Hole spin precession in a (In,Ga)As quantum dot ensemble: From resonant spin amplification to spin mode locking

S. Varwig, A. Schwan, D. Barmscheid, C. Müller, A. Greilich, I. A. Yugova, D. R. Yakovlev, D. Reuter, A. D. Wieck, and M. Bayer

Phys. Rev. B 86, 075321 – Published 31 August 2012

Abstract

Coherent collective phenomena of hole spins confined in an ensemble of (In,Ga)As quantum dots are studied by monitoring their Larmor precession about a magnetic field. Variation of the field strength drives the hole spins from a regime of resonant spin amplification, in which their precession frequency is a unique multiple of the laser repetition rate, to spin mode locking, in which several precession modes are commensurable with the laser repetition rate. In this regime the spin coherence time of individual holes is determined to be 0.7 $μ$ s. In contrast, electron spins in the quantum dots are always trapped in the mode-locking regime due to the strong hyperfine interaction with nuclear spins.

Received 15 June 2012

DOI:https://doi.org/10.1103/PhysRevB.86.075321

Authors & Affiliations

S. Varwig¹, A. Schwan¹, D. Barmscheid¹, C. Müller¹, A. Greilich¹, I. A. Yugova^1,2, D. R. Yakovlev^1,3, D. Reuter⁴, A. D. Wieck⁴, and M. Bayer¹

¹Experimentelle Physik 2, Technische Universität Dortmund, 44221 Dortmund, Germany
²Physical Faculty of St. Petersburg State University, 198504 St. Petersburg, Russia
³Ioffe Physical-Technical Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia
⁴Angewandte Festkörperphysik, Ruhr-Universität Bochum, 44780 Bochum, Germany

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Vol. 86, Iss. 7 — 15 August 2012

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Images

Figure 1
Hole and electron-spin phase synchronization for excitation with single or double pump pulse sequences with $T_{R} = 13.2$ ns and $T_{D} = T_{R} / 6 = 2.2$ ns. Curves are shifted vertically for clarity. Ellipticity (a) and Faraday rotation (b) signals measured under equal conditions for single pulse sequence (the two upper curves in each panel) and double pulse ( $σ^{+}$ co-polarized) sequence (the bottom curves). $T = 6$ K, $B = 2$ T.Reuse & Permissions
Figure 2
(a) Magnetic field dependence of hole spin precession frequency. Line is linear fit. (b) In-plane hole $g$ -factor dependence on sample orientation relative to $B_{y}$ . Line is fit with $g_{h}^{2} = g_{h, x}^{2} \sin^{2} α + g_{h, y}^{2} \cos^{2} α$ and $| g_{h, x} | = 0.146$ and $| g_{h, y} | = 0.068$ . (c) Ellipticity amplitude before the pump pulse as function of temporal separation $T_{R}$ between pulses in single-pump sequence. Line shows calculated dependence with fit parameter $T_{2} = 0.7$ $μ$ s. $B = 2$ T. Excitation pulse area $Θ \approx π$ (45 W/cm $^{2}$ ).Reuse & Permissions
Figure 3
(a) Ellipticity and Faraday rotation signals measured for double pump pulse excitation at the $+ 1$ st burst around a pump-probe delay of $2 T_{D}$ . (b) Ellipticity and Faraday rotation signal strength as a function of energy detuning of probe beam from resonance.Reuse & Permissions
Figure 4
(a) Relaxation kinetics of the FR amplitude at a delay of 2.06 ns (close to $T_{D}$ ) after switching off pump 2. Beforehand, the system was treated for 20 min by the double-pump pulse protocol (Ref. 18). The blue curve was measured with pump 2 blocked at time zero. The black line shows an exponential decay with time $τ = 30$ s fitted to the data. (b) Relaxation kinetics of the ellipticity amplitude at a delay of 4.12 ns (close to the $+ 1$ burst maximum). $B = 2$ T.Reuse & Permissions
Figure 5
Ellipticity as function of pump-probe delay for different magnetic fields (denoted in Fig. 6) and therefore different average precession frequencies. Panel (a) corresponds to the SML regime, and panel (b) to the RSA regime. $T_{R} = 6.6$ ns. Inset (c): Dependence of the precession frequency spread, $Δ ω$ , on magnetic field (calculated with average spin-ensemble frequency $ω \propto B$ ; see text). Solid line is $Δ ω = k ω$ . Dotted line shows $Δ ω = 0.5 ω_{R}$ . Dash-dotted line shows the situation with additional spread, $Δ ω_{0}$ , that does not depend on magnetic field, with $Δ ω = \sqrt{{(Δ ω_{0})}^{2} + {(k ω)}^{2}}$ .Reuse & Permissions
Figure 6
Magnetic field dependence of electron (right axis, lower curve) and hole [left axis, upper solid (red) curve] spin polarizations close to zero pump-probe delay (shortly before pump pulse arrival). Dash-dotted (gray) curve gives results calculated using $| g_{h} | = 0.14$ , $Δ g_{h} = 0.04$ , and $Θ = 1.4 π$ . The hole RSA and SML field ranges are shown by arrows above the curves. For the electron spin polarization only the SML regime is possible. $T_{R} = 6.6$ ns. The arrows with numbers correspond to $ω$ values of (1) 0, (2) $0.5 ω_{R}$ , (3) $ω_{R}$ , (4) $1.5 ω_{R}$ , (5) $2 ω_{R}$ , and (6) $2.5 ω_{R}$ .Reuse & Permissions

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