Protection of center-spin coherence by a dynamically polarized nuclear spin core in a quantum dot

1. 第四届全国冷原子物理和量子信息青年学者学术讨论会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 PRB 82, 045314 (2010). Aug. 3rd, 2010 @ 大连理工大学

2. 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

3. 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 Solid-state architecture of QIP Marcus@Harvard

4. 500 nm • 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 Quantum dots A.C. Johnson’s Thesis, Harvard Univ..

5. 0 1 0 1 0 Qubit decoherence: Interacting with environment → qubit “forgets” its phase No decoherence: Complete decoherence: Qubit decoherence Classical bit Quantum bit (Qubit) Arbitrary superposition of 2 basis states 2 states only

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

7. Decoherence source – hyperfine interaction: Spin decoherence in a QD 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).

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

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

10. 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).

11. 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).

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

13. 1 3 2 DNP process

14. 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).

15. Non-uniform polarization

16. 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.

17. 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.

18. Multiple DNP cycles

19. Polarized core protection effect Polarization 4 2 0

20. 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.

21. Experimental results

22. 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).

23. Protect effect in a QD N=20, Chebshev method

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

25. 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.

26. Thank You!

27. Polarized core protection effect Gaussian model Two region model

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

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

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

31. Experimental results