Nuclear spins in semiconductor quantum dots Alexander Tartakovskii University of Sheffield, UK
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 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
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) 50 25 laser 0-100 0 100 200 300 400 Laser shift (μev) X 0 Zeeman splitting (μev) 250 Rabi T 2 ~ 360 μs 240 π/2 11π 17π 5π 3π π 0 100 200 300 400 τ pulse (μs) Optically detected NMR in a dot -light-induced Knight field -spin-echo in an ensemble of 1000 nuclei
Dynamic nuclear polarisation in a quantum dot
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
Nuclear spin bi-stability (non-resonant pumping) Exciton Zeeman splitting (μev) 250 200 150 B ext =2T B tot =B ext -B N 0 50 100 150 200 Incident power (arb. units) Nuclear spin B N ~2T is switched on/off at the thresholds Energy (ev) bistability 1.3180 1.3184 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
Nuclear spin dynamics (non-resonant pumping) Overhauser shift (μev) 20 0 σ+ excitation InP/GaInP dot B=0 1E-4 1E-3 0.01 0.1 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 0 0.5 0.0 X + B z =4.1T Pump pulse σ +/ t delay Probe pulse 0.1 1 10 100 1000 Delay time t delay (s) X - Nuclear spin decay time (s) 6 4 2 0 diffusion 0.1 1 10 100 Pumping time, t pump (s) Nuclear spin diffusion Makhonin PRB (2008) Nikolaenko PRB Rapid (2009) Makhonin PRB (2009) Chekhovich arxiv (2008)
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
Optical solid effect (theory) σ + (1) σ+ PL line shift (μev) 50 25 laser (1) (2) (2) σ + σ - Resonances with asymmetric shapes 0-100 0 100 200 300 400 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)
Optical solid effect vs pumping via allowed transition σ+ PL line shift (μev) 50 25 laser (1) (2) Nuclear spin pumping rate (2) More efficient spin pumping through forbidden transition 0-100 0 100 200 300 400 Laser shift (μev) (1) x5 Saturation of the allowed transition σ+ PL line shift (μev) 150 125 100 75 50 25 σ+ PL line (2) 100% polarisation possible in theory 0 200 300 400 500 Laser shift (μev)
Experimental observations High B ext B N (T) E PL -E 0 (μev) 0.0 B ext =4.1T -0.2-0.4-0.6 0-10 -20-400 (1) σ+ PL transition σ- PL transition σ+ Laser laser (2) B ext =0 laser -0.1-0.2-0.3 40 30 20 Spin pumping via forbidden transition prevails at B ext =0 hole-charged InP/GaInP dots -420 E 0 =1.83893 ev -80-60 -40-20 0 20 E l -E 0 (μev) E 0 =1.8386 ev -40-20 0 20 40 60 E l - E 0 (μev) 10 Chekhovich submitted to PRL (2009)
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 laser and detected in micro-photoluminescence (PL) B RF Energy (ev) 1.7074 1.7076 1.7078 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 ~ 5.7G B e ~ 6.2G 14.4 14.5 14.6 20.3 20.4 25.8 25.9 Radio frequency (MHz) X 0 Knight field experienced by a nuclear spin at r n e or h σ - σ +
Intrinsic resonance width vs Light-induced broadening cw experiment, laser + RF: Normalised ODNMR signal dark low P high P 25.76 25.80 25.84 25.88 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
Inhomogeneous broadening induced by the laser σ- 25.80 25.85 69 Ga dark Very high optical power: filling factor F 1 ODNMR signal σ+ Number of nuclei 0.0 0.5 1.0 Electron Ψ 2 (r) 25.80 25.85 Radio frequency (MHz) Mapping of the electron wavefunction Addressing nuclei in different part of the dot is possible
Optically detected NMR in a quantum dot Part 2: Nuclear spin coherence
Rabi oscillations in an ensemble of ~1000 nuclear spins X 0 Zeeman splitting (μev) 250 240 π/2 11π 17π 5π 3π π 0 100 200 300 400 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
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/2 0 100 200 300 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
Intrinsic nuclear spin coherence in a single dot ODNMR signal T 2 ~185 μs T* 2 ~30 μs 1 10 100 1000 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
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) 50 25 laser 0-100 0 100 200 300 400 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) 250 240 π/2 5π 3π π 11π 17π 0 100 200 300 400 τ pulse (μs) T 2 Rabi ~ 360 μs
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