Quantum Spintronics Design(NV centers in diamond)

Eisuke Abe
RIKEN Center for Emergent Matter Science2019.09.04
CMD Spintronics Design Course@Osaka UniversityShort CV©Google Earth

2001.4 – 2006.3 (Keio) → Quantum computing (silicon)2006.4 – 2009.12 (ISSP, UT) → Quantum transport (GaAs QDs, Josephson)2010.1 – 2011.6 (Oxford) → Hybrid system (spin–cavity coupling)

2011.7 – 2015.3 (Stanford/RIKEN) → Quantum network (InAs QDs)



2015.4 – 2019.1 (Keio) → Quantum sensing (diamond)

2019.2 – Present (RIKEN) → Quantum computing (Josephson)

Diamond envy
©Lucara Diamond1109 carats, $70M

ρN = 1.77 x 1023 cm-3

C

Diamond NV©Lucara DiamondNV1109 carats, $70M

ρN = 1.77 x 1023 cm-3

C

Diamond NV

S=1N

V

22 x 0.5 mm3, $700 (E6)
[N] < 5 ppb, [NV] < 0.03 ppb

ρN = 1.77 x 1023 cm-3

C

Why a single NV spin?
• Optically active (init. & readout)• Microwave spin control• High coherence (LT–RT–500 K)

Quantum sensing & Quantum network[Biology] Annu. Rev. Phys. Chem. 65, 83 (2014) Schirhagl et al.
[Magnetometry] Rep. Prog. Phys. 77, 056503 (2014) Rondin et al.
[Magnetic resonance] J. Mag. Res. 269, 225 (2016) Wrachtrup et al.
[Quantum technologies] Nature Photon. 12, 516 (2018) Awschalom et al.
[Quantum internet] Science 362, eaam9288 (2018) Wehner et al.

Quantum sensing
Nano-tip
Molecule

Nuclear spin

Living cell
Magnetic structure

NV spinDiamond substrate
ND• Room T. operation• High spatial resolution• Nondestructive• Various modalities• Nano MRI• Probe for CM systems• Biology

Quantum network

Spin–spin entanglement
between distant NVs

Nature 526, 682 (2015) Hensen et al.
Times Cited: 1185 (Google Scholar)

Outline••

Basics of NV centers in diamond–––

Structure
Optical properties
Spin properties

Quantum sensing––––

BasicsCorrelation spectroscopy and detection of nuclear spins
Ultrahigh resolution sensing
Determination of the position of a single nuclear spinOutline••

Basics of NV centers in diamond–––

Structure
Optical properties
Spin properties

Quantum sensing––––

BasicsCorrelation spectroscopy and detection of nuclear spins
Ultrahigh resolution sensing
Determination of the position of a single nuclear spinCrystal & energy level structures• Negatively-charged (NV−)• 4 sp3 orbitals, 6 e− (5 from the defect, 1 captured)• C3v (symmetry axis = quantization axis)

Effective spin-1 system(e2-hole spin-triplet)
ex

ey
a1a’1

Optical transitions
C.B. (Eg = 5.47 eV = 227 nm)(ae-hole)exey

515 nma1|e〉a’1

637 nm(e2-hole)exms = ±1|g〉

2.87 GHz

ms = 0
V.B.

ey
a1a’1

PL spectroscopy
C.B. (Eg = 5.47 eV = 227 nm)

ZPL and PSB
515 nm|e〉637 nmms = ±1|g〉

2.87 GHz

ms = 0V.B.

PL imaging
C.B. (Eg = 5.47 eV = 227 nm)
600–800 nm

Bright spot... single NV?

515 nm|e〉Count rate (cps)637 nmms = ±1|g〉

2.87 GHz

ms = 0V.B.

2.5 μm x 2.5 μm

Photon statistics
C.B. (Eg = 5.47 eV = 227 nm)

One photon at a time
515 nm|e〉637 nmms = ±1|g〉

2.87 GHz

ms = 0V.B.

Non-radiative path
C.B. (Eg = 5.47 eV = 227 nm)

515 nm|e〉1042 nm

637 nmms = ±1|g〉

2.87 GHzms = 0V.B.

Time-resolved fluorescence
C.B. (Eg = 5.47 eV = 227 nm)

The NR channel provides a means toread out and initialize the NV spin

515 nm|e〉

mS = 01042 nm

637 nmms = ±1|g〉mS = −1Difference
2.87 GHz

ms = 0V.B.

