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
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, (2010).
Aug. 3rd, 大连理工大学

2. 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

3. 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
Coherence is important for QIP, especially for solid state architecture.

4. 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

5. Qubit decoherence Classical bit Quantum bit (Qubit)
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

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

7. 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, (2002).
Erlingsson et al., Phys. Rev. B 70, (2004).
Deng & Hu, Phys. Rev. B 73, (R) (2006).
Zhang et al., Phys. Rev. B 74, (2006).
Taylor et al., Phys. Rev. B 76, (2007).

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

9. 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, (R) (2007); 77, (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, (2004).
C. Deng and X. Hu, Phys. Rev. B 73, (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, (2010).
Theories (~1%):
G. Ramon and X. Hu, Phys. Rev. B 75, (R) (2007).
M. Gullans et al., Phys. Rev. Lett. 104, (2010).
W. Zhang et al., Phys. Rev. B 82, (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, (R) (2006); Phys. Rev. B 78, (2008).

12. 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, (2006).

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

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, (R) (2007).

15. Non-uniform polarization

16. Polarization transfer – a two-region model
H0 = 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

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, (2003).
Large N: P-representation
Al-Hassanieh et al., PRL 97, (2006).
态密度矩阵方程 – 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))

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

24. Large bath with P-representation

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