1. Preserving quantum coherence of spins in the presence of noises Ren-Bao Liu Department of Physics, The Chinese University of Hong Kong http://www.phy.cuhk.edu.hk/rbliu PRACQSYS 7/8/14 Cambridge1 www.phy.cuhk.edu.hk/rbliu Funded by Hong Kong RGC, CUHK-FIS, NSFC

2. Ultrasensitive magnetometry Theory: Nan Zhao, Jian-Liang Hu, S.W. Roy Ho, Jones T. K. Wan Experiments: Joerg Wrachtrup group (Stuttgart); Jiangfeng Du group (USTC) Probe to many-body physcs Theory: Shao-Wen Chen, Zhan-Feng Jiang, Wenlong Ma (IoS, CAS), Shushen Li (IoS, CAS), Nan Zhao (CSRC) Experiments: Gary Wolfowicz, John J. L. Morton (UCL) Collaborators PRACQSYS 7/8/14 Cambridge2 www.phy.cuhk.edu.hk/rbliu

3. Outline PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 3 I.Introduction – understanding and withstanding qubit decoherence II.Spin decoherence controlled for ultrasensitive magnetometry – few-body physics in environments III.Qubit decoherence controlled to detecting many-body physics – quantum criticality at high temperature IV.Nuclear spin correlations detected by central spin decoherence – first step toward detecting many-body physics in baths

4. PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 4 Spin qubits in solid-state environments self-assembled dotfluctuation islands NV center in diamond gate-defined dotdonor impurity P:Si

5. A model system: 1 electron spin + N nuclear spins Interaction within bath causing fluctuations and hence qubit decoherence PRACQSYS 7/8/14 Cambridge5 www.phy.cuhk.edu.hk/rbliu

6. Spin decoherence PRACQSYS 7/8/14 Cambridge6 www.phy.cuhk.edu.hk/rbliu

7. Dynamical decoupling control of qubit decoherence PRACQSYS 7/8/14 Cambridge7 www.phy.cuhk.edu.hk/rbliu R. Kubo, J. Phys. Soc. Jpn. 9, 935 (1954); P. W. Anderson, ibid. 9, 316 (1954).

8. Quantum fluctuation vs thermal noise PRACQSYS 7/8/14 Cambridge8 www.phy.cuhk.edu.hk/rbliu static inhomogeneous broadening  B 0

9. Characteristic noise spectrum of a molecule e.g., transitions in a water molecule under zero field O H H PRACQSYS 7/8/14 Cambridge9 www.phy.cuhk.edu.hk/rbliu

10. Dynamical decoupling control of qubit decoherence PRACQSYS 7/8/14 Cambridge10 www.phy.cuhk.edu.hk/rbliu

11. spin decoherence & beyond PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 11  Understanding central spin decoherence (nuclear spin baths) Microscopic quantum theories: Das Sarma, Sham, Liu, Loss, etc )  Protecting spin coherence (by dynamical decoupling) Viola, Lidar, Uhrig, Biercuk, Du, and many other groups The new stage: Using spin decoherence as a resource of detection S(  ) related to thermodynamics & excitations in environment.

12. Outline PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 12 I.Introduction – understanding and withstanding qubit decoherence II.Spin decoherence controlled for ultrasensitive magnetometry – few-body physics in environments III.Qubit decoherence controlled to detecting many-body physics – quantum criticality at high temperature IV.Nuclear spin correlations detected by central spin decoherence – first step toward detecting many-body physics in baths

13. PRACQSYS 7/8/14 Cambridge13 www.phy.cuhk.edu.hk/rbliu NV 13 C Atomic-scale magnetometry & single-molecule NMR N. Zhao et al, Nat. Nanotech. 6, 242 (2011).

14. Central spin decoherence for ultrasensitive sensing PRACQSYS 7/8/14 Cambridge14 www.phy.cuhk.edu.hk/rbliu NV 10 nm below 5 1 H 2 16 O, 100-pulse DD O H H

15. PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 15 A single 13C nuclear spin 3 nm away, Nature Nano 7, 657 (2012) Similar experiments done in Harvard & TU Delft

16. CSRC-QOQI 2014/7/4 www.phy.cuhk.edu.hk/rbliu 16 Nature Physics 10, 21 (2014)

17.  Central spin decoherence for single- molecule NMR  How about detection of transitions (fluctuations) in many-body systems? PRACQSYS 7/8/14 Cambridge17 www.phy.cuhk.edu.hk/rbliu Summary of Part II Schneide, Porras & Schaetz, Rep Prog. Phys (2011)

18. Outline PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 18 I.Introduction – understanding and withstanding qubit decoherence II.Spin decoherence controlled for ultrasensitive magnetometry – few-body physics in environments III.Qubit decoherence controlled to detecting many-body physics – quantum criticality at high temperature IV.Nuclear spin correlations detected by central spin decoherence – first step toward detecting many-body physics in baths

