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Control of individual nuclear spins in diamond

Control of individual nuclear spins in diamond. L. Childress, B. Smeltzer, J. McIntyre Bates College. QNLO 2010. Sensing nuclear spins. Ensemble NMR techniques. NV centers. Measure ensembles of nuclear spins with e.g. pickup coils, micro-atomic magnetometers.

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Control of individual nuclear spins in diamond

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  1. Control of individual nuclear spins in diamond L. Childress, B. Smeltzer, J. McIntyre Bates College QNLO 2010

  2. Sensing nuclear spins Ensemble NMR techniques NV centers Measure ensembles of nuclear spins with e.g. pickup coils, micro-atomic magnetometers Electronic spin as sensitive magnetometer Coupled electron-nuclear spin system Ledbetter et al. 2008 PNAS Sensitivity: ~ 1012 protons Atoms and ions Mixed electron-nuclear hyperfine levels can be precisely controlled and measured MRFM ~103 protons

  3. Nuclear spin environment of the NV Can be viewed as a resource Coherent interactions with proximal nuclear spins in the bath

  4. Outline • Hyperfine structure of the NV center • A check on ab initio theory • Controlling individual nuclear spins in diamond • Polarization, manipulation, and readout of individual nitrogen nuclear spins in diamond • Multifrequency spin resonance • Beyond the RWA: Multiphoton transitions and coherent destruction of tunnelling • Longitudinal excitation: another technique in the toolbox

  5. The spin degree of freedom: Hyperfine structure Excited state ? Ground state ms = ±1 ms = 0 1.1% probability at each lattice site Always Unlike atoms, F is not a good quantum number Weak (few MHz), anisotropic hyperfine interactions

  6. ? ms = ±1 ms = 0 Permanent magnet Experimental techniques: imaging wire ~10 µm 20 m copper wire 532 nm Single photon counting module N.A. 1.3 oil immersion objective fluorescence Dichroic MW Gruber, Science 1997

  7. ? ms = ±1 ms = 0 Experimental techniques: spin resonance wire MW or RF MW or RF excitation Polarization and fluorescence detection of a single NV …and repeat 10,000 times

  8. ? ms = ±1 ms = 0 m = -1 0 1 I Experimental techniques: spin resonance wire Zoom in: hyperfine lines +1/2 -1/2 MW or RF 14N: 2.2 MHz splitting 15N: 3 MHz splitting …and repeat 10,000 times

  9. Hyperfine interactions with proximal 13C spins Measurement of possible hyperfine parameters different proximal 13C lattice sites have different hyperfine splittings % change in fluorescence MW frequency (GHz) Hyperfine interaction depends on 13C lattice site and electronic spin density Gali, PRB 80 241204R 2009

  10. Hyperfine interactions with proximal 13C spins Discrete hyperfine parameters correspond to individual lattice sites observed values agree closely with predictions from ab initio theory allows identification of individual nuclear spin lattice sites +130 MHz 40 G 510 G

  11. NV hyperfine interactions Area of circles ~ hyperfine interaction Nearest-neighbor 13C: 130 MHz 6 NV 14 MHz 14N/15N: 2-3 MHz 4 9 How can we polarize, manipulate, and detect these nuclear spins? …especially the nitrogen nuclear spin?

  12. Polarization, control, and readout of nuclear spins in diamond Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit quantum gate, F. Jelezko et al. 2004 Multipartite Entanglement Among Single Spins in Diamond, P. Neumann et al. 2008 Quantum Register Based on Individual Electronic and Nuclear Spin Qubits in Diamond M. V. Gurudev Dutt, LC,et al 2007 Early techniques work for strongly-coupled 13C spins Our work: Improve signal, extend to nitrogen nuclear spins

  13. Laser excitation Polarization of nuclear spins in diamond Use hyperfine flip-flops in the excited state instead Fuchs 2008, Jacques 2009 The idea: SWAP NV Hard to do precisely with MW pulses Especially for weakly-coupled nitrogen nuclear spins If we can swap the electron and nuclear spin states And repolarize the electron spin We can polarize the electron spin into a well-defined quantum state Then we’ve prepared both spins in a well-defined quantum state Dutt, LC Science 2007

  14. Polarization of nuclear spins in diamond The excited-state level anti-crossing (ESLAC) The nitrogen hyperfine interaction is about 20x larger in the excited state ~ 50 MHz Fuchs et al. 2008 Robust polarization for many nuclear spin species

  15. Nuclear magnetic resonance in diamond B = 510G polarization MW to drive electron spin transitions RF to drive nuclear spin transitions Precise hyperfine parameters Green light off during pulses => working in the electronic ground state Fast NMR control Strong signal Smeltzer 2009 Also Stuttgart

