All optical control of electron spins in quantum dot ensembles - PowerPoint PPT Presentation

All optical control of electron spins in quantum dot ensembles Manfred Bayer Experimentelle Physik II Technische Universität Dortmund JST-DFG workshop, Aachen, 05.-07.03.2008

Acknowledgements A. Greilich, S. Spatzek, I. Yugova, I. Akimov, D. Yakovlev, Technische Universität Dortmund, Germany A. Shabaev and A. Efros Naval Research Laboratory, Washington DC, USA D. Reuter and A. Wieck Ruhr-University of Bochum, Germany

Acknowledgements Research group: „Quantum Optics in Semiconductor Nanostructures “ Borussia Dortmund Fußball heißt das Spiel, Borussia seine Seele!

Quantum information processing Potential of quantum information processing: Potential of quantum information processing: Increase of computational power Increase of computational power Realization of new functionalities for communication Realization of new functionalities for communication Reduction of complexity Reduction of complexity Demand: GaAs Long living coherence InGaAs α + β α β = 0 1 mit , const. GaAs Prerequisite Prerequisite Availability of high quality quantum hardware: Quantum dots! Availability of high quality quantum hardware: Quantum dots!

Qubit-candidates in QDs Electron Exciton Spin 2-level systems Spin is efficiently protected by confinement against efficient relaxation mechanisms in higher-dim. systems.

Attractivity of QD electron spin qu-bits Experiments on QD ensembles!! GaAs Single electron per QD! InGaAs Relaxation times T 1 GaAs in high magnetic field: TU Delft: gated QDs T 1 ~ 10 ms Nature 430, 431 (2004) TU Munich: self-assembled QDs T 1 ~ 10 ms Nature 432, 81 (2004) at zero magnetic field: Dortmund: self-assembled QDs T 1 ~ 0.3 s PRL 98, 107401 (2007)

Single spin vs spin ensembles � Single spin � Single spin � Spin ensemble � Spin ensemble Pro: Pro: avoid inhomogeneities avoid inhomogeneities Pro: Pro: robustness robustness Con: Con: strong spectroscopic signal strong spectroscopic signal fragile fragile weak spectroscopic signal weak spectroscopic signal Con: Con: inhomogeneities inhomogeneities

Outline 1. Introduction 2. Faraday rotation with time resolution 3. Generation of spin coherence 4. Mode-locking of spin coherence 5. Tailoring of mode-locking 6. Electron spin focussing by nuclei 7. Current work

Quantum dot samples Self-assembled quantum dots • 20 layers of InGaAs/GaAs QDs with density ~ 10 10 cm -2 per layer • n-doped 20nm below QD layer - dopant density ~ dot density • thermal annealing (T>900°C for 30s) to use Si-based detectors Non-annealed QD geometry: dome-shaped ~ 25 nm diameter ~ 5 nm height m µ 5 , 0 large oscillator strength!

Experiment optical axis z pump - probe Faraday rotation θ F ∝ M • k probe ∝ M z M M B Sample BIIx B= 3T Δ t ⎛ ⎞ Δ θ F ∝ − ω Δ t exp( ) cos( t ) ⎜ ⎟ θ ∝ − θ F (mrad) * exp T ⎜ ⎟ 2 F * ⎝ T ⎠ 2 Δ t k pump k probe prepare spin polarization Delay time, Δ t (ps)

Spin relaxation characteristic quantities: T 1 relaxation longitudinal relaxation time T 2 decoherence transverse relaxation time T 2 * dephasing ensemble effects (inhomogeneities, measurement variations etc) longitudinal ( T 1 ) transverse ( T 2 ) B B energy T 1 T 2 spin-flip ϕ ↑〉+ ↓〉 ↑〉 + ↓〉 i (| | ) / 2 (| | ) / 2 e

Precession about magnetic field B 0T 1T 2T 3T ω = g μ h B 4T e e B x Faraday rotation(a.u.) z 5T 6T y B X 7T σ + 0 500 1000 1500 time(ps) A. Greilich et al., Phys. Rev. Lett. 96, 227401 (2006)

Electron g-factor tensor ω el , I. Yugova et al., Phys. Rev. B 75, 195325 (2007) g e -1 ) ω (ps 90 fit ω exc 120 60 0.29 g X 0.65 fit 0.28 0.27 150 30 0.58 0.26 g e,x 0.25 0.24 0.56 electron g-factor 0.54 180 0 0.24 PL intensity 0.25 0.54 0.26 210 330 0.27 0.52 0.28 0.65 0.29 240 300 0.50 270 laser considerable variation of g-factor 1.38 1.39 1.40 1.41 1.42 energy (eV) I. Yugova et al., Phys. Rev. B 75, 195325 (2007)

Precession about magnetic field B 0T 1T 2T 3T ω = g μ h B 4T e e B x Faraday rotation(a.u.) 5T z 6T 7T y B X σ + 0 500 1000 1500 time(ps) A. Greilich et al., Phys. Rev. Lett. 96, 227401 (2006)

B Analysis of FR data 9 0,15 FR amplitude A. Greilich et al., Phys. Rev. Lett. 96, 227401 (2006) 8 ⎛− ⎞ 0,10 ( ) t Ω e ( ps -1 ) 7 ⎜ ⎟ ∝ ⋅ Ω exp cos t ⎜ ⎟ e * ⎝ ⎠ T 6 0,05 2 5 2 (ns) 0,00 4 0 1 2 3 Ω = μ h T * g B B (T) e e B 3 ⇓ 2 = 1 0 . 574 g e 0 0,0 0,5 1,0 1,5 2,0 2,5 3,0 B(T) Δ ⇒ ΔΩ = Δ μ ⇒ Δ = ≡ h 0.004 0.7% g g B g e e e B e T 2 *(B=0) > 6ns dephasing in random nuclear magnetic field T 2 *(B=0) > 6ns dephasing in random nuclear magnetic field

