Damping of Rabi oscillations in intensity-dependent photon echoes from exciton complexes in a CdTe/(Cd,Mg)Te single quantum well

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

Phys. Rev. B 96, 075306 – Published 18 August 2017

Abstract

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 ( $X^{-}$ ) and the donor-bound exciton ( $D^{0} X$ ) 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 $π$ 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 ( $D^{0} X$ ). 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 $X^{-}$ and $D^{0} X$ complexes we are able to establish a correlation between the degree of localization and the transition dipole moments determined as $μ (X^{-}$ )=73 D and $μ (D^{0} X$ )=58 D.

Received 20 June 2017

DOI:https://doi.org/10.1103/PhysRevB.96.075306

Physics Subject Headings (PhySH)

Excitons Nanophotonics Trions

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

S. V. Poltavtsev^1,2,*, M. Reichelt³, I. A. Akimov^1,4, G. Karczewski⁵, M. Wiater⁵, T. Wojtowicz^5,6, D. R. Yakovlev^1,4, T. Meier³, and M. Bayer^1,4

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

^*sergei.poltavtcev@tu-dortmund.de

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Issue

Vol. 96, Iss. 7 — 15 August 2017

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Images

Figure 1
Scheme of photon echo detection in reflection geometry. PD denotes the photodetector.
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Figure 2
(a) PL spectrum of the studied sample (black line) with indicated spectral features: donor-bound exciton at $E$ ( $D^{0} X$ )=1.5972 eV, trion at $E$ ( $X^{-}$ )=1.5980 eV, and neutral exciton at $E$ (X)=1.6005 eV. Spectra of laser pulses tuned to $D^{0} X$ , $X^{-}$ , and the localized exciton state ( $X_{L}$ ) are shown by the blue, red, and green lines, respectively. Red dots are the coherence times $T_{2}^{0}$ and blue dots are the homogeneous linewidths $ℏ γ_{0}$ obtained from scans of the PE decays. (b) Transient of FWM signal measured at the trion at $τ_{12} = 40$ ps demonstrating a PE located at $τ_{Ref} = 2 τ_{12} = 80$ ps (circles). The exciting pulses are schematically shown by the dashed line. (c) Decays of the PE amplitude measured at three indicated energies with extracted coherence times $T_{2}^{0}$ .
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Figure 3
Rabi oscillations measured on the various localized exciton complexes in the studied CdTe/(Cd,Mg)Te QW. (a) Dependence of PE amplitude measured on the trion ( $E = 1.5980$ eV) detected at $τ_{Ref} = 2 τ_{12} = 53.3$ ps on both pulse amplitudes. Measurements of PE transients as a function of pulse amplitude: (b) localized exciton at $E$ ( $X_{L}$ )=1.5990 eV, $A_{1}$ is varied at $A_{2} = 3.5$ ${pJ}^{1 / 2}$ ; (c) localized trion at $E$ ( $X^{-}$ )=1.5980 eV, $A_{1}$ is varied at $A_{2} = 3.5$ ${pJ}^{1 / 2}$ ; (d) $A_{2}$ is varied at $A_{1} = 3.5$ ${pJ}^{1 / 2}$ ; and (e) donor-bound exciton at $E$ ( $D^{0} X$ )=1.5972 eV, $A_{1}$ is varied at $A_{2} = 3.4$ ${pJ}^{1 / 2}$ . Upper and lower panels of (c)–(e) are the experimental data (upper row) and the numerical simulations (lower row), respectively. The scales in panels (b)–(e) are normalized to unity.
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Figure 4
Various mechanisms responsible for the damping of the simulated Rabi oscillations. (a) Rabi oscillations without damping mechanisms. (b) Only the spatial integration over the excitation beam is activated and $γ = 1 / T_{2}^{0}$ . (c) Only EID is activated. Upper panels correspond to the first pulse area scan at $Θ_{2} = π / 2$ ; lower panels correspond to the second pulse area scan at $Θ_{1} = π / 2$ . All intensity scales are normalized to unity. The width of the spectral ensemble used in the calculations is $2 \sqrt{2 ln 2} σ = 1.0$ meV and the pulse delay is $τ_{12} = 26.7$ ps.
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Figure 5
Calculated excitation-induced dephasing as a function of the first pulse area $Θ_{1}$ at $Θ_{2} = 0$ : solid and dotted lines are the dephasing times $T_{2} = 1 / γ$ of $X^{-}$ and $D^{0} X$ , respectively; dashed and dash-dotted lines are the dephasing rates $γ$ of $X^{-}$ and $D^{0} X$ , respectively.
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