High-Resolution Two-Dimensional Optical Spectroscopy of Electron Spins

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High-Resolution Two-Dimensional Optical Spectroscopy of Electron Spins

M. Salewski, S. V. Poltavtsev, I. A. Yugova, G. Karczewski, M. Wiater, T. Wojtowicz, D. R. Yakovlev, I. A. Akimov, T. Meier, and M. Bayer

Phys. Rev. X 7, 031030 – Published 14 August 2017

Abstract

Multidimensional coherent optical spectroscopy is one of the most powerful tools for investigating complex quantum mechanical systems. While it was conceived decades ago in magnetic resonance spectroscopy using microwaves and radio waves, it has recently been extended into the visible and UV spectral range. However, resolving MHz energy splittings with ultrashort laser pulses still remains a challenge. Here, we analyze two-dimensional Fourier spectra for resonant optical excitation of resident electrons to localized trions or donor-bound excitons in semiconductor nanostructures subject to a transverse magnetic field. Particular attention is devoted to Raman coherence spectra, which allow one to accurately evaluate tiny splittings of the electron ground state and to determine the relaxation times in the electron spin ensemble. A stimulated steplike Raman process induced by a sequence of two laser pulses creates a coherent superposition of the ground-state doublet which can be retrieved only optically because of selective excitation of the same subensemble with a third pulse. This provides the unique opportunity to distinguish between different complexes that are closely spaced in energy in an ensemble. The related experimental demonstration is based on photon-echo measurements in an $n$ -type $CdTe / (Cd, Mg) Te$ quantum-well structure detected by a heterodyne technique. The difference in the sub- $μ eV$ range between the Zeeman splittings of donor-bound electrons and electrons localized at potential fluctuations can be resolved even though the homogeneous linewidth of the optical transitions is larger by 2 orders of magnitude.

Received 2 January 2017

DOI:https://doi.org/10.1103/PhysRevX.7.031030

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Excitons Spin polarization Spin relaxation Spintronics Trions

Doped semiconductors Quantum wells

Electron spin resonance Four-wave mixing

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

M. Salewski¹, S. V. Poltavtsev^1,2, I. A. Yugova², G. Karczewski³, M. Wiater³, T. Wojtowicz^3,4, D. R. Yakovlev^1,5, I. A. Akimov^1,5, T. Meier⁶, and M. Bayer^1,5

¹Experimentelle Physik 2, Technische Universität Dortmund, 44221 Dortmund, Germany
²Spin Optics Laboratory, St. Petersburg State University, St. Petersburg 198504, Russia
³Institute of Physics, Polish Academy of Sciences, PL-02668 Warsaw, Poland
⁴International Research Centre MagTop, PL-02668 Warsaw, Poland
⁵Ioffe Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia
⁶Department Physik & CeOPP, Universität Paderborn, D-33098 Paderborn, Germany

Popular Summary

Interactions between the different parts of a quantum-mechanical system, such as an organic molecule or a semiconductor, can lead to complex behavior. One way to better understand this behavior is by firing short laser pulses at the system and carefully observing how the light is scattered and absorbed. To reveal the relevant dynamics, these pulses need last for only picoseconds, but the short duration hides subtle energy distinctions such as those seen between different spins of an electron exposed to an electric or magnetic field. We have adapted these techniques to measure such tiny differences and use them to identify different optical transitions that can be excited by the pulses.

Specifically, we demonstrate how two-dimensional Fourier transform spectroscopy can be used to evaluate spin splitting of ground-state electrons. As a host system for the electrons, we chose a semiconductor quantum well in which the electrons were provided by doping with impurities. Our approach is based on stimulated steplike Raman processes in a pulsed excitation regime that allow us to probe the splitting of electron energy levels with high selectivity, even for systems with broad optical transitions. This provides the unique opportunity to distinguish between various carrier complexes, such as electron-hole pairs bound to excess electrons in semiconductors, in ensembles hosting different types of optical excitation.

Our approach allows us to measure the spin dynamics of carriers in the ground state without creating a macroscopic spin polarization. This is attractive for fundamental studies of spin ensembles because the energy input in the system, which may destroy spin coherence, is reduced.

