Nuclear spins in semiconductor quantum dots. Alexander Tartakovskii University of Sheffield, UK

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1 Nuclear spins in semiconductor quantum dots Alexander Tartakovskii University of Sheffield, UK

2 Electron and nuclear spin systems in a quantum dot Confined electron and hole in a dot 5 nm Electron/hole spin can be addressed optically 20 nm QD consists of 10 4 atoms: ensemble of nuclear spins

Spin control in quantum dots Talk by Atac Imamoglu Atatüre

Nature (2008) optical initialisation of hole spin Talk by Guido

electron spin dephasing by nuclear spin preparation Latta arxiv

3 Spin control in quantum dots Talk by Atac Imamoglu Atatüre Science (2006) optical initialisation of electron spin Gerardot Nature (2008) optical initialisation of hole spin Talk by Guido Burkard Talk by Atac Imamoglu Reilly Science (2008) suppressed electron spin dephasing by nuclear spin preparation Latta arxiv (2009) Suppression of fluctuations in the nuclear Overhauser field

4 Talk outline Dynamic nuclear polarisation by resonant optical pumping -optical solid effect Resonant techniques for manipulation of nuclear spins in single QDs σ+ PL line shift (μev) laser Laser shift (μev) X 0 Zeeman splitting (μev) 250 Rabi T 2 ~ 360 μs 240 π/2 11π 17π 5π 3π π τ pulse (μs) Optically detected NMR in a dot -light-induced Knight field -spin-echo in an ensemble of 1000 nuclei

5 Dynamic nuclear polarisation in a quantum dot

6 Dynamic nuclear polarisation each nucleus B tot =B ext ±B e Knight field B e Overhauser DNP via electron-nuclear spin flip-flop nuclear depolarisation field B N electron B tot =B ext ±B N B e,max ~mt, B N,max ~T DNP: electron Zeeman splitting major energy cost of a spin flip-flop E ez = g e μ B B tot

7 Nuclear spin bi-stability (non-resonant pumping) Exciton Zeeman splitting (μev) B ext =2T B tot =B ext -B N Incident power (arb. units) Nuclear spin B N ~2T is switched on/off at the thresholds Energy (ev) bistability Incident power E xz (σ-) Braun PRB (2006) Maletinsky PRB (2006) Tartakovskii PRL (2007) Urbaszek PRB (2007) Skiba-Szymanska PRB (2008) Maximum nuclear polarisation ~40% B ext =2.5T PL

8 Nuclear spin dynamics (non-resonant pumping) Overhauser shift (μev) 20 0 σ+ excitation InP/GaInP dot B=0 1E-4 1E Time (s) Depolarisation time: electron-charged >4000s hole-charged ~100s neutral ~200s Fast rise times from 5 ms at B=0 to ~1 s in high B-fields B N /B N,pump 1.0 X X + B z =4.1T Pump pulse σ +/ t delay Probe pulse Delay time t delay (s) X - Nuclear spin decay time (s) diffusion Pumping time, t pump (s) Nuclear spin diffusion Makhonin PRB (2008) Nikolaenko PRB Rapid (2009) Makhonin PRB (2009) Chekhovich arxiv (2008)

9 Resonant optical pumping of a positively charged dot σ+ pump σ+ pump σ + flip-flop + recombination absorption + flip-flop σ - Electron spin flip due to hyperfine interaction Levels shift due to both B ext and B N

10 Optical solid effect (theory) σ + (1) σ+ PL line shift (μev) laser (1) (2) (2) σ + σ - Resonances with asymmetric shapes Laser shift (μev) Process (2) analogous to the solid effect in ESR: off-centre microwave pumping at ω e ±ω N Collaboration with K. Kavokin (Ioffe, Russia)

11 Optical solid effect vs pumping via allowed transition σ+ PL line shift (μev) laser (1) (2) Nuclear spin pumping rate (2) More efficient spin pumping through forbidden transition Laser shift (μev) (1) x5 Saturation of the allowed transition σ+ PL line shift (μev) σ+ PL line (2) 100% polarisation possible in theory Laser shift (μev)

12 Experimental observations High B ext B N (T) E PL -E 0 (μev) 0.0 B ext =4.1T (1) σ+ PL transition σ- PL transition σ+ Laser laser (2) B ext =0 laser Spin pumping via forbidden transition prevails at B ext =0 hole-charged InP/GaInP dots -420 E 0 = ev E l -E 0 (μev) E 0 = ev E l - E 0 (μev) 10 Chekhovich submitted to PRL (2009)

