Magnetic field sensorswith qubits in diamond

Paola CappellaroMassachusetts Institute of Technology

Nuclear Science and Engineering Department

P. Cappellaro —

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

P. Cappellaro —

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

P. Cappellaro —

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

τ ~ T2*

ω

[T Hz-½]

x yτ

BDCt

P. Cappellaro —

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

x yτ/2

BAC

t

τ/2

τ ~ T2

ω

[T Hz-½]

Spin echo

P. Cappellaro —

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

x yτ/2

BAC

t

τ/2

τ ~ T2

ω

[T Hz-½]

Spin echoRepeated readout, Improved photon coupling

P. Cappellaro —

MRFM (2006)

Atom chip (2005)

NV nano-tip magnetometer

NV ensemble magnetometer1 cm3 sensor

NV B-field imager1 mm pixels

Technology comparison

P. Cappellaro —

Nuclear spin spectroscopy• Detect nuclear spin noise from

high-density samples• Often T2n >> T2e: correlation

from 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)

P. Cappellaro —

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]

P. Cappellaro —

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

Other NV centers

T2 : 630 μs 280 μs, for nN 1015 cm-3 5 x 1015 cm-3

Stanwix, PRB 82, 201201R (2010)

P. Cappellaro —

APPLICATIONS

P. Cappellaro —

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, …

t

B

Action potential

P. Cappellaro —

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

.1nm

B

Δ

Magnetictip

Add magnetic gradientExploit frequency selectivity of AC magnetometry≤ 1nm spatial resolution

P. Cappellaro —

DARK SPIN MAGNETOMETRY

P. Cappellaro —

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

P. Cappellaro —

Dark Spins• Sensitivity enhancement is possible even with

random couplings– Control embedded in spin echo

τ/2

t

τ/2

Sens

orDa

rk S

pins

Sensitivity

For strongly coupled spinsWe achieve the Heisenberg limit,

since

P. Cappellaro —

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

P. Cappellaro —

ADAPTIVE METHODS

P. Cappellaro —

Sensitivity Limits• Two limitations:

1. Noise might limit the evolution time to 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?

P. Cappellaro —

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).

P. Cappellaro —

Adaptive Methods • Update the interrogation scheme based on

previous information (Bayesian method)

• Adaptive rules desiderata:1. Should converge to correct result2. Can achieve a broader measurement bandwidth3. Can converge faster than classical schemes

P. Cappellaro —

Adaptive Methods • Update the interrogation scheme based on

previous information (Bayesian method)

• Adaptive rules desiderata:1. Should converge to correct result2. Can achieve a broader measurement bandwidth3. Can converge faster than classical schemes4. Should be robust against readout (and other) errors

P. Cappellaro —

Noise and Errors• Readout errors propagate in the adaptive

scheme: the QML is lost

C=0.95

P. Cappellaro —

M-pass scheme• Increasing the number of steps recovers the

QML, in the presence of noise and imperfect readout

Update P(j)

Select J’ Set time t’=2t

0 1

x Jt

M=2

Readout contrast C<1

M=n+1N

P. Cappellaro —

M-pass scheme• It recovers the QML even in the presence of

noise and imperfect readout

C=0.95

C=0.85M=n+1

P. Cappellaro —

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?

P. Cappellaro —

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.

P. Cappellaro —

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

P. Cappellaro —

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)

P. Cappellaro —

COMPOSITE PULSE MAGNETOMETRY

P. Cappellaro —

DC magnetometry

Ramsey(high sensitivity, short T2)

• Detection of static magnetic fields

P. Cappellaro —

DC magnetometry

Ramsey(short T2, high sensitivity)

• Detection of static magnetic fields

P. Cappellaro —

DC magnetometry

Ramsey(high sensitivity, short T2)

Rabi* (long T2, low sensitivity)

• Detection of static magnetic fields

*Fedder et al., Appl Phys B 102, 497–502 (2011)

P. Cappellaro —

DC magnetometry

Ramsey(short T2, high sensitivity)

Rabi (long T2, low sensitivity)

• Detection of static magnetic fields

P. Cappellaro —

Ramsey(high sensitivity, short T2)

Rabi (long T2, low sensitivity)

+x -x +x -x +x -x…+x -x

Composite pulses magnetometry

Example: Rotary Echo

• Detection of static magnetic fields

• Compromise: – Longer T2 than Ramsey, higher sensitivity than Rabi

• Corrects for mw instability

P. Cappellaro —

Rotary Echo• Intermediate (variable) T2 and sensitivity

P. Cappellaro —

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

P. Cappellaro —

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

P. Cappellaro —

nNV-GYROA stable, three axis gyroscope in diamond

P. Cappellaro —

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

PQE2012 - P. Cappellaro

nNV-Gyro• Combines efficiency of NV electronic spin• with the stability and long coherence time of

the nuclear spin, – preserved even

at high density

PQE2012 - P. Cappellaro

nNV-gyro sensitivity• Using an echo scheme, the nNV-gyro offers

great stability• It could be combined with MEMS gyro, that

are not stable

P. Cappellaro —

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:1201.5686G. 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. Cappellaro J. 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)