Ren-Bao Liu rbliu@phy.cuhk.hk Department of Physics, The Chinese University of Hong Kong

1. Electron spin decoherence in solid-state nuclear spin baths: Understanding, control, and applications Ren-Bao Liu rbliu@phy.cuhk.edu.hk Department of Physics, The Chinese University of Hong Kong http://www.phy.cuhk.edu.hk/rbliu Funded by Hong Kong RGC, NSFC, CUHK Focused Investments Scheme www.phy.cuhk.edu.hk/rbliu

2. Thanks to Wen Yang (postdoc, now @UCSD) Nan Zhao (Postdoc) Jian-Liang Hu (PhD student) Zhen-Yu Wang (PhD student) Sai-Wah Ho (MPhil student) Jones Z. K. Wan (Postdoc) Jiangfeng Du, Xing Rong, Ya Wang, Jiahui Yang, Pu Huang, Xi Kong, Pengfei Wang, Fazhan Shi (experimentalists @ USTC) Lu J. Sham (UCSD) Wang Yao (UCSD, now @ HKU) Wen Yang Nan Zhao Z. Y. Wang www.phy.cuhk.edu.hk/rbliu

3. Outline • Introduction - Semiclassical theory: Gone can be back • Introduction - Quantum theory: Passive can be active • A difference between the two: Strong can be weak • An application of decoherence: Bad can be good www.phy.cuhk.edu.hk/rbliu

4. I. Spin decoherence & control:Semiclassical theory R. Kubo, J. Phys. Soc. Jpn. 9, 935 (1954). P. W. Anderson, J. Phys. Soc. Jpn. 9, 316 (1954). www.phy.cuhk.edu.hk/rbliu

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

6. Coherence of the slow and the swift It works when the snails’ speeds are kept constant (but random). www.phy.cuhk.edu.hk/rbliu

7. Pictorial Spin Dynamics Schrödinger equation The spin precesses about the magnetic field www.phy.cuhk.edu.hk/rbliu

8. y Hahn echo x rotation 180o about x-axis Works perfectly for static fluctuations. Dynamical Fluctuations www.phy.cuhk.edu.hk/rbliu

9. Decoherence control by spin-flips (rooted in spin echo) Semiclassical picture of decoherence www.phy.cuhk.edu.hk/rbliu

10. II. Quantum theory Local magnetic field is a Q-number (quantum field) Classical noise, static inhomogeneous broadening www.phy.cuhk.edu.hk/rbliu

11. Relevant systems: Electron spin in solids for qubits self-assembled dot interface fluctuation islands gate-defined dot donor impurity P:Si NV center in diamond www.phy.cuhk.edu.hk/rbliu

12. 1 electron spin + N nuclear spins in the bath In GaAs QD, e.g., e-N: MHz >> N-N: kHz In type-IIa diamond, e.g., NV--13C: kHz >> 13C - 13C: 10 Hz The nuclear spins (bath) within a range and the electron spin (qubit) form a relatively close system. www.phy.cuhk.edu.hk/rbliu

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

14. Decoherence by quantum entanglement Bifurcated bath evolution  which-way info known  decoherence www.phy.cuhk.edu.hk/rbliu

15. Quantum many-body theory for spin bath dynamics Step stones: 0. Semiclassical spectral diffusion theory, Anderson, Kubo (1956) 1. Cluster expansion, Witzel & Das Sarma (2005) 2. Pair-correlation: Yao, RBL & Sham (2006). Cluster-correlation expansion (a generalization of textbook cluster expansion to finite systems, good for nano-science): W. Yang & RBL, Phys. Rev. B 78, 085315 (2008). www.phy.cuhk.edu.hk/rbliu

16. Experiments vs. theory WITHOUT fitting parameters Phosphorus donor spins in silicon Nitrogen-vacancy center spin in diamond Black: Experiment [Lukin et al Science (06)] Blue: CCE calculation (Nan Zhao, unpublished) Black: Experiment [Lyon et al, PRB (2003)] Red: CCE calculation (Nan Zhao, unpublished) www.phy.cuhk.edu.hk/rbliu

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

18. Resurrecting from ashes: When disentangled W. Yao, RBL, and L. J. Sham, Phys. Rev. Lett. 98, 077602 (07). Observable if thermal fluctuation suppressed: Duncan Steel, Amir Yacoby, …? www.phy.cuhk.edu.hk/rbliu

19. Dynamical disentanglement and dynamical decoupling Talks in this ASI by Lu Sham, Goetz Uhrig, Jiangfeng Du, Jiangbin Gong, S. Das Sarma, Amir Yacoby, Joerg Wrachtrup Reviews, e.g., W. Yang, Z. Y. Wang and R. B. Liu, Front. Phys.6, 2 (2011). Z. Y. Wang and R. B. Liu, Chapter 15 in Quantum Error Correction, eds. D. Lidar et al (Cambridge U Press, in press) www.phy.cuhk.edu.hk/rbliu

20. NV center spins in diamond: Hot qubit • Chemical stability • Deep level: thermal stability • Weak Spin-orbit interaction (light C atoms, coherence @ RT) • Low 13C abundance • Transparent (optical access) • Non-toxic (medicine) Quantum coherence time is long @ RT in this US$10.8M worth type-IIa diamond, good for for solid-state quantum computing & magnetometry, http://news.yahoo.com www.phy.cuhk.edu.hk/rbliu

21. Pure-dephasing model for NV center spin in nuclear spin bath e- 13C interaction >> 13C - 13C interaction  About 500 13C spins form a “close” bath NV spin splitting hyperfine Bath spin interaction (dipole-dipole + Zeeman energy) Bath Hamiltonian conditioned on center spin state: www.phy.cuhk.edu.hk/rbliu

