonic oscillators for very weak excitation. The transmission spectrum of a cavity filled with two-level atoms shows this doublet at low values of the driving intensity, but only a single peak at high values. The evolution from a doublet to a singlet is governed by the anharmonic response of the system as the driving intensity increases. The anharmonicity can grow to a point where frequency hysteresis appears in the transmission spectrum. This work investigates theoretically with a semiclassical model the transition from the doublet into the singlet. The stability of the different solutions is analysed as the parameters of atomic and cavity detuning vary. The model is extended to include the experimentally relevant transverse profile of the cavity mode as well as the standing wave structure of the field.
Summary form only given. The two peaks of the vacuum Rabi splitting behave like simple harmonic oscillators for very weak excitation. The transmission spectrum of a cavity filled with a collection of two-level atoms shows this doublet and, for sufficiently high intensities, its evolution into a single peak. As the excitation increases anharmonicity grows in the oscillators to a point where frequency hysteresis appears in the transmission spectrum. The saturation of the transition of the two-level atoms is responsible for the nonlinearity that causes the anharmonicity. This work investigates the transition from the doublet into the singlet. We include the possibility of a detuning between the atomic and cavity resonances.
We measure the transmission spectrum of an optical cavity filled with two-level atoms. For small intensities, the coupling between atoms and a single mode of the cavity splits the spectrum into two normal modes: the vacuum Rabi peaks. We gradually decouple the system in two ways and study the evolution of the vacuum Rabi peaks. First we lower the atom-cavity coupling frequency through its intensity dependence, showing that the peaks shift, deform, exhibit frequency hysteresis, and eventually merge into a single peak that approaches the empty cavity resonance. Second we detune the atoms and the cavity mode and observe an avoided crossing. The normal modes of the coupled system transform into the two resonances of the uncoupled system. We map out the transition region and find good agreement with theoretical predictions.
The spectrum radiated by an initially excited two-level atom in a very-high-Q cavity is studied. We consider the situation where the frequency of the vacuum field cavity mode is varied time-dependently during Rabi cycles. Under the resonance condition where the modulation frequency is the same as the vacuum Rabi frequency, we show that the vacuum Rabi splitting can be further split into two doublets. The relative heights of spectral peaks are shown to depend on the modulation phase. Furthermore, we show that the interference between different spectral peaks can break the symmetry of the spectrum.
In this dissertation we study the interaction of a single atom with a single mode of the electromagnetic field in an optical cavity. We emphasize strong coupling conditions, where the dipole coupling strength is larger than the dissipation rates of the cavity and the atom. By exciting the coupled atom and cavity mode with an external field, the excited-state spectroscopy of the coupled system is explored. Both quantum mechanical and semiclassical calculations are performed and their results are compared. In the limit of a weak driving field, both results show a two-peak ("vacuum" Rabi) spectrum. With increased strength of the driving field, differences are observed. The quantum calculation shows a multi-peak ( two "vacuum" Rabi peaks plus additional peaks) spectrum, while the semiclassical calculation does not. These additional peaks are produced by transitions between the excited states of the Jaynes-Cummings IV Hamiltonian indicative of the quantum nature of the coupled atom-cavity-mode system.
A composite atom-cavity system exhibits complex behavior with respect to spontaneous emission, resonance fluorescence, and transmission spectra.1–3 An early investigation1 showed that for an atom in an ideal cavity, the spontaneous-emission spectra show a doublet splitting in the case of very weak excitation. This splitting, which arises from vacuum-field Rabi oscillation, is regarded as an inherently quantum phenomenon.1,2 However, recent experiments and theoretical analyses have demonstrated that the multiatom vacuum Rabi splitting may be regarded as a feature of linear dispersion theory.3 This approach is dramatically different from the one employed in QED descriptions of the problem.