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Physical review. B, Condensed matter

Theory of Rabi splitting in cavity-embedded quantum wells

Stefan Jorda

Published Dec 15, 1994• 22 citations
Publisher

Abstract

We present a quantum theory of interaction between quantum-well excitons and electromagnetic eigenmodes of a multilayer dielectric cavity. The coupled exciton-photon modes are obtained by analyzing the exciton spectral function. The design of the cavity allows us to obtain enhanced spontaneous emission or a normal-mode splitting. We find very good agreement with the normal-mode splitting data of Weisbuch et al. [Phys. Rev. Lett. 69, 3314 (1992)].

DOI
10.1103/physrevb.50.18690

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We present a quantum theory of interaction between quantum-well excitons and electromagnetic eigenmodes of a multilayer dielectric cavity. The coupled exciton-photon modes are obtained by analyzing the exciton spectral function. The design of the cavity allows us to obtain enhanced spontaneous emission or a normal-mode splitting. We find very good agreement with the normal-mode splitting data of Weisbuch et al. [Phys. Rev. Lett. 69, 3314 (1992)].
The spectral response of a monolithic semiconductor quantum microcavity with quantum wells as the active medium displays mode splitting when the quantum wells and the optical cavity are in resonance. This effect can be seen as the Rabi vacuum-field splitting of the quantum-well excitons, or more classically as the normal-mode splitting of coupled oscillators, the excitons, and the electromagnetic field of the microcavity. An exciton oscillator strength of 4\ifmmode\times\else\texttimes\fi{}1012{10}^{12}1012 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$ is deduced for 76-\AA{} quantum wells.
Semiconductor quantum microcavities are interesting physical systems in which fundamental interactions between light and excitons can be explored. For example, in the weak - coupling limit, modified excitonic spontaneous emission can be observed. In the strong-coupling limit, the cavity field modes and the quantum well exciton modes become coupled; the normal modes of the system are "cavity-polaritons" [1,2]. For in-plane wavevectors k// near zero, the normal modes are split by the dipole coupling between the excitons and the cavity vacuum field. This splitting is often referred to as a vacuum-Rabi splitting (VRS), as it has the same physical origin as the VRS observed in the interactions of atoms with single-mode cavities. The physical system in this work consists of a λ planar microcavity formed by two distributed-Bragg reflectors, with five GaAs quantum wells situated in the center of the cavity. In all the experiments described here, the exciton and cavity modes are on resonance (the low-field VRS is 6 meV for this sample).
Temperature and electric-field tuning of the vacuum Rabi splitting of the coupled exciton-photon state in a semiconductor microcavity is reported. A very good fit to the coupling of the heavy- and light-hole excitons to the cavity photon mode, as a function of temperature, is obtained from a theoretical model for the reflectivity spectra. In addition, the variation of Rabi splitting with an applied electric field is well accounted for by the calculated variation of exciton oscillator strength with the electric field. Electro-optic control of the vacuum Rabi splitting is demonstrated.
We demonstrate the simultaneous dressing of both vacuum-to-exciton and exciton-to-biexciton transitions of a single semiconductor quantum dot in a high-Q micropillar cavity, using photoluminescence spectroscopy. Resonant two-photon excitation of the biexciton is achieved by spectrally tuning the quantum dot emission with respect to the cavity mode. The cavity couples to both transitions and amplifies the Rabi frequency of the likewise resonant continuous wave laser, driving the transitions. We observe strong-field splitting of the emission lines, which depend on the driving Rabi field amplitude and the cavity-laser detuning. A dressed state theory of a driven 4-level atom correctly predicts the distinct spectral transitions observed in the emission spectrum, and a detailed description of the emission spectra is further provided through a polaron master equation approach which accounts for cavity coupling and acoustic phonon interactions of the semiconductor medium.
We theoretically study pump and probe spectra of a quantum dot (QD) embedded in a microcavity in the cavity QED treatment. Energy levels of a QD are modeled by a four-level system consisting of the ground state, right and left-polarized excitons, and a biexciton. As a cavity-QED effect, four spectral peaks appear when the pump field frequency is tuned to the lower or upper level constituting the vacuum-field Rabi splitting. In addition, the spectral intensity dramatically enhances due to the cavity effect. The enhancement rate is independent of the coupling energy between exciton and cavity photons when the well-defined vacuum-field Rabi splitting is formed.
Low-temperature time-resolved luminescence experiments with 3-ps resolution have been performed on quantum-well excitons embedded in a nonguiding half-wave microcavity that displays the exciton-photon mode splitting. The spontaneous-emission dynamics of each of the two split components was studied as a function of the exciton-cavity detuning under resonant optical excitation. The spontaneous-emission decay rate is significantly modified with respect to the cavityless situation and its detuning dependence is accounted for by the strong radiative coupling between the radiant exciton states and the cavity photon modes. \textcopyright{} 1996 The American Physical Society.