Long lasting spin coherence z 2 < * A. Greilich et al., Science 313, 341 (2006) 5 T ns B= 0T y Faraday rotation B X B= 1T σ + B= 6T 2 Dephasing time T* 2 (ns) negative delay positive delay fit, Δ g e =0.005 -5 0 0 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 tim e (p s) 1 pulse 1 pulse 2 pulse 3 pulse 4 0 0 2 4 6 8 10 Magnetic Field (T) coherence outlasts pulse repetition period & dephasing time. time (ns)

Spin mode locking 0.58 0.57 0.56 0.55 norm. PL intensity electron g-factor 0.54 0.53 0.52 0.51 QD emission g-factor 0.50 laser precession frequency 0.49 1.37 1.38 1.39 1.40 1.41 1.42 1.43 Energy (eV) QD ensemble offers broad distribution of g-factors μ π 2 g B ω = = ⋅ = ⋅ Ω laser pulse separation: e B N N laser pulse separation: further e R h T T R = 13.2ns T R = 13.2ns selection: R phase synchronization of spin subsets by laser

Spin synchronization scheme N=4 phase synchronization condition N N-1 N+1 π 2 ω = ⋅ N N+2 N-2 N=6 e T R N+3 N-3 N=8 precession frequency mode out of phase pump T R pulses probe time

A. Greilich et al., Science 313, 341 (2006) Spin mode locking π 2 ω = ⋅ N e T R 2 = 3 . 0 T µs

Transverse spin relaxation time laser repetition period T R varied by pulse-picker from 13.2 to 990 ns A. Greilich et al., Science 313, 341 (2006) Faraday rotation amplitude B = 6 T 200 Faraday rotation amplitude T 2 = 3.0 μ s 150 100 T R = 13.2 ns -1000 -500 0 500 1000 1500 50 B = 6 T Time (ps) T = 2 K 0 0.2 0.4 0.6 0.8 1.0 Pulse repetition period, T R ( μ s ) decay time gives single dot coherence time T 2 = 3.0 μ s four orders of magnitude longer than ensemble dephasing T 2 *=0.4ns at B=6T!

Clocking of spin modes B= 6T only first pump is on FR amplitude (arb. units) two-pulse experiment: two-pulse experiment: pump-pulse split into two beams pump-pulse split into two beams with variable time delay in between with variable time delay in between -1000 0 1000 2000 3000 4000 time (ps) A. Greilich et al., Science 313, 341 (2006)

Clocking of spin modes only first pump is on B= 6T FR amplitude (arb. units) only second pump is on T D = 1.8ns T R / T D = 7 -1000 0 1000 2000 3000 4000 time (ps) A. Greilich et al., Science 313, 341 (2006)

Clocking of spin modes only first pump is on B= 6T FR amplitude (arb. units) only second pump is on +1 burst -1 burst both pumps are on T R / T D = 7 T D = 1.8ns -1000 0 1000 2000 3000 4000 time (ps) A. Greilich et al., Science 313, 341 (2006)

Clocking of spin modes +1 burst T R T R Faraday rotation -1 burst +2 burst pump 2 T D pump 1 - 2 0 0 0 0 2 0 0 0 4 0 0 0 6 0 0 0 t i m e ( p s ) π π 2 2 ω = ⋅ ⋅ ω = ⋅ ⋅ ⇒ spins echoes every T D N K N L − e e T T T D R D redistribution of precession frequencies

A. Greilich et al., Science 313, 341 (2006) Spin mode locking π 2 ω = ⋅ N e T R 2 = 3 . 0 T µs

Negative delay FR amplitude model A explanation for no nuclei 0,2 similar FR amplitudes 0,0 A neg before and after A pos Faraday rotation amplitude -0,2 pump pulse arrival model 0,4 B π with nuclei 2 N 0,2 ω = = μ + h ( ) / g B B 0,0 e e B N T -0,2 R -0,4 C nuclei create magnetic field experiment (arb. units) such that all electron spins in the ensemble contribute to mode-locking -1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 Time (ns) A. Greilich et al., Science 317, 1896 (2007)

Electron-nuclei spin flip-flop how do electrons and nuclei communicate? electron spin hyperfine interaction ( ) ( ) r r r 2 α = ⋅ φ R V v A I S α α α 0 nuclear spins ~ 100.000 nuclei per QD change CB CB HF HF of nuclear N N VB VB field π Random walk 2 N ω = = μ + h ( ) / g B B e e B N T until mode-locking is fulfilled! R

Ultralong memory Do the long-living nuclear spins show up in the FR studies? T pump 1 T R -T Faraday rotation amplitude 1 2 1 2 pum p D D pulses pum p 1 only T R = 13.2 ns pump 2 burst 1 pum p 1 + 2 burst 2 pum p 1 (after two-pulse exposition) 12.3 m in 16 m in burst 0 B = 6 T T = 6 K 7.2 m in 2.6 m in -1 0 1 2 3 4 5 Time (ns) A. Greilich et al., Science 317, 1896 (2007)