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arXiv:0807.2882 · Nature Physics

Nonlinear response of the vacuum Rabi resonance

Lev S. Bishop, Jerry M. Chow, Jens Koch, Andrew Houck, Michel Devoret, E. V. Thuneberg, S. M. Girvin, Robert J. Schoelkopf

Published Dec 7, 2008• 285 citations
arXivHTMLPDF
DOI
10.1038/nphys1154

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Recently, several research groups have reported investigations of vacuum-field Rabi splittings (VRS) in the linear response of strongly coupled semiconductor microcavities [1-4]. We have previously reported on the dynamics of time-domain vacuum Rabi oscillations, which are most easily understood in the framework of cavity exciton-polaritons, in which the in-plane momentum k|| is conserved [2], so that at each k|| a single cavity mode interacts with only a single mode of the electromagnetic field (Jaynes-Cummings model). In high Q semiconductor microcavities, the strong coupling between two-dimensional excitons and planar distributed- Bragg-reflector cavity modes results in several-meV splittings observable in the reflectivity or absorption spectrum. In the low excitation regime, the VRS is independent of light intensity incident on the cavity, since the vacuum-Rabi frequency exceeds the externally-driven Rabi frequency (in which case the Jaynes-Cummings model is equivalent to the linear dispersion of the coupled exciton-cavity system). As the incident light intensity is increased, two different effects may be expected to contribute to the nonlinear response. First, as long as the excitonic absorption is equivalent to a two-level system, higher-lying states of the Jaynes-Cummings ladder might be observable. Second, at high intensity phase-space filling and Coulomb screening of the exciton states results in a reduced oscillator strength which leads to a reduced VRS; this effect has no analogue in the case of atom-cavity systems. In this paper, we apply several ultrafast nonlinear techniques to investigate the nonlinear response of semiconductor microcavities.
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.