Quantum Spintronics Design(NV centers in diamond)

Eisuke Abe
RIKEN Center for Emergent Matter Science2020.09.02
CMD Spintronics Design Course(Online)

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)

Quantum technologies
Silicon (2001—2006, Keio & 2010—2011, Oxford)
Superconducting circuits (2019—, RIKEN)

Quantum Computing

Self-assembled quantum dot(2011—2015, Stanford)

Quantum Network

NV center in diamond(2015—2019, Keio)

Quantum Sensing

Quantum technologies
Quantum Computing

NV center in diamond(2015—2019, Keio)

Quantum Network

Quantum Sensing

Outline••

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

Quantum sensing––––

DC magnetometry
AC magnetometry
Detection of proton spin ensemble
Ultrahigh resolution sensing

Outline••

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

Quantum sensing––––

DC magnetometry
AC magnetometry
Detection of proton spin ensemble
Ultrahigh resolution sensing

Diamond envy

C©GIA

ρN = 1.77 x 1023 cm-3

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

S=1Not like…

VNC

©GIA

ρN = 1.77 x 1023 cm-3

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)
exey
a1a’1

Energy levels
C.B. (Eg = 5.47 eV = 227 nm)

ms = ±1|e〉 m = 0s|m〉637 nmms = ±1|g〉

2.87 GHz
ms = 0V.B.

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

515 nmms = ±1|e〉 m = 0s|m〉637 nm|g〉2.87 GHz
ms = 0V.B.

2.5 μm x 2.5 μm

Count rate (cps)ms = ±1

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

One photon at a time

515 nmms = ±1|e〉 m = 0s|m〉637 nmms = ±1|g〉

2.87 GHz
ms = 0V.B.

PL = 1.0 mW

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

The non-radiative & spin-selective channel provides
a means to read out & initialize the NV spin

515 nmms = ±1|e〉 m = 0mS = 0s|m〉637 nmmS = −1Difference

ms = ±1|g〉

2.87 GHz
ms = 0V.B.

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

Zero-field splitting 𝐻 = 𝐷𝑆𝑧2
D = 2.87 GHz

515 nmms = ±1|e〉 m = 0s|m〉637 nmms = ±1

ms = 0 ↔ ±1|g〉

2.87 GHz
ms = 0V.B.

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

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

515 nmB0 ‖ NV-axis

ms = ±1|e〉 m = 0s

637 nm2γeB0

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

Laser

SPCM
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 mmAIP Advances 10, 025206 (2020)
Misonou et al.

Outline••

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

Quantum sensing––––DC magnetometry
AC magnetometry
Detection of proton spin ensemble
Ultrahigh resolution sensing

Quantum sensing with NV centers••••••

B, E, T, S...
DC & AC modes
Wide temperature range
Nondestructive
High spatial resolution
Various modalities

Nanodiamond & biology

Nature 500, 54 (2013)

Near-surface NV center & NMR
Scanning probe & condensed matter

Science 351, 836 (2016)
Rev. Sci. Instrum. 87, 063703 (2016); Nature 549, 252 (2017)

Outline••

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

Quantum sensing––––

DC magnetometry
AC magnetometry
Detection of proton spin ensemble
Ultrahigh resolution sensingDC magnetometry
Single NV in bulk (mS = 0 ↔ −1)

DC sensitivity𝜂sn(cw) =FWHM (MHz)𝛿𝛿𝛾e 𝐶 𝐼0Contrast (%)

8.2 MHz(0.18)(30 kcps)0.5Count rate (/s)→ 10 μT/Hz0.5

High sensitivity = Narrow δν, high C, high I0
J. Appl. Phys. 123, 161101 (2018) Abe & Sasaki

Vector magnetometry
Ensemble NV at the surface (mS = 0 ↔ ±1)

𝐻(𝑖)= 𝐷 𝑆𝑧𝑖≈ 𝐷 𝑆𝑧𝑖22+ 𝛾e 𝑩0 ⋅ 𝑺(𝑖)+ 𝛾e 𝐵0 cos 𝛽𝑖 𝑆𝑧
δB𝑖

B0 = 7.4 mTN4N1β1VN3N2β1 = 29o, β2 = 132o, β3 = 109o, β4 = 83oRev. Sci. Instrum. 87, 053904 (2016) Sasaki et al.
J. Appl. Phys. 123, 161101 (2018) Abe & Sasaki

Magnetic imaging: Biology
M. magneticum AMB-1 bacterium(470 nm for bacterial
viability assays)

Magnetosome (Fe3O4 nanoparticle)
37 G(660 nm for bright-field imaging)

Nature 496, 486 (2013) Le Sage et al.