CW ODMR
C.B. (Eg = 5.47 eV = 227 nm)

515 nm|e〉

Laser
MW1042 nm

637 nm(Sweep frequency)

SPCM
ms = ±1|g〉

2.87 GHz

ms = 0V.B.

TimeCW ODMR at B0 = 0C.B. (Eg = 5.47 eV = 227 nm)

Zero-field splitting 𝐻 = 𝐷𝑆𝑧2
D = 2.87 GHz

515 nm|e〉1042 nm

637 nmms = ±1|g〉

ms = 0 ↔ ±12.87 GHz

ms = 0V.B.

CW ODMR at B0 > 0
C.B. (Eg = 5.47 eV = 227 nm)

Zeeman 𝐻 = 𝐷𝑆𝑧2 + 𝛾e 𝐵0 𝑆𝑧
γe = 28 MHz/mT

515 nmB0 ‖ NV-axis|e〉637 nm2γB0

ms = ±1|g〉

ms = 0 ↔ −1

ms = 0 ↔ 1

2.87 GHz

ms = 0V.B.

B0 = 4.7 mT (2.87±0.132 GHz)

Experimental setup(Fiber laser& fiber AOM)

Spectrometer

515 nm

600–800 nm

LaserSPCM
Dichroic BS

HWP

Timing analyzer

PBS

Fiber coupler

SPCM

Objective

QWP AOM

100 MHz (IQ)
AWG

DiamondVector SG

2.87 GHz
Amplifier

Permanent magnet &XYZ-translation stage
Stripline & XYZ-piezo stage(XY-galvo + Z-piezo & 1-axis magnet)

Experimental setup

Experimental setup

380 mm

200 mmQubit & coherence"0" ≡ 𝑚𝑠 = 0

Ψ = 𝛼 0 + 𝛽|1〉"1" ≡ 𝑚𝑠 = −1

T2: measure of how long a superposition state is preserved

Rabi oscillation
Initialization

Microwave

ReadoutTp

π/2-pulse

π-pulsePulse ODMR
Initialization

Change fmw

Readout

Long (narrowband) π-pulse

Tp = 1292 ns
ms = ±12.87 GHz

14N (I = 1)2γB0

2.1 MHz
2.1 MHzmI = 1mI = 0mI = −1

ms = 0Hyperfine coupling with 14N nucleus of
the NV center itself

Ramsey interference
Initialization

π/2

π/2ReadoutτTπ/2 = 31.5 ns
fosc = 2.1 MHz
T2* = 0.50 μs

π/2-pulse (x)π/2-pulse (x)t=0t=τ

Spin echo
Initialization

ππ/2τSign of phase accumulation

Readout

τPositive

Negative

Phase accumulation
by DC field

π/2-pulse (x)t=0π/2π/2-pulse (-x)π-pulse (y)t = τ(−)

t = τ(+)

t = 2τ

Spin echo
Initialization

ππ/2τReadout

π/2τT2 = 364 μs“Collapse and revival”• Interaction with the nuclear spin bath ([13C] = 1.1%)• fc = γCB0 = 10.705 kHz/mT x 4.7 mT = 50.3 kHz• Revival at 2nτ = 2n/fc = 41.8 x n μs

Coherence time
T2 = 71 μs
p = 1.3

Stretched exponential decay2𝜏
exp −𝑇2𝑝

CVD growth of shallow single NV centers• Hydrogen-terminated• ~5 nm from the surface• [12C] = 99.999%

Outline••

Basics of NV centers in diamond–––Structure
Optical properties
Spin properties

Quantum sensing––––

BasicsCorrelation spectroscopy and detection of nuclear spins
Ultrahigh resolution sensing
Determination of the position of a single nuclear spin

Quantum sensing
Nano-tip
Molecule

Nuclear spin

Living cell
Magnetic structure

NV spinDiamond substrate
ND• Room T. operation• High spatial resolution• Nondestructive• Various modalities• Nano MRI• Probe for CM systems• Biology

Nuclear spin sensing

Nuclear spin

NV spin

Ext. field B0

Molecule

fac

Diamond substrate

Nuclear spins precess at fac = a few kHz–MHz under B0
Weak AC magnetic field on the NV spin (11 nT@dNV = 5 nm)
Detect using quantum coherenceAC magnetometry
CP (N = 4)

π/2

π

τ/2ππ

ττ

πτ

π/2

τ/2

Sign of phase accumulation

AC field at fac = 1/2τπBac

Sensor phase buildup = decrease of coherence𝑡𝛾𝐵ac � cos 2𝜋𝑓ac 𝑡 𝑑𝑑0φ = 8τγBac/π

Rev. Mod. Phys. 89, 035002 (2017) Degen et al.