22. Anomalous decoherence effect in a quantum bath The stronger, the weaker Theory: N. Zhao, Z. Y. Wang & RBL, PRL 106, 217205 (2011). Experiments: P. Huang et al. Nature Comm. 2, 570 (2011) Can quantum bath be approximated by a classical noise? www.phy.cuhk.edu.hk/rbliu

23. Spin decoherence: The oldwife tale double-coherence Single-coherence www.phy.cuhk.edu.hk/rbliu

24. Free-induction decay due to thermal (classical) noises from 13C spins N. Zhao, Z. Y. Wang & RBL, PRL 106, 217205 (2011). www.phy.cuhk.edu.hk/rbliu

25. FID experiment & theory Single coherence Multi-coherence Time (ms) www.phy.cuhk.edu.hk/rbliu

26. Spin decoherence: When the bath is small (therefore quantum) www.phy.cuhk.edu.hk/rbliu

27. Anomalous decoherence in a quantum bath Stronger “noises”  weaker decoherence ! Stronger noises on qubit  Stronger control over environment! N. Zhao, Z. Y. Wang & RBL, PRL 106, 217205 (2011) B=0.3 Tesla www.phy.cuhk.edu.hk/rbliu

28. Conditional bath evolution at high field: Nuclear spin pair-flips NV www.phy.cuhk.edu.hk/rbliu

29. Multi-transition: Pseudo-fields for the two e-spin states are almost anti-parallel  slower decoherence www.phy.cuhk.edu.hk/rbliu

30. Single-transition: Pseudo-fields for the two e-spin states are not (anti-)parallel  faster decoherence www.phy.cuhk.edu.hk/rbliu

31. Experimental verification At this weak field, decoherence due mainly to single nuclear spin precessing. Insensitive to specific interactions. Observable in other systems, e.g., singlet-triplet transitions? B=5 Gauss. Calculation w/o fitting parameters www.phy.cuhk.edu.hk/rbliu

32. Atomic-scale magnetometry using NV spin coherence 2>>1+1 1 nucleus is featureless; 2 (or more) nuclei have characteristic. N. Zhao, J. L. Hu, S. W. Ho, J. T. K. Wan, & RBL, Nature Nanotech. 6, 242(2011). www.phy.cuhk.edu.hk/rbliu

33. Decoherence by pairwise flip-flop Hahn echo, B=0.15 T dimer dimer only NV incl. all 13C spins Previously noted by Maze et al (PRB 2008) Dimer: interaction strength ~ hyperfine energy cost  large-amplitude flip-flop Many incoherent pairs  smooth decoherence Rare coherent pairs  coherent oscillations www.phy.cuhk.edu.hk/rbliu

34. A dancing couple out of random walkers UDD1 UDD2 a dimer @ 1.2nm; B=0.15 T UDD3 UDD4 Uhrig DD: Coherence time prolonged by DD, oscillations due to the dimer are pronounced. UDD5 www.phy.cuhk.edu.hk/rbliu

35. Atomic-scale magnetometry of a dimer A dimer @ ~1.2nm from NV; B=.15 T, tilted from [111] by 10° NV center spin decoherence vs. time & B-field direction Azimuth angle f from [1-10] Contribution by the dimmer only www.phy.cuhk.edu.hk/rbliu

36. Fingerprint screening www.phy.cuhk.edu.hk/rbliu

37. NMR of a 13C2 molecule? 13C NV Even better if NMR of real single molecules outside diamond could be detected. www.phy.cuhk.edu.hk/rbliu

38. Noise spectrum due to weak coupling to a molecule Weak hyperfine coupling Transition between nuclear spin states Noise spectrum e.g., transitions in a water molecule under zero field H H O www.phy.cuhk.edu.hk/rbliu

39. Many-pulse DD: Suppressing noises but one @ a certain frequency background noise Dynamical decoupling suppresses noises Noise @ right frequency is enhanced by a factor of N2 (N: # of pulses) c.f. optical grating effect www.phy.cuhk.edu.hk/rbliu

40. Toward single molecule NMR Spin coherence of an NV center 10 nm below 51H216O or 12C1H4 molecules, under 100-pulse periodic dynamical decoupling, at zero B-field 13C NV H 12C H H H H H O www.phy.cuhk.edu.hk/rbliu

41. Single-molecule NMR: Cascade amplification of weak signals single photon detection single electron spin resonance coupling to single nuclear spin nearby coupling to distant nuclear spins noises @ fingerprint frequencies amplified by many-pulse dynamical decoupling 1015 Hz 1 eV 103 Kelvin GHz MHz kHz fingerprint oscillation of nuclear spin clusters • Features: • Full information about nuclear spin interaction(c..f. liquid-state NMR: dipolar intra-molecule interaction averaged to zero by rapid rotation of molecules under B field) • High-resolution of resonances (c.f., solid-state NMR: inter-molecule interaction causes large broadening) www.phy.cuhk.edu.hk/rbliu

42. Summary • quantum theory and hence control schemes; • Anomalous effect in quantum bath: Stronger “noises” may cause slower decoherence; • Atomic-scale magnetometry of single nuclear spin clusters at distance; • Single-molecule NMR by many-pulse DD Perspective: Single center spins as media for detecting physics and manipulating information in a quantum bath (e.g., nuclear spins) For more, visit http://www.phy.cuhk.edu.hk/rbliu www.phy.cuhk.edu.hk/rbliu