Presentation on theme: "第四届全国冷原子物理和量子信息青年学者学术讨论会"— Presentation transcript:
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 dotWenxian 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. LiuI 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
2Introduction and experimental background A two-region model OutlineIntroduction and experimental backgroundA two-region modelDNP process: formation of a polarized coreProtection effect on the center-spin coherenceNumerical simulations and discussions of experimental resultsConclusions
3Solid-state architecture of QIP Atomic/OpticalCavity QEDLong coherence timeNot easily interactedNot easily scaledSolid-stateQuantum dotsEasily scalableEasily interactedNot so great coherenceCoherence is important for QIP, especially for solid state architecture.
4Quantum dots 500 nm Experimental conditions: A.C. Johnson’s Thesis, Harvard Univ..Experimental conditions:QD size ~ 100 100 10 nm3Low temperature ~ 100 mKLow magnetic field 100 mTCoherence time ~ 10 nsSpatial degree of freedom frozen
5Qubit decoherence Classical bit Quantum bit (Qubit) Arbitrary superposition of 2 basis states2 states onlyQubit decoherence:Interacting with environment → qubit “forgets” its phaseNo 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
6Free induction decayPetta et al., Science 309, 2180 (2005)10 ns
7Spin decoherence in a QD Decoherence source – hyperfine interaction:S – electron spin-1/2Ik – 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).
8Preserve coherence via spin echo Petta et al., Science 309, 2180 (2005)Dephasing only
9Dynamical decoupling 10 ns τ = 0.1 FIDNRDPDDRPDSDDSRPDPCDD2τ = 0.110 nsRequires 2-axis short pulses (<1 ns).Zhang et al., Phys. Rev. B 75, (R) (2007); 77, (2008).
10Preserve 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 electronExperiments (~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).
11Uniform 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).
12Uniform polarization effect (II) QSAGaussianRandomp = 0.46p = 0.76Numerical cases: different QD shapes (a) random and (b) box (uniform).Lines: analytical results.Zhang et al., Phys. Rev. B 74, (2006).
20Two-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.
22Numerical methods Small N: Chebyshev expansion Dobrovitski et al., PRE 67, (2003).Large N: P-representationAl-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))
25Protection 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.