AC magnetometry
CP (N = 4)

π/2π

τ/2ππ

τ

τπ

τ

π/2

τ/2

Sign of phase accumulation

AC field at fac ≠ 1/2τMultiple oscillations between π-pulses average out the sensor phaseRev. Mod. Phys. 89, 035002 (2017) Degen et al.

Nuclear spin sensing
fc = 387.5 kHz• Single NV center in a natural abundant diamond ([13C] = 1.1%, dNV ~ 50 μm)• Sweep τ & repeat (f = 1/2τ, Δτ = 31.3 ns, N = 16)• fc = γCB0 = 10.705 kHz/mT x 36.2 mT
Phys. Rev. B 98, 121405 (2018) Sasaki et al.

Correlation spectroscopy
AC field at fac

α2α1

ts = Nτtcorr

Accumulate more phaseif tcorr = m/fac

Nature Commun. 4, 1651 (2013) Laraoui et al.
Phys. Rev. Appl. 4, 024004 (2015) Kong et al.
Nature Commun. 6, 8527 (2015) Staudacher et al.
Phys. Rev. Lett. 116, 197601 (2016) Boss et al.

Correlation spectroscopy
AC field at fac

α2

α1

Sensor is in |ms = 0〉,|−1〉(T1 limited)
ts = Nτtcorr

No gain of the phase iftcorr = (m+1/4)/fac

The transition probability for random phases
𝑝 𝑡1

11 𝛾𝐵ac 𝑡s 2
≈ 1−cos(2𝜋𝑓ac 𝑡corr )𝜋22Nature Commun. 4, 1651 (2013) Laraoui et al.
Phys. Rev. Appl. 4, 024004 (2015) Kong et al.
Nature Commun. 6, 8527 (2015) Staudacher et al.
Phys. Rev. Lett. 116, 197601 (2016) Boss et al.

Correlation spectroscopy
AC field at fac

α2α1Sensor is in |ms = 0〉,|−1〉(T1 limited)
ts = Nτ

tcorr

Where to look at?
••

ft = 1/2τ = 301.6 kHz
τ = 1.7875 μs

Phys. Rev. B 98, 121405 (2018) Sasaki et al.

Correlation spectroscopy of a nucleus
No decay up to 100 μs

f1 = f215.6
kHzkHz1 = 215.6

ff00==387.5
387.5kHzkHz

Phys. Rev. B 98, 121405 (2018) Sasaki et al.

Correlation spectroscopy of a nucleus
Hamiltonian of NV–13C coupled system

𝐻 = 𝑓c 𝐼𝑧 + 𝑚𝑠 = −1 〈−1|(𝐴∥ 𝐼𝑧 + 𝐴⊥ 𝐼𝑥 )→ No hyperfine field when |ms = 0〉

f1 = fc + A’‖ (ms = −1)

f0 = fc (ms = 0)

A’‖ = −171.9 kHz(f0 + f1)/2 = 301.55 kHz → dip

Phys. Rev. B 98, 121405 (2018) Sasaki et al.

Coherent control of a nuclear spin
Hamiltonian of NV–13C coupled system

𝐻 = 𝑓c 𝐼𝑧 + 𝑚𝑠 = −1 〈−1|(𝐴∥ 𝐼𝑧 + 𝐴⊥ 𝐼𝑥 )→ The single 13C n-spin rotates about the A⊥ axis𝐴∥𝜏 ≈ 𝑓c +2

Phys. Rev. B 98, 121405 (2018) Sasaki et al.

Conditional rotation of a nuclear spin
CP (N = 4)π/2π

τ/2ππττπ

τ

π/2

τ/2

Evolution of n-spin vector|ms = 0〉Start from |ms = 0〉
|ms = −1〉

Q-axis of n-spin

zStart from |ms = −1〉

Coherent control of a nuclear spin
Transition probability of the NV spin

𝑁𝜙cp
12𝑃X = 1 − (1 − 𝒏0 ⋅ 𝒏−1 ) sin
22−1Phys. Rev. Lett. 109, 137602 (2012) Taminiau et al.

fcp = 10.2 kHz ≈ A’⊥ /2
PX < 0.5 → single

Phys. Rev. B 98, 121405 (2018) Sasaki et al.

Determination of hf constants
Magnetic dipole int. + contact hf int.

