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Preserving quantum coherence of spins in the presence of noises

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. Funded by Hong Kong RGC, CUHK-FIS, NSFC. Collaborators. Ultrasensitive magnetometry

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Preserving quantum coherence of spins in the presence of noises

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

  2. Collaborators Ultrasensitive magnetometry Theory: Nan Zhao, Jian-Liang Hu, S.W. Roy Ho, Jones T. K. Wan Experiments: JoergWrachtrup 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) www.phy.cuhk.edu.hk/rbliu

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

  4. Spin qubits in solid-state environments self-assembled dot fluctuation islands NV center in diamond gate-defined dot donor impurity P:Si www.phy.cuhk.edu.hk/rbliu

  5. A model system: 1 electron spin + N nuclear spins Interaction within bath causing fluctuations and hence qubitdecoherence www.phy.cuhk.edu.hk/rbliu

  6. Spin decoherence www.phy.cuhk.edu.hk/rbliu

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

  8. Quantum fluctuation vs thermal noise static inhomogeneous broadening DB0 www.phy.cuhk.edu.hk/rbliu

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

  10. Dynamical decoupling control of qubit decoherence www.phy.cuhk.edu.hk/rbliu

  11. spin decoherence & beyond • 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(w) related to thermodynamics & excitations in environment. www.phy.cuhk.edu.hk/rbliu

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

  13. Atomic-scale magnetometry & single-molecule NMR N. Zhao et al, Nat. Nanotech. 6, 242 (2011). NV 13C Laser B MW www.phy.cuhk.edu.hk/rbliu

  14. Central spin decoherence for ultrasensitive sensing H H NV 10 nm below 51H216O, 100-pulse DD O 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 www.phy.cuhk.edu.hk/rbliu

  16. Nature Physics 10, 21 (2014) www.phy.cuhk.edu.hk/rbliu

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

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

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

  20. Detection of quantum criticality by a probe spin 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 www.phy.cuhk.edu.hk/rbliu

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

  22. Quantum fluctuation vs thermal noise static inhomogeneous broadening DB0 At high temperature, thermal noise >> quantum fluctuation Spin echo can remove the static thermal noise effect www.phy.cuhk.edu.hk/rbliu

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

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

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

  26. Summary of Part III Suppress thermal noise to single out quantum noise by spin echo quantum face transition www.phy.cuhk.edu.hk/rbliu

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

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

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

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

  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 Many-body correlations manipulated. www.phy.cuhk.edu.hk/rbliu

  32. Decoherence under DD: Formalism www.phy.cuhk.edu.hk/rbliu

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

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

  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: www.phy.cuhk.edu.hk/rbliu

  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) 4th-order pair correlation: 4th-order 3- or 4-spin correlations: www.phy.cuhk.edu.hk/rbliu

  37. Underlining many-body processes: Odd pulse number Even pulse number www.phy.cuhk.edu.hk/rbliu

  38. LCE-V4z contains 3- & 4-spin correlations 4-body correlations dominate www.phy.cuhk.edu.hk/rbliu

  39. Experiments vs theory [P] = 3x1014/cm3 Temperature: 6K W. L. Ma et al.arXiv:1404.2717 www.phy.cuhk.edu.hk/rbliu

  40. Summary of Part IV • 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? www.phy.cuhk.edu.hk/rbliu

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