Nuclear spin control in diamond Lily Childress Bates College nanomri 2010
Hyperfine structure of the NV center: Excited state? Ground state m s = ±1 m s = 0 H = S + gµ S 2 z B z r s r r + S A N I N + S A i I i 13 C spins
Experimental techniques: spin resonance? wire Zoom in: hyperfine lines m s = ±1 m s = 0 m I = -1 0 1 +1/2-1/2 14 N: 2.2 MHz splitting 15 N: 3 MHz splitting MW or RF excitation Polarization and fluorescence detection of a single NV
13 C Hyperfine structure Different proximal 13 C lattice sites have different hyperfine splittings Nearest neighbor off scale! % change in fluorescence MW frequency (GHz) Hyperfine splitting depends on 13 C lattice site and electronic spin density Gali, PRB 80 241204R 2009
NV hyperfine interactions Area of circles ~ hyperfine interaction Nearestneighbor 13 C: 130 MHz 6 NV 14 N/ 15 N: 2-3 MHz 14 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, et al 2007 Early techniques work for strongly-coupled 13 C spins Our work: Improve signal, extend to nitrogen nuclear spins
Polarization of nuclear spins in diamond The idea: Use hyperfine flip-flops instead! Jacques 2009 NV SWAP Hard to do precisely with MW pulses If we can swap the electron and nuclear spin states Especially for weakly-coupled nitrogen nuclear spins 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 Jacques et al. 2009 Robust polarization for many nuclear spin species
B = 510G polarization Nuclear magnetic resonance in diamond MW to drive electron spin transitions RF to drive nuclear spin transitions Green light off during pulses => working in the electronic ground state Precise hyperfine parameters Fast NMR control Strong signal Smeltzer 2009
Readout of single nuclear spins in diamond Working at the ESLAC ~ 510 G we can directly distinguish nuclear spin states! m m m m s s s s = 0, m = 0, m = 1, m = 1, m =+ 1 = 0 Steiner 2010 I I I I = 0 = 1 already fully polarized bright 1singlet pass to polarization dark 2 singlet passes to polarization darker 3 singlet passes to polarization darkest Simple, robust nuclear spin readout mechanism
Coherence properties of nitrogen nuclear spins Initial measurements indicate that 14 N dephasing time can be close to the electron spin lifetime 14 N dephasing Electron spin decay The 15 N dephasing time ~ 1ms can be extended with spin echo Spin echo
What happens if you send in MW and RF simultaneously? MW to drive electron spin transitions RF to drive nuclear spin transitions It s a rather surprising pineapple
Multifrequency excitation of the NV center in diamond Low magnetic field data: no nuclear spin polarization ESLAC data: 14 N polarization (also different RF amplifier) ENDOR This has nothing to do with nuclear spins. It s purely a two-level system.
Multifrequency excitation of the NV center in diamond Features are characteristic of a two-level system with: weak MW B field NV axis strong RF B field NV axis Simulations: H r r = S + gµ ) z B ( B cos( ω t) + B cos( ω t+ ϕ ) S MW MW RF RF r H = 1 2 δ +Ω Ω RF cos( ωt) MW Ω δ Ω MW RF cos( ωt)
Multifrequency excitation of the NV center in diamond Features are characteristic of a two-level system with: weak MW B field NV axis strong RF B field NV axis A useful tool? Floquet analysis Multiphoton transitions RF z ensures intermediate state is not far detuned Coherent destruction of tunneling Ω RF ~ several MHz ~ ω Behavior beyond the RWA easily accessible H = 1 2 δ +Ω Ω RF cos( ωt) MW Ω δ Ω MW RF cos( ωt)
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
Conclusion and outlook Hyperfine structure opportunity to prepare and detect single nuclear spins in a solid preparation and detection of a single NMR molecule creates many new possibilities checks on ab initio theory for the electronic structure multiple proximal nuclear spins a quantum register integrated excitation circuits strong field regime accessible multifrequency and multiaxis excitation but faces many challenges relatively fast electronic T2* requires decoupled control techniques non-negligible electron spin decay rates T1 imperfect preparation and detection scaling up through spin-spin or optical channels
Many thanks to Bates NV Lab Benjamin Smelzter `10 Jean McIntyre `10 Kyle Enman `09 Yuanyuan Jiang `09 Gabe Ycas Gurudev Dutt Mikhail Lukin and you for your attention! Funding: Bates College, HHMI, Research Corporation