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Protection of center-spin coherence by a dynamically polarized nuclear spin core in a quantum dot Wenxian Zhang ( 张文献 ) 复旦大学 光科学与工程系 J.-L. Hu, J. Zhuang, J. Q. You, R.-B. Liu Aug. 3rd, 2010 @ 大连理工大学 第四届全国冷原子物理和量子信息青年学者学术讨论会 PRB 82, 045314 (2010).

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Outline Introduction and experimental background A two-region model DNP process: formation of a polarized core Protection effect on the center-spin coherence Numerical simulations and discussions of experimental results Conclusions

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Solid-state architecture of QIP Atomic/Optical Cavity QED Long coherence time Not easily interacted Not easily scaled Solid-state Quantum dots Easily scalable Easily interacted Not so great coherence Marcus@ Harvard

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Quantum dots A.C. Johnson’s Thesis, Harvard Univ.. Experimental conditions: QD size ~ 100 100 10 nm 3 Low temperature ~ 100 mK Low magnetic field 100 mT Coherence time ~ 10 ns Spatial degree of freedom frozen 500 nm

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Qubit decoherence Qubit decoherence: Interacting with environment → qubit “forgets” its phase No decoherence:Complete decoherence: Classical bitQuantum bit (Qubit) 0 1 0 1 0 2 states only Arbitrary superposition of 2 basis states

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Free induction decay 10 ns Petta et al., Science 309, 2180 (2005)

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Spin decoherence in a QD Decoherence source – hyperfine interaction: S – electron spin-1/2 I k – k-th nuclear spin located at r k (also assume 1/2) Merkulov et al., Phys. Rev. B 65, 205309 (2002). Erlingsson et al., Phys. Rev. B 70, 205327 (2004). Deng & Hu, Phys. Rev. B 73, 241303(R) (2006). Zhang et al., Phys. Rev. B 74, 205313 (2006). Taylor et al., Phys. Rev. B 76, 035315 (2007).

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Preserve coherence via spin echo Petta et al., Science 309, 2180 (2005) Dephasing only

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Dynamical decoupling Zhang et al., Phys. Rev. B 75, 201302(R) (2007); 77, 125336 (2008). FID NRD PDD RPD SDD SRPD PCDD2 τ = 0.1 10 ns

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Preserve coherence via polarization I. Uniform nuclear polarization (> 90% ) G. Burkard, D. Loss, and D. P. DiVincenzo, Phys. Rev. B 59, 2070 (1999). W. A. Coish and D. Loss, Phys. Rev. B 70, 195340 (2004). C. Deng and X. Hu, Phys. Rev. B 73, 241303(R) (2006). 1. Thermal polarizaiton in strong magnetic field – 10% 2. Spin dependent optical pumping – 60% II. Non-uniform nuclear polarization – DNP via electron Experiments (~1%): D. J. Reilly et al., Science 321, 817 (2008); Phys. Rev. Lett. 104, 236802 (2010). Theories (~1%): G. Ramon and X. Hu, Phys. Rev. B 75, 161301(R) (2007). M. Gullans et al., Phys. Rev. Lett. 104, 226807 (2010). W. Zhang et al., Phys. Rev. B 82, 045314 (2010).

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Uniform polarization effect (I) Deng and Hu, Phys. Rev. B 73, 241303(R) (2006); Phys. Rev. B 78, 245301 (2008). N = 10 5, envelope of correlation function G ⊥ Polarization is uniform. 10 times extension of dephasing time if P>90%

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Uniform polarization effect (II) QSA Gaussian Random Gaussian Random p = 0.46p = 0.76 Zhang et al., Phys. Rev. B 74, 205313 (2006).

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DNP process 1 2 3 123 Electron spin:0+2* Nuclear spin:0-2

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Double quantum dots Unpolarized Maximally polarized A k = A, uniform Scaled with N=10 5 Zamboni Effect 50 times longer Ramon and Hu, Phys. Rev. B 75, 161301(R) (2007).

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Non-uniform polarization

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Polarization transfer – a two-region model H 0 = 0 H 0 = 6 Saturation at long time in large magnetic fields, I k z ~ (A k / H 0 ) 2. A 1 = 10 A 2 I1I1 I2I2

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Polarization ratio (single DNP cycle) r ≡ P 1 / P 2 = (A 2 / A 1 ) 2 in medium-to-large magnetic fields. Strongly coupled spins have higher polarization. A 2 / A 1 = 0.1 I 1 / I 2 r

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Multiple DNP cycles

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Polarized core protection effect Polarization 0 2 4

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Two-region model Two effects are separable: 1.T 1/2 is determined by b 2 = (N 2 ) 1/2 A 2 instead of b = (N 1 A 1 2 +N 2 A 2 2 ) 1/2 ; 2.Protection effect of the polarized core: What skirt spins decoheres is not a single electron spins but a compound of an electron spin and a polarized nuclear spin core, which further makes the coherence time longer and make T 1/2 increase linearly with N 1.

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Experimental results

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Numerical methods Small N: Chebyshev expansion Dobrovitski et al., PRE 67, 056702 (2003). Large N: P-representation Al-Hassanieh et al., PRL 97, 037204 (2006).

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Protect effect in a QD N=20, Chebshev method

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Large bath with P-representation N=20N=256

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40 times extension of DNP with P = 0.7 (N=20), 0.25 (N=256) and P k ~ A k 2 ; Linear decay at large polarizations; Small oscillations at short times; Abrupt increase of T 1/2 if P is larger than a critical value P C but much smaller than 1; P C decreases with N increasing; Polarized nuclear spin core is formed if P > P C ; Protection effect of the polarized core. Protection effect: Summary

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Thank You!

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Polarized core protection effect Gaussian model Two region model

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Exponential increase of T 1/2 Perturbation results (Fermi golden rule): Gaussian Ak

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DNP effect I SxSz N=20 Gaussian Ak P = 0.68

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Double quantum dot Gaussian Ak, N = 21 DNP, Pk ~ Ak 2 P = 0.7 Not related?

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Experimental results

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