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Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR)

Vacuum Rabi splitting enhances resonant optical nonlinearity in semiconductor quantum well microcavity exciton system

Masahiro Takeoka, F. Kaunari

Published Jan 20, 2003• 0 citations
Publisher

Abstract

Electromagnetic induced transparency (EIT) in condensed media, especially in a semiconductor, is attractive for nonlinear applications, because of its high density, compactness, and flexibility in artificial design. However, fast relaxation time and fermionic character of electrons obstructs the realization of EIT in semiconductor materials. We propose a resonant parametric conversion scheme which is applicable to the semiconductor quantum well (QW) microcavity (MC) exciton system. Because of its large oscillator strength, the semiconductor QW MC excitons show the large vacuum Rabi splitting which can be larger than the phase relaxation broadening of the media. It is found that when the coupling strength of the MC mode and the medium transition is larger than any other Rabi frequency and relaxation rate, the nonlinear susceptibility term becomes dominant compared to the linear susceptibility term.

DOI
10.1109/cleopr.1999.814695

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Electromagnetic induced transparency (EIT) in condensed media, especially in a semiconductor, is attractive for nonlinear applications, because of its high density, compactness, and flexibility in artificial design. However, fast relaxation time and fermionic character of electrons obstructs the realization of EIT in semiconductor materials. We propose a resonant parametric conversion scheme which is applicable to the semiconductor quantum well (QW) microcavity (MC) exciton system. Because of its large oscillator strength, the semiconductor QW MC excitons show the large vacuum Rabi splitting which can be larger than the phase relaxation broadening of the media. It is found that when the coupling strength of the MC mode and the medium transition is larger than any other Rabi frequency and relaxation rate, the nonlinear susceptibility term becomes dominant compared to the linear susceptibility term.
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.
Recent progress in vertical surface-emitting-laser-diode technology has raised considerable interest in cavity-QED effects in high-quality vertical semiconductor microcavities. When an excitonic transition and a single cavity mode are strongly coupled, the normal modes of the system are coupled modes split by the vacuum-Rabi frequency, corresponding in the time domain to an oscillation of the excitation between modes of exciton and photon character. Recently, the vacuum-Rabi splitting and preliminary observations of time-domain oscillation in semiconductor quantum microcavities have been reported.1,2 In this paper we investigate rigorously the time-domain vacuum-Rabi oscillation by femtosecond upconversion and pump-probe techniques.
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).
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.
Recently, cavity quantum electrodynamic (QED) effects in semiconductor microcavities have been of considerable interest since, in the weak-coupling regime they play an important role in selectively increasing spontaneous emission into the lasing mode of vertical-cavity surface-emitting lasers (VCSEL’s) [1,2], enabling low-threshold, high speed, and high efficiency. In a strong-coupling regime, the normal modes of the coupled system are superpositions of the exciton and cavity modes. Hence the impulsively excited system will evolve in time with the energy oscillating between the exciton and cavity modes. This is known as a vacuum-Rabi oscillation (VRO), with a frequency of Ω=d¯⋅E¯/@@h, where d¯ is the transition dipole moment of atoms and E¯ the vacuum-field strength. Of course, VRO are observable only when the cavity lifetime and exciton dephasing time are long enough compared to VRO period. Recently, Weisbuch et al. [3] have reported an observation of the normal-mode vacuum Rabi splitting in 2-D-exciton/planar-DBR microcavities. The observed splittings were as large as 6 meV in reflection and transmission spectra, implying 690-fs vacuum Rabi oscillations.