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Physical Review A

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

J. Gripp, S. L. Mielke, Luis A. Orozco, H. J. Carmichael

Published Nov 1, 1996• 57 citations
Publisher

Abstract

We have experimentally observed the evolution of the vacuum Rabi doublet into a singlet in the transmission spectrum of a cavity filled with a collection of two-level atoms. For very weak excitation the peaks behave like simple harmonic oscillators, but become anharmonic as the excitation increases. The anharmonicity grows to a point where hysteresis appears in the transmission spectrum, eventually causing the two peaks to merge into one.

DOI
10.1103/physreva.54.r3746

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We have experimentally observed the evolution of the vacuum Rabi doublet into a singlet in the transmission spectrum of a cavity filled with a collection of two-level atoms. For very weak excitation the peaks behave like simple harmonic oscillators, but become anharmonic as the excitation increases. The anharmonicity grows to a point where hysteresis appears in the transmission spectrum, eventually causing the two peaks to merge into one.
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.
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.
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.
We report experimental measurements of the transmission spectrum of an optical cavity coupled with cold Rb atoms. We observe the multiatom vacuum Rabi splitting of a composite cavity and atom system. When a coupling field is applied to the atoms and induces the resonant two-photon Raman transition with the cavity field in a $\ensuremath{\Lambda}$-type system, we observe a cavity transmission spectrum with two vacuum Rabi sidebands and a central peak representing the intracavity dark state. The central peak linewidth is significantly narrowed by the dark-state resonance and its position is insensitive to the frequency change of the empty cavity.
When a single atom interacts with one mode of an optical cavity and the coupling to the cavity mode is sufficiently large, the spectroscopic response of the composite system to a weak probe is a doublet, with peaks located at the eigenfrequencies of the one-quantum excited states of the Jaynes–Cummings Hamiltonian. So far as these one-quantum states are concerned the spectroscopy of the Jaynes–Cummings model is the same as that of coupled, damped harmonic oscillators. This equivalence has been used to observe a doublet spectrum (the so-called "vacuum" Rabi splitting) by exciting a collective dipole oscillator inside an optical cavity.1,2 At higher levels of excitation the spectroscopy of the Jaynes–Cummings model differs markedly from that of coupled harmonic oscillators. Coupled harmonic oscillators give a doublet at all excitation levels; because of its noncommensurate excited state energies the Jaynes–Cummings model gives a multitude of additional peaks. In this paper we show how the excited states of the Jaynes–Cummings Hamiltonian can be probed by driving a cavity containing a single atom with broadband chaotic light. For a sufficiently large dipole coupling strength the spectrum of the light scattered out of the cavity mode shows peaks at the many resonance frequencies of the Jaynes–Cummings Hamiltonian. A similar multipeaked spectrum is seen in transmission. The spectrum of the light reflected from the cavity shows corresponding absorption dips superimposed on the broadband input.
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.