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Vol. 7, Iss. 3 — July - September 2017

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Images

Figure 1
(a) Scheme of the pulse sequence and the photon-echo signal that is detected in the $k_{S} = k_{3} + k_{2} - k_{1}$ direction. (b) Energy-level diagram and optical transitions for the trion ( $X^{-}$ ) or the donor-bound exciton ( $D^{0} X$ ), which are localized in the semiconductor QW structure. The characters correspond to the polarization of the optical transition parallel (H) and perpendicular (V) to the magnetic field. (c,d) Double-sided Feynman diagrams for the HHH and HVV polarization configurations, respectively. For VVV and VHH, the resulting diagrams are identical to HHH and HVV if the states $| 3 ⟩$ and $| 4 ⟩$ are exchanged. For the full set of diagrams, see also Sec. 2 of the supplementing material [29].
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Figure 2
Contour plots of the 2D Fourier rephasing spectra $S_{I} (Ω_{1}, Ω_{3})$ in the copolarized HHH (a) and in cross-polarized HVV (b) polarization configurations after Eqs. (7) and (8), respectively. The following parameters are used: $ℏ {\bar{Ω}}_{0} = 1.6 eV$ , $ℏ Γ = ℏ / σ = 1 meV$ , $ℏ γ = ℏ / T_{2} = 10 μ eV$ , and $ℏ ω_{L} = 100 μ eV$ .
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Figure 3
Contour plots of the absolute value of the Raman coherence 2D Fourier spectra in the copolarized HHH (a) and cross- polarized HVV (b) polarization configuration and their cross sections at the optical frequency $Ω_{3} = {\bar{Ω}}_{0}$ (c,d), respectively. The following parameters are used: $ℏ {\bar{Ω}}_{0} = 1.6 eV$ , $ℏ Γ = ℏ / σ = 1 meV$ , $ℏ γ_{r} = ℏ γ_{T} = 10 μ eV$ , $ℏ γ_{1, e} = ℏ γ_{2, e} = 0.3 μ eV$ , $ℏ ω_{L} = 24 μ eV$ , and $t_{1} = 26.7 ps$ .
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Figure 4
(a) Schematic illustration of the heterodyne-detected photon echoes in reflection geometry. BS and PD denote the beam splitter and photodiode, respectively. (b) PL spectrum (the solid line) of the investigated 20-nm-thick $CdTe / (Cd, Mg) Te$ QW structure measured at temperature $T = 2 K$ for above-barrier excitation with photon energy 2.33 eV. The laser spectrum is shown by the dashed line. (c) Time-resolved cross correlation of the resulting FWM signal $| E_{S} (t_{3}) |$ measured for $t_{1} = 27 ps$ and $t_{2} = 33 ps$ as well as $ℏ ω = 1.597 eV$ . The signal is given by photon echoes involving different pulse sequences: ${PPE}_{12}$ and ${PPE}_{13}$ correspond to the two-pulse sequences 1-2 and 1-3, respectively. ${SPE}_{123}$ corresponds to the three-pulse sequence 1-2-3.
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Figure 5
Spectral dependence of the $A_{PPE}$ and $A_{SPE}$ transients at $B = 0$ . (a,b) $A_{PPE}$ and $A_{SPE}$ measured as a function of $2 t_{1}$ and $t_{2}$ , respectively. The SPE is measured for $t_{1} = 27 ps$ . (c) Spectral dependence of $A_{PPE}^{0} = A_{PPE} (t_{1} = 0)$ , $ℏ γ$ and $ℏ / T_{1}$ , evaluated from the exponential fits to the echo transients for different photon energies $ℏ ω$ [see the solid lines in (a) and (b)].
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Figure 6
(a) Contour plot of the long-lived SPE measured in the HVV polarization configuration as a function of the excitation photon energy $ℏ ω$ and delay time $t_{2}$ . The data are taken at $B = 260 mT$ , $t_{1} = 27 ps$ . The solid black lines indicate the signal level with 10% of the maximum intensity. (b) Exemplary transients for given photon energies of 1.5972 eV and 1.5985 eV corresponding to optical excitation of the $D^{0} X$ and $X^{-}$ complexes, respectively. (c) Spectral dependence of the long-lived SPE signal strength $A_{SPE}^{e, 0} = A_{SPE}^{e} (t_{2} = 0)$ (left axis), the linewidth $ℏ γ_{2, e}$ (left axis), and the electron $g$ factor (right axis) evaluated from the $A_{SPE} (t_{2})$ transients at $B = 260 mT$ . (d) The 2DFTS Raman coherence image $| S_{I}^{⊥} (Ω_{2}, Ω_{3}) |$ reconstructed from (c). The spectral dependence of $ℏ ω_{L}$ is shown by the dots.
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