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Physical review. B, Condensed matter

Vacuum Rabi coupling enhancement and Zeeman splitting in semiconductor quantum microcavity structures in a high magnetic field

T. A. Fisher, A. M. Afshar, Maurice S. Skolnick, David M. Whittaker, J.S. Roberts

Published Apr 15, 1996• 88 citations
Publisher

Abstract

Reflectivity spectra of high-quality quantum microcavity structures are investigated in high magnetic fields from 0 to 14 T. Over this field range we observe an increase in the vacuum Rabi splitting by a factor of 1.4, due to the magnetic-field-induced increase of exciton oscillator strength. In addition, exciton Zeeman splitting is seen. We demonstrate that this splitting arises from the independent interaction of each exciton spin component with the corresponding circularly polarized cavity photon mode. We also report anomalous broadening of the higher-energy polariton feature in high magnetic field, raising doubts that the same broadening seen at zero magnetic field is due to coupling of the cavity mode with higher discrete and continuum exciton states.

DOI
10.1103/physrevb.53.r10469

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Reflectivity spectra of high-quality quantum microcavity structures are investigated in high magnetic fields from 0 to 14 T. Over this field range we observe an increase in the vacuum Rabi splitting by a factor of 1.4, due to the magnetic-field-induced increase of exciton oscillator strength. In addition, exciton Zeeman splitting is seen. We demonstrate that this splitting arises from the independent interaction of each exciton spin component with the corresponding circularly polarized cavity photon mode. We also report anomalous broadening of the higher-energy polariton feature in high magnetic field, raising doubts that the same broadening seen at zero magnetic field is due to coupling of the cavity mode with higher discrete and continuum exciton states.
Tuning of the vacuum Rabi exciton-photon coupling in semiconductor quantum microcavity structures by external electric and magnetic fields is presented. Contrasting effects due to the two external perturbations are found, principally due to the decrease of exciton oscillator strength in electric field and increase of oscillator strength in magnetic field. The strong coupling limit is easily achieved in these high quality structures with line widths on resonance as small as 1 meV. In addition to the tuning phenomena, the effects of exciton Zeeman splitting on the spectra and unexpected linewidth narrowing phenomena on resonance are reported.
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.
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.
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.
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).
We study the quantum-well magnetoexcitons by the variational method in the strong coupling regime of excitons with microcavity photons. In such strong coupling regime, we find that the coupling between the exciton internal state and center of mass motion can be neglected. Through the calculations, we find that the magnetic field can reduce the exciton exchange interaction to 30% as Lw=30 nm with Lw being the quantum well width. This is in contrast to the magnetic-field enhancement in the exciton Rabi splitting. In this work, we obtain that a magnetic field can enhance the exciton Rabi splitting up to 1.6 times in the case of Lw=30 nm. They both originate from the local enhancement in the exciton internal state due to the magnetic field. In addition, we analyze the behavior of the magnetic response of the exciton energy, Rabi splitting, and exchange interaction in manipulating the polariton parametric scattering, and widening the microcavity applications.