19. 1D transverse field Ising model PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 19 FM PM gap No finite-temperature phase transition QC at zero temperature Excitation is gapless @ QC

20. Detection of quantum criticality by a probe spin PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 20 H.T. Quan, Z. Song, X. F. Liu, P. Zarnardi & C. P. Sun, PRL 96, 140604 (06) QC at zero temperature Diverging fluctuation at critical point  rapid probe spin decoherence

21. At high temperature, feature at QC vanishes PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 21 S. W. Chen, Z. F. Jiang & RBL, New J Phys (2013) high T (small  ), thermal fluctuation conceals quantum criticality To observe quantum criticality: temperature << interaction nano-Kelvin or pico-Kelvin needed for nuclear spins or cold atoms!

22. Quantum fluctuation vs thermal noise PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 22 static inhomogeneous broadening  B 0 At high temperature, thermal noise >> quantum fluctuation Spin echo can remove the static thermal noise effect

23. What if thermal fluctuation removed? PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 23 Quantum criticality can be seen even @ infinite temperature Hahn echo at infinite temperature At time >> inverse interaction energy, critical feature is seen S. W. Chen, Z. F. Jiang & RBL, New J Phys (2013)

24. t ~ 1/T PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 24 Susceptibility at different 1/T and spin echo signal at different t S. W. Chen, Z. F. Jiang & RBL, New J Phys (2013)

25. Decoherence function & susceptibility PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 25 Probe spin coherence (time) ~ susceptibility (inverse temperature) Spin echo removes static thermal fluctuation and reveals quantum fluctuation.

26. Summary of Part III PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 26 quantum face transition  nanokelvin  millisecond  picokelvin  second Suppress thermal noise to single out quantum noise by spin echo

27. Outline PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 27 I.Introduction – understanding and withstanding qubit decoherence II.Qubit decoherence for ultrasensitive magnetometry – few-body physics in environments III.Qubit decoherence controlled to detect many-body physics: – quantum criticality at high temperature IV.Nuclear spin correlations detected by central spin decoherence – first steps toward detecting many-body physics in noises

28. Many-body correlations in a nuclear spin bath (Si:P) PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 28 P donor electron spin coupled to 29 Si nuclear spins  decoherence V – intra-bath interaction b z – local field by hf coupling

29. Qubit-bath model for pure dephasing Overhauser field operator Bath spin interaction (dipole- dipole, Zeeman energy, etc.) New view: Center spin imposes interaction on bath PRACQSYS 7/8/14 Cambridge29 www.phy.cuhk.edu.hk/rbliu Old View: Bath imposes (quantum) noise on center spin

30. Decoherence by quantum entanglement Bifurcated bath evolution  which-way info known  decoherence PRACQSYS 7/8/14 Cambridge30 www.phy.cuhk.edu.hk/rbliu Many-body correlations in baths built up during decoherence.

31. Recoherence by disentanglement (quantum erasure) Bifurcated bath evolution  which-way info known  less coherence left qubit flip  bath pathways exchange directions  pathway intercross  which-way info erased  recoherence PRACQSYS 7/8/14 Cambridge31 www.phy.cuhk.edu.hk/rbliu Many-body correlations manipulated.

32. Decoherence under DD: Formalism PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 32

33. Linked-cluster expansion (LCE) Interaction picture (focus on the bath correlations): Saikin et al, Phys. Rev B 75.125314 (2007) PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 33

34. Linked Feynman diagrams up to fourth order: PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 34 Leading 3- & 4-spin correlations Leading pair-correlation

35. Pulse number-parity effect Theorectical results (CCE): B//[110] Bath: 5000 nuclear spins within 8 nm from the P donor. Odd pulse number: Even pulse number: PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 35

36. DD to suppress quantum fluctuation CPMG eliminates quantum fluctuations (in the leading order) at echo time RBL, W. Yao & L. J. Sham, Intl. J. Mod. Phys. B 22, 27 (2008) PRACQSYS 7/8/14 Cambridge36 www.phy.cuhk.edu.hk/rbliu 4 th -order pair correlation: 4 th -order 3- or 4-spin correlations:

37. Underlining many-body processes: Odd pulse number Even pulse number PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 37

38. LCE-V 4z contains 3- & 4-spin correlations 4-body correlations dominate PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 38

39. W. L. Ma et al.arXiv:1404.2717 Experiments vs theory [P] = 3x10 14 /cm 3 Temperature: 6K PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 39

40. Summary of Part IV PRACQSYS 7/8/14 Cambridge www.phy.cuhk.edu.hk/rbliu 40  Many-body correlations built up and manipulated during central spin decoherence (at “high” temperature).  Dynamical decoupling to separate second-order (two-body) and fourth-order (three-body and four-body) correlations in the nanoscale nuclear spin bath.  Precursor of sensing long-range correlations?