3 cos 2 𝜃 − 1𝐴∥ ∝𝑟33 cos 𝜃 sin 𝜃𝐴⊥ ∝𝑟3A‖ = −173.1 kHzA⊥ = 22.3 kHz

A‖ = −175.1±2.1kHzA⊥ = 21.9±0.2 kHz

DFT: New J. Phys. 20, 023022 (2018)
Nizovtsev et al.

(r, θ) = (6.84 Å, 94.8o)

Phys. Rev. B 98, 121405 (2018) Sasaki et al.

Toward single-molecular imaging• Information of the positions of the individual nuclei→ Accurate measurement of e–n int. const’s (A∥ , A⊥ ) ≈ (r, θ)→ Lack of information on the azimuthal angle ϕ• Spectral resolution→ Easy to resolve isotopes→ Need to measure J-couplings & chemical shifts (ppm!)→ Limited by sensor/memory lifetimes (T2e/n, T1e/n)

Nuclear spin

NV spinToward single-molecular imaging• Information of the positions of the individual nuclei→ Accurate measurement of e–n int. const’s (A∥ , A⊥ ) ≈ (r, θ)→ Lack of information on the azimuthal angle ϕ• Spectral resolution→ Easy to resolve isotopes→ Need to measure J-couplings & chemical shifts (ppm!)→ Limited by sensor/memory lifetimes (T2e/n, T1e/n)

Nuclear spin

NV spinAC magnetometry
CP (N = 4)

π/2π

τ/2ππ

ττπ

τ

π/2

τ/2Sign of phase accumulation

AC field at fac = 1/2τ

φ = 8γBacτ/π

φ=0• φ depends on the initial phase α of the AC field (φ ∝ cos α)

AC magnetometry
AC field at fac
α1

α2

α3

α4

ts = Nτ• φ depends on the initial phase α of the AC field (φ ∝ cos α)• Average over random αα5Ultrahigh resolution sensing
AC field at fac
α1

α3

α2

α4

α5

ts = Nτ

tL
I(α1)

I(α2)

I(α3)

I(α4)

I(α5)

• φ depends on the initial phase α of the AC field (φ ∝ cos α)• Average over random α• If the data acq. is periodic, adjacent α’s are related by αk+1 = 2π factL+ αkScience 356, 832 (2017) Schmitt et al.; Science 356, 837 (2017) Boss et al.; Nature 555, 351 (2018) Glenn et al.

Ultrahigh resolution sensing
AC field at fac
α1α3

α2α4α5ts = Nτ

tL
I(α1)

I(α2)

I(α3)

I(α4)

I(α5)

LOScience 356, 832 (2017) Schmitt et al.; Science 356, 837 (2017) Boss et al.; Nature 555, 351 (2018) Glenn et al.

Ultrahigh resolution sensing
Bac = 96.5 nT & fac = 2.001 MHz applied from a coil, detected by a single NV center
T = 300 sec
FWHM = 3.73 mHz

T = 900 sec
FWHM = 1.22 mHz

T = 1800 sec
FWHM = 0.601 mHz

T = 3600 sec
FWHM = 0.304 mHz

J. Appl. Phys. 123, 161101 (2018) Abe & Sasaki

Ultrahigh resolution sensing
FWHM = T −1 (not a fit)

SNR ∝ T 0.5•••

Spectral resolution not limited by sensor/memory lifetimes (T2e/n, T1e/n)
Only limited by the stability of LO (essentially infinite)
Resolution = T −1 & SNR ∝ T 0.5 → Precision ∝ T −1.5

J. Appl. Phys. 123, 161101 (2018) Abe & Sasaki

NMR spectroscopy
Data from Harvard: Nature 555, 351 (2018) Glenn et al.

•••
•
•

[NV] ≈ 3 x 1017 cm−3
# of NV ≈ 5 x 109
Vdetect ≈ 25 pL# of protons ≈ 2.5 x 1015
RF pulse → FID
See also: Science 357, 67 (2017) Aslam et al. (Wrachtrup, Stuttgart)[B0 = 3 T, fe = 87 GHz, T1n = 260 s]

NMR spectroscopy
Data from Harvard: Nature 555, 351 (2018) Glenn et al.

