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Two-Photon Rabi Splitting and Optical Stark Effect in Microcavities

Iacopo Carusotto, Giuseppe Carlo La Rocca

Published Mar 1, 2000• 0 citations
Publisher

Abstract

We have investigated resonant two-photon absorption and second harmonic generation in a microcavity geometry. In a single beam arrangement, the transmission depends on the intensity according to a simple two-level picture with an intensity-dependent coupling; at resonance, in particular, the system exhibits a two-photon Rabi splitting. In a pump and probe arrangement, the presence of the strong incident pump beam substantially modifies the absorption spectrum of the weak probe beam: for moderate pump intensities the behaviour can be interpreted as a two-photon version of the well-known optical Stark effect. At higher intensities, more complicated hyper-Raman processes take place, which give also rise to gain in well-determined spectral regions. Finally, we have shown how the non-linear coupling coefficient appearing in the model Hamiltonian is related to the material constants and geometrical parameters of a specific microcavity configuration.

DOI
10.1002/1521-396x(200003)178:1<173::aid-pssa173>3.0.co;2-u

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We have investigated resonant two-photon absorption and second harmonic generation in a microcavity geometry. In a single beam arrangement, the transmission depends on the intensity according to a simple two-level picture with an intensity-dependent coupling; at resonance, in particular, the system exhibits a two-photon Rabi splitting. In a pump and probe arrangement, the presence of the strong incident pump beam substantially modifies the absorption spectrum of the weak probe beam: for moderate pump intensities the behaviour can be interpreted as a two-photon version of the well-known optical Stark effect. At higher intensities, more complicated hyper-Raman processes take place, which give also rise to gain in well-determined spectral regions. Finally, we have shown how the non-linear coupling coefficient appearing in the model Hamiltonian is related to the material constants and geometrical parameters of a specific microcavity configuration.
We have studied two-photon nonlinear optical effects arising in a microcavity geometry from resonant two-photon absorption or second-harmonic generation. The transmission spectrum of the cavity is shown to depend on light intensity according to a simple two-level picture with an intensity-dependent coupling: at resonance the system exhibits a two-photon Rabi splitting. The absorption spectrum of a weak probe beam in a pumped cavity is found to strongly depend on pump intensity and detuning; the resulting effect is a sort of two-photon analogue of the usual optical Stark effect. For moderate pump intensities a two-level picture with a pump-dependent coupling can account for the main results, while at higher intensities new unexpected features show up; in particular, we predict the appearance of gain in well-determined spectral regions due to hyper-Raman processes. Finally, we have shown how the coupling coefficients appearing in our formalism can be obtained from a detailed knowledge of the material and geometrical properties of a specific system. For illustrative purposes, we have estimated the required light intensities using realistic data for a GaAs-based semiconductor microcavity.
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 biexciton optical Stark-effect under resonant pumping between the exciton and biexciton levels is studied theoretically. The probabilities of biexciton two-photon absorption of a weak probe light and of one-photon biexciton-exciton transition are calculated. The optical Stark splitting manifests itself in two-photon biexciton absorption through two absorption peaks spaced 2 (Omega) apart. Omega is the Raby frequency. In the luminescence spectrum due to biexciton-exciton one-photon transition three luminescence maxima appear which are shifted with respect to the luminescence maximum in the case without pumping.
The theory of the optical Stark effect is developed for quantum-size structures. The effect is due to the interaction of the electron system with intense light, whose frequency, (omega) , is in resonance between two subbands in the conduction band. The probe light of the frequency (Omega) falls in resonance with the adjacent transition between the ground state and the state with an electron-hole pair. In the quasi-steady-state mode, the singularities in the interband (Omega) -light absorption spectra are related to the critical points of the bands, rearranged by the (omega) - light. The shape of the higher conduction band can be evaluated from the spectral positions of the singularities. In the case of two-photon interband transitions, a sharp dependence of the absorption on the light intensity is predicted. In the non-steady-state mode, the probe beam consists of two femtosecond (Omega) -light pulses following each other with the delay time, (tau) d. The dependence of energy, absorbed from the second pulse, on the (tau) d value is calculated. Under the (omega) -pumping, one of the two phenomena should be observed, depending on the type of band structure, namely, the decay of the induced polarization with the characteristic time approximately 1/(omega) R or oscillations with the frequency approximately (omega) R, where (omega) R is the Rabi frequency. The principal effect, controlling the decay of the Rabi oscillations, is the spreading of the packet of states generated by the (Omega) -light pulse.
Abstract In this paper, we examine the three-level optical Stark effect of excitons in InGaAs/InAlAs quantum dots using renormalized wavefunction formulation. The system was assumed to be irradiated by two lasers in which a strong laser dynamically couples electron-quantized levels, while a weaker laser probes interband absorption. Our results show that, in the presence of the resonant strong laser, two new absorption peaks of excitons appear in the absorption spectrum as a clear indication of the effect. In addition, we propose that the formation of the effect in low-dimensional structures could have connection to the splitting of electron levels. Furthermore, we seek to explain the essential dependence of the amplitude and position of two peaks on pump field detuning.
We study transients in resonantly coupled three-level systems. Two of the levels are coupled by intense two-photon pumping, and the third one provides a probing level. Adiabatically eliminated levels appear in effective system parameters. Experimentally, this model is applicable, e.g., in resonantly enhanced parametric and harmonic generation in atomic vapors. A distinguishing feature in the system is the appearance of ac Stark shifts in the probe spectra when pumping at the two-photon resonance. The nutation signal is shown to give information on the effective two-photon Rabi frequency and on the decay rate of the dipole-forbidden two-photon coherence. Free-induction decay is strongly dominated by population-induced effects; Raman-like peaks introduced by Stark shifts may show large instantaneous gain. Gaussian pump pulses are investigated to investigate effects arising from the temporal sweeping of the two-photon Rabi flipping and the modulation of the Stark shifts. The results also provide relevant information on the gain dynamics of coherently pumped lasers.