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Physical Review Letters

Coherent Dynamics of Excitonic Nonlinear Optical Response in the Nonperturbative Regime

Hailin Wang, H.Q. Hou, B. E. Hammons

Published Oct 12, 1998• 33 citations
Publisher

Abstract

We report experimental and theoretical studies of the transient nonlinear response from semiconductor microcavities. We show that, in the nonperturbative regime, oscillations in time-integrated transient four-wave mixing do not correspond to normal mode oscillations of either the exciton or photon population in the cavity. Coherent nonlinear responses arising from band filling, excitation-induced dephasing, and renormalized electric fields feature highly distinctive dynamical behaviors. Coherent dynamics in transient four-wave mixing reflects interference between these nonlinear processes.

DOI
10.1103/physrevlett.81.3255

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We report experimental and theoretical studies of the transient nonlinear response from semiconductor microcavities. We show that, in the nonperturbative regime, oscillations in time-integrated transient four-wave mixing do not correspond to normal mode oscillations of either the exciton or photon population in the cavity. Coherent nonlinear responses arising from band filling, excitation-induced dephasing, and renormalized electric fields feature highly distinctive dynamical behaviors. Coherent dynamics in transient four-wave mixing reflects interference between these nonlinear processes.
Summary form only given. Optical interactions in semiconductor microcavities embedded with quantum wells enter a nonperturbative regime when the dipole coupling rate between the exciton and the cavity mode exceeds relevant decay rates. In this regime, coherent energy exchange between the exciton and the cavity mode, i.e. normal mode oscillation (NMO), takes place when the cavity mode is excited impulsively by a short laser pulse. Similar coherent oscillations have also been observed in transient four-wave mixing (FWM) responses. In this paper, we present experimental and theoretical studies on the nature of oscillations in these transient FWM responses. We show that, in contrast to earlier beliefs, oscillations in time-integrated transient FWM do not correspond to NMO of the exciton or photon populations. Theoretical studies further reveal that FWM arising from different physical mechanisms including band filling, excitation-induced dephasing, and renormalized electric fields is characterized by highly distinct coherent dynamics. Oscillations in transient FWM reflect interference between these coherent optical processes and can be used as a unique probe for exciton many-body interactions in the nonperturbative regime.
We present a coherent nonlinear optical study of composite exciton-cavity systems in the strong-coupling regime. Quantum oscillations in a transient four-wave-mixing response show the creation of a coherent superposition state between the two normal modes of the composite system and demonstrate in the time domain the coherent energy exchange between the exciton and cavity. The deep oscillation persists when the cavity resonance is far detuned from the exciton resonance. The result shows that dynamics of the nonlinear response can be in a nonperturbative regime while dynamics of the linear response remains in a perturbative regime.
Summary form only given. The ultrafast nonlinear optical response of semiconductor-microcavities (SMCs) in the nonperturbative regime is attracting growing interest for exploring fundamental light-matter interactions in many-particle quantum systems, as well as for the future implementations of ultrafast photonic devices. In spite of many investigations, the coherent dynamics of excitonic nonlinear-response in the nonperturbative regime has not been fully understood. Open questions are how strong exciton-cavity coupling affects exciton-exciton (X-X) interactions, and how in turn the X-X correlation influences the nonlinear response of SmCs. We investigate these open questions and show that the nonperturbative regime provides an unprecedented tool for investigating four-particle correlations.We start from the equations for the third order exciton polarization and cavity field describing quantum optical effects and coherent nonlinear optics in SMCs, perform the semiclassical factorization and include multiple scattering processes.
We report on the optical response of a semiconductor microcavity featuring a strong exciton–photon coupling. The weak excitation regime is investigated experimentally by means of time-resolved transmission and four-wave mixing experiments. The influence of electronic disorder on the coherent exciton–photon dynamics is discussed in terms of the solutions of the Maxwell-Bloch equations. The high excitation regime is investigated by using transient sub-picosecond pump–probe experiments. Optical amplification of the probe beam (up to a factor of five), as well as a fundamental change of the optical spectra, have been found close to and above the exciton saturation density. The observed oscillations are corresponding to the Rabi frequency of the excitons in the pump field.
The normal modes in a nonperturbatively coupled quantum-well semiconductor microcavity are linear superpositions of the QW exciton and cavity mode when the QW exciton transition is resonant with the cavity mode. When the lower normal mode is excited by a phase-locked pair of optical pulses, the nonlinear response of a probe pulse tuned to the upper mode is controlled. Thus the normal modes are coupled in their nonlinear optical response due to the nonlinearity of the exciton underlying the two normal modes. The cavity enhancement of the excitonic nonlinearity gives rise to a large signal; modulating the relative phase of the excitation pulses produces a differential reflectivity of up to 10%. Besides the coherent control of normal modes which is explainable with in the frame of semiclassical models, we observe a purely quantum mechanical phenomenon in our system. The quantum correlations between the field and carrier density lead to intraband coherences which live much longer than the interband dephasing time.
We investigate a GaAs/(Ga,Al)As Fabry-P\'erot microcavity, into which (In,Ga)As quantum wells have been inserted. The cavity is wedge shaped, i.e., the detuning between the bare-exciton resonance and the bare optical cavity mode depends on the spatial position on the sample. Linear transmission spectra reveal a well-resolved Rabi splitting of 8 meV at resonance, an inhomogeneously broadened exciton transition of 4--5-meV width, and an 0.7-meV-wide Fabry-P\'erot mode. The time-resolved transmission exhibits deep beatings and a subpicosecond exponential decay: a behavior similar to that foreseen in the strong-coupling regime and in the absence of electronic disorder. Conversely, the four-wave mixing response appears weakly influenced by the cavity and not much different from what is expected for bare excitons. A photon echo, dephasing times as long as 50 ps, and only weak Rabi oscillations are observed. The experimentally observed features can be explained by a model based on the numerical solutions of the Maxwell-Bloch equations. This model confirms the dramatic influence structural disorder in the quantum wells has on the coherent nonlinear exciton-photon dynamics.