Transcript Childress
Control of individual nuclear spins in diamond L. Childress, B. Smeltzer, J. McIntyre Bates College QNLO 2010 Sensing nuclear spins Ensemble NMR techniques Measure ensembles of nuclear spins with e.g. pickup coils, micro-atomic magnetometers NV centers Electronic spin as sensitive magnetometer Coupled electron-nuclear spin system Ledbetter et al. 2008 PNAS Sensitivity: ~ 1012 protons MRFM ~103 protons Atoms and ions Mixed electronnuclear hyperfine levels can be precisely controlled and measured Nuclear spin environment of the NV Can be viewed as a resource Coherent interactions with proximal nuclear spins in the bath 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 The spin degree of freedom: Hyperfine structure Excited state ? Ground state ms = ±1 ms = 0 Always H S gB S z S AN I N S A1 3C I 1 3C 2 z Unlike atoms, F is not a good quantum number 1.1% probability at each lattice site Weak (few MHz), anisotropic hyperfine interactions Experimental techniques: wire imaging ? ms = ±1 ms = 0 ~10 µm 532 nm Single photon counting module N.A. 1.3 oil immersion objective fluorescence Dichroic 20 m copper wire Permanent magnet MW Gruber, Science 1997 Experimental techniques: ? wire spin resonance ms = ±1 ms = 0 MW or RF …and repeat 10,000 times MW or RF excitation Polarization and fluorescence detection of a single NV Experimental techniques: ? ms = ±1 ms = 0 MW or RF …and repeat 10,000 times wire spin resonance Zoom in: hyperfine lines mI = -1/2 +1/2 -1 0 1 14 15N: N: 2.2 MHzsplitting splitting 3 MHz Hyperfine interactions with proximal 13C spins Measurement of possible hyperfine parameters % change in fluorescence different proximal 13C lattice sites have different hyperfine splittings MW frequency (GHz) Hyperfine interaction depends on 13C lattice site and electronic spin density Gali, PRB 80 241204R 2009 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 NV hyperfine interactions Area of circles ~ hyperfine interaction Nearestneighbor 13C: 130 MHz 6 NV 14N/15N: 14 MHz 2-3 MHz 9 4 How can we polarize, manipulate, and detect these nuclear spins? …especially the nitrogen nuclear spin? 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 Polarization of nuclear spins in diamond Use hyperfine flip-flops in the excited state instead The idea: Fuchs 2008, Jacques 2009 NV SWAP Hard to do precisely with MW pulses Especially for weakly-coupled nitrogen nuclear spins If we can swap the electron and nuclear spin states Laser excitation We can polarize the electron spin into a welldefined quantum state And repolarize the electron spin Then we’ve prepared both spins in a well-defined quantum state Dutt, LC Science 2007 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 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 Readout of single nuclear spins in diamond Working at the ESLAC ~ 510 G we can directly distinguish nuclear spin states! ms 0, mI 1 already fully polarized bright ms 0, mI 0 1 singlet pass to polarization dark ms 1, mI 0 2 singlet passes to polarization darker ms 1, mI 1 3 singlet passes to polarization darkest Steiner 2010 Simple, robust nuclear spin readout mechanism 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 13C lattice sites A Spin echo Millisecond dephasing times – long-lived quantum memory 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), J.Taylor et al, (07) Can we turn on L.Jiang, and off hyperfine flip-flops in the excited state? Need nuclear spins to be unaffected by optical transitions! 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 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 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. Numerical simulations Features are characteristic of a twolevel system with: • weak MW B field NV axis • strong RF B field || NV axis H Sz gB BMW cos(MW t ) BRF cos(RFt ) S 1 RF cos(t ) MW H cos( t ) 2 MW RF Quasistatic behavior Observed effects: • Low frequency splitting • Multiphoton transitions • Missing resonances RF MW 1 RF cos(t ) MW H cos( t ) 2 MW RF Quasistatic regime: ω < t Extremal detunings ±2ΩRF most likely Multiphoton resonances Observed effects: • Low frequency splitting • Multiphoton transitions • Missing resonances Floquet theory 2 1 0 -1 -2 3 2 RF photons 1 0 -1 m=0 1 RF cos(t ) MW H cos( t ) 2 MW RF m=-1 RF MW MW flips the spin; RF doesn’t Intermediate state detuned only by ~ω Explains dependence on orientation of fields Analytic approach i(n )t 1 RF cos( t ) An 0 e MW H t ) n cos( 2 RF Hint MW i(n )t 0 An e n Explains observed multiphoton transitions and missing resonances – “coherent destruction of tunneling” Effective Rabi frequency for n-RF photon transition MW 2RF An Jn 2 RF Strong-field effects in an easilyaccessible regime Applications for longitudinal excitation? 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 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 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? 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 Cappellaro et al. 2009 PRL • 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? Opportunities and challenges remain Many thanks to Bates NV Lab Benjamin Smelzter `10 Jean McIntyre `10 Kyle Enman `09 Yuanyuan Jiang `09 Amrita Roy ‘11 Janith Rupasinghe ‘13 Gabe Ycas UC Boulder … and you for your attention! Funding: Bates College, HHMI, Research Corporation