  16. Readout of single nuclear spins in diamond Working at the ESLAC ~ 510 G we can directly distinguish nuclear spin states! Steiner 2010 Simple, robust nuclear spin readout mechanism

  17. Coherence properties of nuclear spins 14N dephasing time can be close to the electron spin lifetime 14N Electron spin decay Dephasing times are widely variable, but can be extended with echo techniques Spin echo 13C lattice sites A Millisecond dephasing times – long-lived quantum memory

  18. Outlook: Scaling up with optical connections • Idea: encode and store qubits in nuclear spins • Entangle electrons (probabilistically) without destroying nuclear qubits • Perform deterministic quantum gates between remote nuclei via electron-nuclear coupling: “teleportation based gates” • Operations between any pairs at random locations can be performed simultaneously:purely optical scaling possible • quantum repeaters for long-distance communication L.C., J.Taylor, A.Sorensen. M.D. Lukin PRL 06 • fault tolerant quantum computation with very high error threshold E.Knill, Naure (2004), L.Jiang, J.Taylor et al, (07) Can we turn on and off hyperfine flip-flops in the excited state? Need nuclear spins to be unaffected by optical transitions!

  19. What happens if you send in MW and RF simultaneously? Weak MW to drive electron spin transitions Strong RF to drive nuclear spin transitions …a pineapple

  20. Multifrequency excitation of the NV center in diamond Low magnetic field data: no nuclear spin polarization ESLAC data: 14N polarization • Low frequency splitting • Multiphoton transitions • Missing resonances

  21. Multifrequency excitation of the NV center in diamond Low magnetic field data: no nuclear spin polarization ESLAC data: 14N polarization (also different, stronger, RF amplifier) The major features have nothing to do with nuclear spins. It’s purely a two-level system effect.

  22. Numerical simulations • Features are characteristic of a two-level system with: • weak MW B field  NV axis • strong RF B field || NV axis

  23. Quasistatic behavior • Observed effects: • Low frequency splitting • Multiphoton transitions • Missing resonances RF MW Quasistatic regime: ω < t Extremal detunings ±2ΩRF most likely

  24. Multiphoton resonances • Observed effects: • Low frequency splitting • Multiphoton transitions • Missing resonances Floquet theory m=-1 2 1 0 -1 -2 RF MW flips the spin; RF doesn’t Intermediate state detuned only by ~ω m=0 Explains dependence on orientation of fields MW 3 2 1 0 -1 RF photons

  25. Analytic approach Effective Rabi frequency for n-RF photon transition Explains observed multiphoton transitions and missing resonances – “coherent destruction of tunneling” Strong-field effects in an easily-accessible regime Applications for longitudinal excitation?

  26. Polarization and readout away from the ESLAC Goal: drive hyperfine flipflops within the excited state when we want them…and not when we don’t! • “normal” MW excitation would just flip the electron spin without affecting the nuclear spin very much • Longitudinal MW excitation has the effect of bringing the states into resonance without flipping the spin Proposed method: Use a microwave magnetic field oriented parallel to the electron & nuclear spin quantization axis

  27. Polarization and readout away from the ESLAC Idea: Apply microwaves || NV axis:they cannot flip the spins directly, but they can bring hyperfine flipflops into resonance Floquet theory calculation incorporated into a 3-level rate equation model to predict equilibrium polarization

  28. Polarization and readout away from the ESLAC: Initial tests Geometry: Microwave field 45 degrees from NV axis => compare theory & experiment • Predict and observe a weak polarization effect Is this useful?

  29. Conclusion and outlook • Spin physics in diamond: preparation and detection of a single NMR molecule • What next? • Higher-fidelity control over electron-nuclear spin registers using dynamically decoupled gates • Scaling up for QIS: NV-NV (Neumann 2010), NV-photon (Togan 2010) • can this be done in a manner that doesn’t entangle a nuclear spin? • Magnetometry (Taylor 2008, Maze 2008, Balasubramanian 2008) • can this be used to look at single spins outside of diamond? • Coupling to resonators and cavities for cavity QED and hybrid systems (Kubo 2010) • Other defect centers with similar or better properties? Cappellaro et al. 2009 PRL • Opportunities and challenges remain

  30. Many thanks to Benjamin Smelzter `10 Jean McIntyre `10 Kyle Enman `09 Yuanyuan Jiang `09 Amrita Roy ‘11 Janith Rupasinghe ‘13 Gabe Ycas  UC Boulder Bates NV Lab … and you for your attention! Funding: Bates College, HHMI, Research Corporation

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