Magnetic field sensors with qubits in diamond

1. Magnetic field sensorswith qubits in diamond Paola Cappellaro Massachusetts Institute of Technology Nuclear Science and Engineering Department

2. Promise of qt. metrology • Improved sensitivity • Entangled states • Feedback, adaptive methods • Nano-scale probes • Proximity to target, nano-materials or biology applications • Robust metrology • Clocks, based on fundamental physics laws

3. Challenges in qt. metrology • Fragility of entangled states • Improved sensitivity implies higher sensitivity to external noise • Complexity of control for multi-qubit systems • Qubit addressability, control robustness and fidelity • Unavailable or inefficient quantum readout • Many-body observables, imperfect readouts

4. Single-spin magnetometer • Detect magnetic field with Ramsey-type experiment • Shot-noise limited sensitivity (minimum resolvable field) • Limited by dephasing time • Limited by low contrast y x ω τ BDC τ~ T2* t [T Hz-½]

5. Single-spin magnetometer • Detect magnetic field with Ramsey-type experiment • Shot-noise limited sensitivity (minimum resolvable field) • Limited by dephasing time • Limited by low contrast y x ω τ/2 τ/2 BAC τ~ T2 t [T Hz-½] Spin echo

6. Single-spin magnetometer • Detect magnetic field with Ramsey-type experiment • Shot-noise limited sensitivity (minimum resolvable field) • Limited by dephasing time • Limited by low contrast y x ω τ/2 τ/2 BAC τ~ T2 t [T Hz-½] Spin echo Repeated readout, Improved photon coupling

7. Technology comparison MRFM (2006) NV nano-tip magnetometer Atom chip (2005) NV B-field imager1 mm pixels NV ensemble magnetometer1 cm3 sensor

8. Nuclear spin spectroscopy • Detect nuclear spin noise fromhigh-density samples • Often T2n >> T2e: correlationfrom scan to scan • We can measure the correlation And reconstruct the correlation function from KM(τ) and find the power spectral density of the nuclear spin field BN φ SEM image of fixated E. Coli and simulated scan. Brighter regions correlate with high spin density. Meriles, ...Cappellaro, JCP 133, 124105 (2010)

9. Many-spins magnetometer • Improve the sensitivity by increasing the number of NV’s • δB per volume ~ 1/√n (n density) • Using quantum enhanced techniques, we could approach the Heisenberg limit [T Hz-½] [T Hz-½]

10. Many-spins magnetometer • High density by Nitrogen implantation + annealing • Conversion factor f ~ 10-40 % • 2 error sources • Use dynamical decoupling control techniques N (epr) spins OtherNV centers T2 : 630 μs  280 μs, for nN 1015 cm-3 5 x 1015 cm-3 Stanwix, PRB 82, 201201R (2010)

11. Applications

12. B t Action potential B-field imager • High density, macroscopic samples • Signal collected on CCD • Diamond divided into pixels • Imaging of magnetic surfaces • Hard disk drives, cell dynamics, brain function, …

13. Δ B Nano-tip magnetometer • Goal: detect a single spin • A single NV center close to the surface • r0 ~ 10nm from source  1H field: BH ~ 3 nT • Many spins contribute to the signal • Add magnetic gradient • Exploit frequency selectivity of AC magnetometry • ≤ 1nm spatial resolution Magnetictip .1nm

14. Dark Spin Magnetometry

15. … Parameter estimation • Harness the bath of “dark” nitrogen spins • B-field is sensed by dark spins, in turns detected by the bright NV center spin • Parameter estimation via ancillary qubits • Effective evolution: Goldstein, Cappellaro et al., arXiv:1001.0089

16. Dark Spins • Sensitivity enhancement is possible even with random couplings • Control embedded in spin echo • Sensitivity • For strongly coupled spins Sensor τ/2 τ/2 Dark Spins • We achieve the Heisenberg limit, • since t

17. Sensitivity Scaling • Novel type of entangled state • Dark spins and NV decoherence times are similar • Robust against decoherence • Same noise, N-times more signal • Compromise between strong coupling and decoherence

18. Adaptive Methods

19. Sensitivity Limits • Two limitations: 1. Noise might limit the evolution timeto 2. Ambiguity in phase limits to • Repeated measurements yield the sensitivity • This is the SQL in the total time • Is there a better way to use the time than doing N equal measurements?

20. Quantum Metrology Limit • Goal: scaling with resources (QML) • Entangled states (squeezing) can achieve the QML with the number of probes*, • but they are usually fragile or difficult to prepare. • Adaptive readout schemes can achieve the QML in the total measurement time , • no entanglement is required *P. Cappellaro et al., PRA 80, 032311 (2009); PRL 106, 140502 (2011); PRA (2012).

