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arXiv:1803.10651 · Physics of the Solid State

Photon Echo from Localized Excitons in Semiconductor Nanostructures

S. V. Poltavtsev, I. A. Yugova, Ilya A. Akimov, D. R. Yakovlev, M. Bayer

Published Aug 1, 2018• 28 citations
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Abstract

An overview on photon echo spectroscopy under resonant excitation of the exciton complexes in semiconductor nanostructures is presented. The use of four-wave-mixing technique with the pulsed excitation and heterodyne detection allowed us to measure the coherent response of the system with the picosecond time resolution. It is shown that, for resonant selective pulsed excitation of the localized exciton complexes, the coherent signal is represented by the photon echoes due to the inhomogeneous broadening of the optical transitions. In case of resonant excitation of the trions or donor-bound excitons, the Zeeman splitting of the resident electron ground state levels under the applied transverse magnetic field results in quantum beats of photon echo amplitude at the Larmor precession frequency. Application of magnetic field makes it possible to transfer coherently the optical excitation into the spin ensemble of the resident electrons and to observe a long-lived photon echo signal. The described technique can be used as a high-resolution spectroscopy of the energy splittings in the ground state of the system. Next, we consider the Rabi oscillations and their damping under excitation with intensive optical pulses for the excitons complexes with a different degree of localization. It is shown that damping of the echo signal with increase of the excitation pulse intensity is strongly manifested for excitons, while on trions and donor-bound excitons this effect is substantially weaker.