13 Optically detected NMR in a quantum dot Part 1: Light-induced Knight shift

Experimental method for ODNMR in a dot laser PL GaAs/AlGaAs strain-free dots 69 Ga, 71 Ga, 75 As nuclei with spin 3/2, ~10 4 in total B ext B N excited by the

14 Experimental method for ODNMR in a dot laser PL GaAs/AlGaAs strain-free dots 69 Ga, 71 Ga, 75 As nuclei with spin 3/2, ~10 4 in total B ext B N excited by the laser and detected in micro-photoluminescence (PL) B RF Energy (ev) PL intensity RF off RF on RF excitation leads to change in Overhauser field B N

Light-induced Knight field in a dot 215 75 As 69 Ga 71 Ga X 0 Zeeman splitting (μev) 210 135 σ+ σ- 2B e B e ~ 12G B e ~ 5.

15 Light-induced Knight field in a dot As 69 Ga 71 Ga X 0 Zeeman splitting (μev) σ+ σ- 2B e B e ~ 12G B e ~ 5.7G B e ~ 6.2G Radio frequency (MHz) X 0 Knight field experienced by a nuclear spin at r n e or h σ - σ +

16 Intrinsic resonance width vs Light-induced broadening cw experiment, laser + RF: Normalised ODNMR signal dark low P high P Laser+RF NMR in the dark : RF Laser read read Laser time Radio frequency (MHz) time Knight shift: increase of timeaveraged B e (filling factor F ) Resonance broadening: B e fluctuations

17 Inhomogeneous broadening induced by the laser σ Ga dark Very high optical power: filling factor F 1 ODNMR signal σ+ Number of nuclei Electron Ψ 2 (r) Radio frequency (MHz) Mapping of the electron wavefunction Addressing nuclei in different part of the dot is possible

18 Optically detected NMR in a quantum dot Part 2: Nuclear spin coherence

19 Rabi oscillations in an ensemble of ~1000 nuclear spins X 0 Zeeman splitting (μev) π/2 11π 17π 5π 3π π τ pulse (μs) T 2 Rabi ~ 360 μs S N π/2 Laser RF read Laser Fast and slow decay components in the driven oscillations time π 3/2π

20 Nuclear spin-echo in a single dot ODNMR spin echo signal τ 0 =100 μs laser RF laser time π/2 τ0 π τ π/ Delay time τ (μs) Spin-echo method to measure coherence time T 2 S N π/2 wait τ 0 wait τ measure refocus by π pulse π/2

21 Intrinsic nuclear spin coherence in a single dot ODNMR signal T 2 ~185 μs T* 2 ~30 μs τ (μs) Spin-echo: intrinsic coherence, T 2 π/2 τ π τ π/2 No refocusing π-pulse: effective coherence, T 2 * π/2 2τ π/2

22 Conclusions Resonant optical excitation leads to dynamic nuclear polarisation -Pumping via spin-forbidden transition may result in 100% nuclear spin polarisation σ+ PL line shift (μev) laser Laser shift (μev) Combination of optical and RF pumping allows flexible control of nuclear spins in a dot -Ensembles of ~1000 nuclear spins are addressed by optical detection of NMR - Resonant RF frequency is manipulated by light-induced Knight fields - Coherent control of 1000 nuclear spins X 0 Zeeman splitting (μev) π/2 5π 3π π 11π 17π τ pulse (μs) T 2 Rabi ~ 360 μs

23 People Maxim Makhonin Evgeny Chekhovich Maurice Skolnick University of Sheffield, UK Theory: Kirill Kavokin Ioffe Institute St Petersburg, Russia InP samples: Andrey Krysa University of Sheffield, UK GaAs samples: Pascale Senellart, Aristide Lemaître LPN-CNRS, Marcoussis, France

arxiv: v1 [cond-mat.mes-hall] 26 Aug 2010

arxiv: v1 [cond-mat.mes-hall] 26 Aug 2010 Direct measurement of the hole-nuclear spin interaction in single quantum dots E. A. Chekhovich 1, A. B. Krysa 2, M. S. Skolnick 1, A. I. Tartakovskii 1 1 Department of Physics and Astronomy, University