第四届全国冷原子物理和量子信息青年学者学术讨论会 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 I will be pushed down, even by a weakest lady. I will be standing firmly once I am against a wall, even pushed by a strongest man. Protection provided by the wall. PRB 82, 045314 (2010). Aug. 3rd, 2010 @ 大连理工大学

Introduction and experimental background A two-region model 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

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 Coherence is important for QIP, especially for solid state architecture.

Quantum dots 500 nm Experimental conditions: A.C. Johnson’s Thesis, Harvard Univ.. Experimental conditions: QD size ~ 100  100  10 nm3 Low temperature ~ 100 mK Low magnetic field  100 mT Coherence time ~ 10 ns Spatial degree of freedom frozen

Qubit decoherence Classical bit Quantum bit (Qubit) 0 1 0 1 0 Arbitrary superposition of 2 basis states 2 states only Qubit decoherence: Interacting with environment → qubit “forgets” its phase No decoherence: Complete decoherence: 量子计算 和 并行计算 （DNA计算机）的差别 Dwave – 16 个量子比特

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

Spin decoherence in a QD Decoherence source – hyperfine interaction: S – electron spin-1/2 Ik – k-th nuclear spin located at rk (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).

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

Dynamical decoupling 10 ns τ = 0.1 FID NRD PDD RPD SDD SRPD PCDD2 τ = 0.1 10 ns Requires 2-axis short pulses (<1 ns). Zhang et al., Phys. Rev. B 75, 201302(R) (2007); 77, 125336 (2008).

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).

Uniform polarization effect (I) N = 105, envelope of correlation function G⊥ Polarization is uniform. 10 times extension of dephasing time if P>90% Deng and Hu, Phys. Rev. B 73, 241303(R) (2006); Phys. Rev. B 78, 245301 (2008).

Uniform polarization effect (II) QSA Gaussian Random p = 0.46 p = 0.76 Numerical cases: different QD shapes (a) random and (b) box (uniform). Lines: analytical results. Zhang et al., Phys. Rev. B 74, 205313 (2006).

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

Double quantum dots Unpolarized Maximally polarized Ak = A, uniform Scaled with N=105 Zamboni Effect 50 times longer Ramon and Hu, Phys. Rev. B 75, 161301(R) (2007).

Non-uniform polarization

Polarization transfer – a two-region model H0 = 0 H0 = 6 I1 A1 = 10 A2 I2 Saturation at long time in large magnetic fields, Ikz ~ (Ak / H0)2.

Polarization ratio (single DNP cycle) I1 / I2 r A2 / A1 = 0.1 r ≡ P1 / P2 = (A2 / A1)2 in medium-to-large magnetic fields. Strongly coupled spins have higher polarization.

Multiple DNP cycles

Polarized core protection effect Polarization 4 2

Two-region model Two effects are separable: T1/2 is determined by b2 = (N2)1/2 A2 instead of b = (N1 A12+N2 A22)1/2 ; 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 T1/2 increase linearly with N1.

Experimental results

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). 态密度矩阵方程 – 10-12 核自旋 薛定谔方程 – 20-30 初始态-单位密度矩阵-的近似， 1/sqrt(dim(Hilbert space))

Protect effect in a QD N=20, Chebshev method

Large bath with P-representation

Protection effect: Summary 40 times extension of DNP with P = 0.7 (N=20), 0.25 (N=256) and Pk ~ Ak2; Linear decay at large polarizations; Small oscillations at short times; Abrupt increase of T1/2 if P is larger than a critical value PC but much smaller than 1; PC decreases with N increasing; Polarized nuclear spin core is formed if P > PC; Protection effect of the polarized core.

Thank You!

Polarized core protection effect Gaussian model Two region model

Exponential increase of T1/2 Perturbation results (Fermi golden rule): Gaussian Ak

DNP effect I Sx Sz N=20 Gaussian Ak P = 0.68

Double quantum dot Gaussian Ak, N = 21 DNP, Pk ~ Ak2 P = 0.7 Not related?

Experimental results