DOI
10.1134/s1063783418080188

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An overview on photon echo spectroscopy under resonant excitation of the exciton complexes in semiconductor nanostructures is presented. The use of four-wave-mixing technique with the pulsed excitation and heterodyne detection allowed us to measure the coherent response of the system with the picosecond time resolution. It is shown that, for resonant selective pulsed excitation of the localized exciton complexes, the coherent signal is represented by the photon echoes due to the inhomogeneous broadening of the optical transitions. In case of resonant excitation of the trions or donor-bound excitons, the Zeeman splitting of the resident electron ground state levels under the applied transverse magnetic field results in quantum beats of photon echo amplitude at the Larmor precession frequency. Application of magnetic field makes it possible to transfer coherently the optical excitation into the spin ensemble of the resident electrons and to observe a long-lived photon echo signal. The described technique can be used as a high-resolution spectroscopy of the energy splittings in the ground state of the system. Next, we consider the Rabi oscillations and their damping under excitation with intensive optical pulses for the excitons complexes with a different degree of localization. It is shown that damping of the echo signal with increase of the excitation pulse intensity is strongly manifested for excitons, while on trions and donor-bound excitons this effect is substantially weaker.
AbstractAn overview on photon echo spectroscopy under resonant excitation of the exciton complexes in semiconductor nanostructures is presented. The use of four-wave-mixing technique with the pulsed excitation and heterodyne detection allowed us to measure the coherent response of the system with the picosecond time resolution. It is shown that, for resonant selective pulsed excitation of the localized exciton complexes, the coherent signal is represented by the photon echoes due to the inhomogeneous broadening of the optical transitions. In case of resonant excitation of the trions or donor-bound excitons, the Zeeman splitting of the resident electron ground state levels under the applied transverse magnetic field results in quantum beats of photon echo amplitude at the Larmor precession frequency. Application of magnetic field makes it possible to transfer coherently the optical excitation into the spin ensemble of the resident electrons and to observe a long-lived photon echo signal. The described technique can be used as a high-resolution spectroscopy of the energy splittings in the ground state of the system. Next, we consider the Rabi oscillations and their damping under excitation with intensive optical pulses for the excitons complexes with a different degree of localization. It is shown that damping of the echo signal with increase of the excitation pulse intensity is strongly manifested for excitons, while on trions and donor-bound excitons this effect is substantially weaker.
We present results on photon echo spectroscopy for resonant excitation of localized charged exciton complexes (trions) in CdTe/CdMgTe semiconductor quantum wells. We demonstrate that the Zeeman splitting of resident electron spin levels in transverse magnetic field leads to quantum beats in the photon echoes with the Larmor precession frequency. This allows us to perform a coherent transfer of optical excitation into a spin ensemble and to observe long-lived photon echoes. Our approach can be used as a tool for remarkably high resolution spectroscopy of the ground state levels: We are able to resolve splittings between the spin levels with sub-µeV precision and to distinguish between different types of electrons in the ensemble, namely electrons either bound to donors or localized on quantum well potential fluctuations. To that end we show that stimulated step-like Raman processes in the two-pulse excitation scheme allow us to probe the electron spin ensemble with high selectivity and precision even for systems with broad optical transitions. Next, Rabi oscillations for exciton complexes with different degree of localization are detected by photon echo spectroscopy. We observe that an increase of the area of either the first or the second pulse leads to a significant decrease of the photon echo signal, which is strongest for the neutral excitons and less pronounced for the donor-bound exciton complex.
We study Rabi oscillations detected in the coherent optical response from various exciton complexes in a 20-nm-thick CdTe/(Cd,Mg)Te quantum well using time-resolved photon echoes. In order to evaluate the role of exciton localization and inhomogeneous broadening we use selective excitation with spectrally narrow ps pulses. We demonstrate that the transient profile of the photon echo from the localized trion (${\mathrm{X}}^{\ensuremath{-}}$) and the donor-bound exciton (D0X{\mathrm{D}}^{0}\mathrm{X}D0X) transitions strongly depends on the strength of the first pulse. It acquires a non-Gaussian shape and experiences significant advancement for pulse areas larger than $\ensuremath{\pi}$ due to non-negligible inhomogeneity-induced dephasing of the oscillators during the optical excitation. Next, we observe that an increase of the area of either the first (excitation) or the second (rephasing) pulse leads to a significant damping of the photon echo signal, which is strongest for the neutral excitons and less pronounced for the donor-bound exciton complex (D0X{\mathrm{D}}^{0}\mathrm{X}D0X). The measurements are analyzed using a theoretical model based on the optical Bloch equations which accounts for the inhomogeneity of optical transitions in order to reproduce the complex shape of the photon echo transients. In addition, the spreading of Rabi frequencies within the ensemble due to the spatial variation of the intensity of the focused Gaussian beams and excitation-induced dephasing are incorporated in our model, which is able to explain the fading and damping of Rabi oscillations. By analyzing the results of the simulation for ${\mathrm{X}}^{\ensuremath{-}}$ and D0X{\mathrm{D}}^{0}\mathrm{X}D0X complexes we are able to establish a correlation between the degree of localization and the transition dipole moments determined as $\ensuremath{\mu}({\mathrm{X}}^{\ensuremath{-}}$)=73 D and $\ensuremath{\mu}({\mathrm{D}}^{0}\mathrm{X}$)=58 D.
Coherent optical spectroscopy such as four-wave mixing and photon echo generation deliver rich information on the energy levels involved in optical transitions through the analysis of polarization of the coherent response. In semiconductors, it can be applied to distinguish between different exciton complexes, which is a highly non-trivial problem in optical spectroscopy. We develop a simple approach based on photon echo polarimetry, in which polar plots of the photon echo amplitude are measured as function of the angle φ between the linear polarizations of the two exciting pulses. The rosette-like polar plots reveal a distinct difference between the neutral and charged exciton (trion) optical transitions in semiconductor nanostructures. We demonstrate this experimentally by photon echo polarimetry of a CdTe/(Cd, Mg)Te quantum well. The echoes of the trion and donor-bound exciton are linearly polarized at the angle 2φ with respect to the first pulse polarization and their amplitudes are weakly dependent on φ. While on the exciton the photon echo is co-polarized with the second exciting pulse and its amplitude scales as cosφ.
Coherent optical spectroscopy such as four-wave mixing and photon echo generation deliver detailed information on the energy levels involved in optical transitions through the analysis of polarization of the coherent response. In semiconductors, it can be applied to distinguish between different exciton complexes, which is a highly non-trivial problem in optical spectroscopy. We develop a simple approach based on photon echo polarimetry, in which polar plots of the photon echo amplitude are measured as function of the angle φφφ between the linear polarizations of the two exciting pulses. The rosette-like polar plots reveal a distinct difference between the neutral and charged exciton (trion) optical transitions in semiconductor nanostructures. We demonstrate this experimentally by photon echo polarimetry of a 20-nm-thick CdTe/(Cd,Mg)Te quantum well at temperature of 1.5~K. Applying narrow-band optical excitation we selectively excite different exciton complexes including the exciton, the trion, and the donor-bound exciton D0^00X. We find that polarimetry of the photon echo on the trion and D0^00X is substantially different from the exciton: The echoes of the trion and D0^00X are linearly polarized at the angle 2φ2φ2φ with respect to the first pulse polarization and their amplitudes are weakly dependent on φφφ. While on the exciton the photon echo is co-polarized with the second exciting pulse and its amplitude scales as cos⁡φ\cosφcosφ.
We report on magnetic field-induced oscillations of the photon echo signal from negatively charged excitons in a CdTe/(Cd,Mg)Te semiconductor quantum well. The oscillatory signal is due to Larmor precession of the electron spin about a transverse magnetic field and depends sensitively on the polarization configuration of the exciting and refocusing pulses. The echo amplitude can be fully tuned from the maximum down to zero depending on the time delay between the two pulses and the magnetic-field strength. The results are explained in terms of the optical Bloch equations accounting for the spin level structure of electrons and trions.