All-optical tomography of electron spins in (In,Ga)As quantum dots

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All-optical tomography of electron spins in (In,Ga)As quantum dots

S. Varwig, A. René, Sophia E. Economou, A. Greilich, D. R. Yakovlev, D. Reuter, A. D. Wieck, T. L. Reinecke, and M. Bayer

Phys. Rev. B 89, 081310(R) – Published 28 February 2014

Abstract

We demonstrate the basic features of an all-optical spin tomography on picosecond time scale. The magnetization vector associated with a mode-locked electron spin ensemble in singly charged quantum dots is traced by ellipticity measurements using picosecond laser pulses. After optical orientation the spins precess about a perpendicular magnetic field. By comparing the dynamics of two interacting ensembles with the dynamics of a single ensemble we find buildup of a spin component along the magnetic field in the two-ensemble case. This component arises from a Heisenberg-like spin-spin interaction.

Received 6 December 2013
Revised 11 February 2014

DOI:https://doi.org/10.1103/PhysRevB.89.081310

Authors & Affiliations

S. Varwig¹, A. René¹, Sophia E. Economou², A. Greilich¹, D. R. Yakovlev^1,3, D. Reuter^4,*, A. D. Wieck⁴, T. L. Reinecke², and M. Bayer¹

¹Experimentelle Physik 2, Technische Universität Dortmund, 44221 Dortmund, Germany
²Naval Research Laboratory, Washington, D.C. 20375, USA
³Ioffe Physical-Technical Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia
⁴Angewandte Festkörperphysik, Ruhr-Universität Bochum, 44780 Bochum, Germany

^*Present address: Universität Paderborn, Department Physik, 33098 Paderborn, Germany.

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Issue

Vol. 89, Iss. 8 — 15 February 2014

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Images

Figure 1
(a) Photoluminescence spectrum of the (In,Ga)As/GaAs QD ensemble (black trace). Laser spectra, each with a FWHM of 1 meV having central photon energies of 1.388 (rotation pulse, RP), 1.390 (pump 1), and 1.396 eV (pump 2). (b) Ellipticity measurements when only pump 1 probe (bottom) and pump 2 probe (top) are applied. The probe in each case was degenerate with the corresponding pump. (c) Ellipticity traces of the spin ensemble probed in resonance with the QD subset excited by pump 1 without pump 2 (blue [gray]) and with pump 2 (red [light gray]). When interacting with the second QD subset a phase shift in the spin precession up to $π$ (at $\sim$ 5 ns) builds up relative to the case without pump 2.
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Figure 2
(a) Scheme of spin tomography without pump 2: The spin vector of the ensemble excited by pump 1, represented by the blue (gray) arrow, points originally along the $z$ direction and then precesses in the $y z$ plane about the magnetic field along $x$ . When the spins are pointing along the $y$ axis the RP rotates them quasi-instantaneously by $π / 2$ about the optical $z$ axis. Now pointing along the $x$ axis they no longer precess so that there is no spin component along the probe-sensitive $z$ axis. (b) With pump 2: The interaction of the two spin ensembles excited by the two pumps potentially leads to emergence of a spin component along the magnetic field. If the RP is applied when the spin in the precession plane points along $- y$ , the emerging component becomes oriented normal to $B$ so that it can be measured from its subsequent precessional motion. (c) Ellipticity traces without (top) and with pump 2 applied (bottom). The RP is hitting in both cases 6.2 ns after pump 1. In the lower trace an oscillation emerges after the $π / 2$ rotation, indicating an $x$ component of the spin vector.
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Figure 3
(a) Ellipticity traces with and without pump 2 (red [light gray] and blue [gray], respectively) for different delays of RP (green [gray] arrows) relative to pumps 1 and 2 arrivals (red [gray] arrow). The delay is chosen such that RP hits in a rising edge of an oscillation (spins pointing along $y$ ). The red (light gray) traces (with pump 2) show oscillations after the spin rotation induced by the RP, while the blue (gray) ones do not, except in the two lowest curves where echo contributions are still visible. (b) $x$ component of the spin ensemble addressed by pump 1, $S_{1, x}$ , in dependence on the RP delay.
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Figure 4
Model calculations of two interacting spins. The evolution of the $x$ component is shown by increasing the time delay between RP and pump 1. Each RP position demonstrates two conditions: without and with spin 2 acting on spin 1. Dashed lines show the evolution of the $x$ component.
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