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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.
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Gripp et al. (1996) studied this question.
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