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Physical Review B

Dephasing of coherences between σ+ and σ− exciton states in a ZnSe single quantum well

Hans Peter Wagner, Suvranta K. Tripathy

Published Mar 18, 2004• 4 citations
Publisher

Abstract

We investigate interband coherences as well as coherences between ${\ensuremath{\sigma}}^{+}$ and ${\ensuremath{\sigma}}^{\ensuremath{-}}$ exciton states in a 10 nm thick ZnSe/ZnMgSe single quantum well by spectrally resolved three-pulse degenerate four-wave mixing using circularly polarized 100 fs pulses. Polarization and intensity dependent measurements are performed to identify the coherent processes responsible for the nonlinear signal into the ${\mathbf{k}}_{3}+{\mathbf{k}}_{2}\ensuremath{-}{\mathbf{k}}_{1}$ direction and to study the influence of Coulomb scattering on the dephasing rates. The experiments reveal nearly equal zero-density dephasing rates for coherences between ${\ensuremath{\sigma}}^{+}$ and ${\ensuremath{\sigma}}^{\ensuremath{-}}$ heavy- and/or light-hole exciton states as compared to the dephasing rate of the interband coherence between these states and the ground state. The measurements also demonstrate that exciton--exciton scattering destroys the phase coherence between heavy- and light-hole excitons about three times more effectively than the coherence between ${\ensuremath{\sigma}}^{+}$ and ${\ensuremath{\sigma}}^{\ensuremath{-}}$ heavy-hole excitons. The characteristic features of the experimental results are explained and reproduced by numerical calculations of the optical Bloch equations for a ten-level model including excitation induced dephasing.

DOI
10.1103/physrevb.69.125325

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Spectrally resolved and time-integrated degenerate four-wave mixing (FWM) experiments with ultra-short pulses have been used to investigate the relaxation times and coherent interactions of excitons in the Boltzmann and in the quantum kinetic regime in ZnSe single quantum wells.Three-pulse FWM experiments using 100 fs pulses in a 10 nm thick ZnSe/ZnMgSe single quantum well reveal nearly equal zero-density dephasing rates for coherences between + σ and - σ heavy-and/or light-hole exciton states as compared to the dephasing rate of the interband coherence between these states and the ground state.The measurements also demonstrate that exciton-exciton scattering destroys the phase coherence between heavy-and light-hole excitons about three times more effectively than the coherence between + σ and + σ heavy-hole excitons.The different coherent nonlinear signals obtained in a three-beam FWM experiment are explained and reproduced by numerical calculations of the optical Bloch equations for a ten-level model including excitation induced dephasing (EID).Two-beam FWM experiments using 30 fs pulses on a 10 nm ZnSe quantum well reveal marked quantum beats and a pronounced non-exponential decay for delay times smaller ~500 fs.The pronounced peak at pulse overlap is attributed to rapid destructive interference of the created polarization and to spin dependent quantum kinetic effects caused by the transient formation of an electron-hole (eh) pair grating.The three-beam FWM trace shows a bi-exponential decay which is attributed to a nonlinear polarization that is caused by the interaction of polarization 3 k with both an exciton grating and an eh-pair grating.Model calculations using the OBEs of a two level system that includes ∑ -+
We describe a novel three-pulse degenerate four-wave mixing configuration that permits the direct observation of the coherence between the σ+ and the σ− exciton states in a GaAs quantum well excited in a two-photon process. It is found that the phase coherence between the two single heavy-hole exciton states decays with a time constant that is considerably longer than the dephasing time of the coherence between these states and the ground state (interband coherence). All the experimental data are well described by numerical solutions of the optical Bloch equations for a phenomenological multilevel model.
The coherent control of excitonic and biexcitonic polarization in pulse-transmission and four-wave-mixing (FWM) experiments is analysed with real time resolution. As a model system a ZnSe single quantum well is exclusively excited at the heavy-hole exciton and exciton–biexciton resonance. In pulse-transmission experiments the coherent control of excitonic polarization is shown for low excitation intensities. At elevated excitation intensities the dephasing time of the polarization is found to be strongly dependent on the relative phase of two phase-locked laser pulses which perform the coherent manipulation of the polarization. In FWM experiments the separate coherent control of the excitonic and biexcitonic FWM polarization is demonstrated which enables a coherent manipulation of the amplitude and phase of exciton–biexciton beats which are observed on the FWM polarization transients.
We investigate the spectral and thermal dependence of an exciton resonant all-optical and phase coherent photorefractive effect in a ZnSe single quantum well by four-wave mixing using 90fs90\phantom{\rule{0.3em}{0ex}}\mathrm{fs}90fs pulses. The observed phase coherence is attributed to an exciton-induced formation of an electron grating within the quantum well. The diffracted signal exhibits an exponential decay that is equal to the exciton dephasing rate and it shows a pronounced suppression at the temporal overlap of incident pulses. With decreasing photon energy the diffracted signal traces reveal faster decay and the exciton transition is shifted towards lower energies indicating an increasing electron concentration within the quantum well. In temperature dependent measurements we observe a filling of the signal dip at pulse overlap and a transition from the photorefractive effect to a ${\ensuremath{\chi}}^{(3)}$ four-wave-mixing process below 35K35\phantom{\rule{0.3em}{0ex}}\mathrm{K}35K. Additional experiments using a cw pump laser are consistent with the proposed mechanism of the observed photorefractive effect. The phase coherent photorefractive signal is reproduced by a phenomenological model that is based on the optical Bloch equations for a five-level system.
Biexcitonic complexes in a ZnSe single quantum well are investigated by spectrally resolved four-wave mixing (FWM). The formation of heavy-heavy-hole XXh{\mathrm{XX}}_{h}XXh​ and of mixed heavy-light-hole XXm{\mathrm{XX}}_{m}XXm​ biexcitons showing binding energies of ${\ensuremath{\Delta}}_{h}=4.8\mathrm{meV}$ and ${\ensuremath{\Delta}}_{m}=2.8\mathrm{meV}$ is identified by polarization selection rules. The coherent dynamics of the FWM response and the observed FWM intensity ratio between the XXh{\mathrm{XX}}_{h}XXh​ and XXm{\mathrm{XX}}_{m}XXm​ biexciton-induced nonlinear signals are in agreement with the solution of an extended optical Bloch equation.