21. Adaptive Methods • Update the interrogation scheme based on previous information (Bayesian method) • Adaptive rules desiderata: • Should converge to correct result • Can achieve a broader measurement bandwidth • Can converge faster than classical schemes

22. Adaptive Methods • Update the interrogation scheme based on previous information (Bayesian method) • Adaptive rules desiderata: • Should converge to correct result • Can achieve a broader measurement bandwidth • Can converge faster than classical schemes • Should be robust against readout (and other) errors

23. Noise and Errors • Readout errors propagate in the adaptive scheme: the QML is lost C=0.95

24. M-pass scheme • Increasing the number of steps recovers the QML, in the presence of noise and imperfect readout 0 1 t x J Readout contrast C<1 M=2 M=n+1 N Update P(j) Set time t’=2t Select J’

25. M-pass scheme • It recovers the QML even in the presence of noise and imperfect readout C=0.95 M=n+1 C=0.85

26. Efficiency • When is the adaptive method good? • Large frequency range (short ) • If a “single measurement” might be better (Fourier limit) • If large overhead per measurement, adaptive method might not be so good • Is there a better application of the adaptive method?

27. Quantum Parameter • The adaptive method can measure quantum parameters • Example: random filed due to a nuclear spin bath • 2-pass scheme still yields the QML Simulation: 1 NV in bath of 1.1% C-13, initially in thermal state.

28. Bath Narrowing • Example: nuclear spin bath of NV center • Knowledge of the “quantum parameter” corresponds to “narrowing” of the bath NV spectrum with thermal bath NV spectrum after bath narrowing via adaptive scheme

29. Increase Coherence • Adaptive measurement of nuclear bath achieves longer coherence time • Adaptive method fixes the state of the bath • Good efficiency: frequency spread s.t. • No further need for dynamical-decoupling • DD often limits the fields that can be sensed (or the tasks in QIP that can be performed)

30. Composite Pulse Magnetometry

31. DC magnetometry • Detection of static magnetic fields

32. DC magnetometry • Detection of static magnetic fields

33. DC magnetometry • Detection of static magnetic fields *Fedderet al., ApplPhys B 102,497–502 (2011)

34. DC magnetometry • Detection of static magnetic fields

35. Composite pulses magnetometry • Detection of static magnetic fields Example: Rotary Echo +x -x • Compromise: • Longer T2 than Ramsey, higher sensitivity than Rabi • Corrects for mw instability +x -x +x -x +x -x …

36. Rotary Echo • Intermediate (variable) T2 and sensitivity

37. Sensitivity • Higher sensitivity, robust against mw noise • Flexible scheme, adapting to expt. conditions

38. Conclusions • Quantum metrology offers many challenges but even more diverse opportunities for improvement • Control techniques • Adaptive methods • Harnessing the “environment” • Applications • Detection of static magnetic fields with NV centers • Nuclear spin bath narrowing

39. A stable, three axis gyroscope in diamond nNV-gyro

40. Spin Gyroscope • Spins are sensitive detectors of rotation • NMR gyroscopes require large volumes because of inefficient polarization and readout • NV centers in diamond • allow fast polarization & readout • have much poorer stability

41. nNV-Gyro • Combines efficiency of NV electronic spin • with the stability and long coherence time of the nuclear spin, • preserved evenat high density

42. nNV-gyro sensitivity • Using an echo scheme, the nNV-gyro offers great stability • It could be combined with MEMS gyro, that are not stable

43. Funding NIST DARPA (QuASAR) AFOSR MURI (QuISM) Publications N. Bar-Gill, L. M. Pham, C. Belthangady, D. Le Sage, P. Cappellaro, J. R. Maze, M. D. Lukin, A. Yacoby, R. Walsworth, Nature Comm. 3, 858 (2012) A. Ajoy and P. Cappellaro "Stable Three-Axis Nuclear Spin Gyroscope in Diamond" arXiv:1205.1494 (2012) P. Cappellaro, Phys. Rev. A 85, 030301(R) (2012) P. Cappellaro, G. Goldstein, J. S. Hodges, L. Jiang, J. R. Maze, A. S. Sørensen, M. D. Lukin, Phys. Rev A 85, 032336 (2012) L. M. Pham, N. Bar-Gill, C. Belthangady, D. Le Sage, P. Cappellaro, M. D. Lukin, A. Yacoby, R. L. Walsworth, arXiv:1201.5686 G. Goldstein, P. Cappellaro, J. R. Maze, J. S. Hodges, L. Jiang, A. S. Sørensen, M. D. Lukin, Phys. Rev. Lett. 106, 140502 (2011) L.M. Pham, D. Le Sage, P.L. Stanwix, T.K. Yeung, D. Glenn, A. Trifonov, P. Cappellaro, P.R. Hemmer, M.D. Lukin, H. Park, A. Yacoby and R.L. Walsworth, New J. Phys. 13 045021 (2011) C. A. Meriles, L. Jiang, G. Goldstein, J. S. Hodges, J. R. Maze, M. D. Lukin and P. CappellaroJ. Chem. Phys. 133, 124105 (2010) P.L. Stanwix, L.M. Pham, J.R. Maze, D. Le Sage, T.K. Yeung, P. Cappellaro, P.R. Hemmer, A. Yacoby, M.D. Lukin, R.L. Walsworth, Phys. Rev. B 82, 201201(R) (2010)