J-coupling

Chemical shift

See also: Science 357, 67 (2017) Aslam et al. (Wrachtrup, Stuttgart)[B0 = 3 T, fe = 87 GHz, T1n = 260 s]

Toward single-molecular imaging• Information of the positions of the individual nuclei→ Accurate measurement of e–n int. const’s (A∥ , A⊥ ) ≈ (r, θ)→ Lack of information on the azimuthal angle ϕ• Spectral resolution→ Easy to resolve isotopes→ Need to measure J-couplings & chemical shifts (ppm!)→ Limited by sensor/memory lifetimes (T2e/n, T1e/n)

Nuclear spin

NV spinHow to determine ϕ?

Transition probability of the NV spin after the detection of a single nuclear spin

1 1
𝑃Y = − cos 𝜙 − 𝜙n sin 𝑁𝜙cp
2 2Azimuthal angle of the nuclear Bloch vector: 2𝜋𝑓p 𝑡 + 𝜙n (0)Phys. Rev. B 98, 121405 (2018) Sasaki et al.

Ensemble vs. single
RF pulse

RF pulse

The initial state matters→ Dynamic nuclear polarization (DNP)

13
Determination of ϕ of a C n-spin
1.

DNP (PulsePol)

2.

RF pulse@ms = −1

3.

Wait t (n-spin precesses)

4.

AC sensing

f1 = 215.6 kHz (ms = −1)

f0 = fc (ms = 0)

Phys. Rev. B 98, 121405 (2018) Sasaki et al.

PulsePol
Hamiltonian engineering••

DNP condition: 2τpol = k/fn (k: odd, fn: nuclear Larmor frequency)
Average Hamiltonian ∝ 𝑆+ 𝐼− + 𝑆− 𝐼+ , ∝ 𝑆+ 𝐼+ + 𝑆− 𝐼−[PulsePol] Sci. Adv. 4, eaat8978 (2018) Schwartz et al.
Phys. Rev. B 98, 121405 (2018) Sasaki et al.

PulsePol

ft/5

fc/5

ft/3

fc/3ftfc

Phys. Rev. B 98, 121405 (2018) Sasaki et al.

PulsePol

ft/5fc/5

ft/3fc/3ft

fc

Phys. Rev. B 98, 121405 (2018) Sasaki et al.

13
Determination of ϕ of a C n-spin
1.

DNP (PulsePol)

2.

RF pulse@ms = −1

3.

Wait t (n-spin precesses)

4.

AC sensing

Phys. Rev. B 98, 121405 (2018) Sasaki et al.

13
Determination of ϕ of a C n-spin t → 1 ms (undersampling) fp = 215.79 kHz ≈ f1 = 215.6 kHz
 ϕ − ϕn(0) = 334.0o ϕn(0) = 89.2o (Real-space n-spin trajectory)

Phys. Rev. B 98, 121405 (2018) Sasaki et al.

ϕn(0): Real-space n-spin trajectory
ϕrf = 0o

Direction of the RF field
Bloch vector@t = 0 (Considering the rotation axis of the n-spin & detuning)
Full simulation based on the Bloch equation (Tilt of q-axis, pulse delay...)Phys. Rev. B 98, 121405 (2018) Sasaki et al.

13Determination of ϕ of a C n-spin t → 1 ms (undersampling) fp = 215.79 kHz ≈ f1 = 215.6 kHz
 ϕ − ϕn(0) = 334.0o ϕn(0) = 89.2o (Real-space n-spin trajectory)→ ϕ = 247.8±4.1oPhys. Rev. B 98, 121405 (2018) Sasaki et al.

Observation of weakly coupled 13C n-spins
Ultrahigh resolution sensing (N = 2)

ftfc
•••

fc = 387.5 kHz
RF pulse@ms = 0N = 2 to minimize
back actions from NV

Phys. Rev. B 98, 121405 (2018) Sasaki et al.

Observation of weakly coupled 13C n-spins
Ultrahigh resolution sensing (N = 2)

Phys. Rev. B 98, 121405 (2018) Sasaki et al.

Summary• Tools for single-molecule imaging/structural analysis
are being developed→ Determination of the position of a single n-spin[1,2]→ Ultrahigh resolution sensing on single n-spins[1,3,4]• Other issues: Create high-quality “shallow” NVs, accurately
position single molecules/proteins near the sensor etc[1] Phys. Rev. B 98, 121405 (2018) Sasaki, Itoh & Abe (arXiv.1806.00177)[2] Phys. Rev. Lett. 121, 170801 (2018) Zopes et al. (arXiv.1807.04559)[3] Nature Commun. 10, 594 (2019) Pfender et al. (arXiv.1806.02181)[4] Nature 571, 230 (2019) Cujia et al. (arXiv.1806.08243)→ Suppressing back actions by weak measurement