Magnetic imaging: Biology
Magnetotactic bacteria (MTB) adhered to the diamond surface(100 x 30 µm2 area with 400 nm resolution)“Live”“Indeterminate”

Dried MTB

“Dead”Nature 496, 486 (2013) Le Sage et al.

Magnetic imaging: Biology
Measured

Simulated

γ = 9.27 x 10-24 Am2Vector plots

Nature 496, 486 (2013) Le Sage et al.

Magnetic imaging: Geoscience

Geochem. Geophys. Geosyst. 18, 3254 (2017) Glenn et al.

Magnetic imaging: Geoscience

https://www.sciencemag.org/news/2020/04/diamondmicroscope-reveals-slow-crawl-earth-s-ancient-crust
https://paleomag.fas.harvard.edu/Geochem. Geophys. Geosyst. 21, e2020GC009147 (2020) Fu et al.

Outline••

Basics of NV centers in diamond–––

Structure
Optical properties
Spin properties and control

Quantum sensing––––

DC magnetometry
AC magnetometry
Detection of proton spin ensemble
Ultrahigh resolution sensing

Nuclear spin sensing
Immersion oil

Detection volume ≈ (dNV)3
dNV
Science 339, 561 (2013)

Diamond

NV spinNature Commun. 6, 8527 (2015)

Nuclear spins precess at fac = a few kHz–MHz under B0
Weak AC magnetic field on the NV spin
Detect using quantum coherenceMagnetic resonance
Torque equation (Larmor precession)

𝐵0 DC field𝑑𝝁= 𝝁 × 𝛾𝑩0𝑑𝑑

Rest frame:
Seen to rotate at 𝛾𝐵0

Gyromagnetic ratio

Magnetic moment: 𝝁 = 𝛾𝑱𝛾𝐵0𝝁Ω

𝑥�

𝑥

Frame rotating at angular velocity 𝛀:
Rotate slower…why?

Joseph Larmor(1857–1942)(from Wikipedia)

Magnetic resonance𝑧̂𝐵0

𝐵0 DC field

Ω𝛾𝑥�

𝛾𝐵0𝝁

Rest frame:
Seen to rotate at 𝛾𝐵0

Ω

𝑥�

𝑥

Frame rotating at angular velocity 𝛀:
Rotate slower…why?

DC field along the 𝑧 direction becomes weakerMagnetic resonance𝑧̂𝐵0Ω𝛾

𝐵0 DC field

Effective magnetic fieldΩ𝐵eff = 𝐵1 𝑥� + 𝐵0 −𝑧̂𝛾𝐵1𝑥�AC field rotating in the 𝑥𝑥 plane at Ω𝛾𝐵0𝝁Rest frame:
Seen to rotate at 𝛾𝐵0Ω𝑥�

𝑥

Frame rotating at angular velocity 𝛀:
Rotate slower…why?

DC field along the 𝑧 direction becomes weakerMagnetic resonanceRest (non-resonant) frame

Frame rotating at 𝛀 = 𝜸𝜸𝟎𝜇𝑧̂ (𝑡 = 0)𝝁π/2 pulse−𝜇𝑦� (𝑡 = 4/𝛾𝐵1 )𝐵1−𝜇𝑧̂ (𝑡 = 2/𝛾𝛾1 )π pulse𝑥�• Rotations about the ±𝑥�, ±𝑦� axes are realized byadjusting the microwave phases• Rotation about the 𝑧̂ axis is superposed whenobserved from the rest (non-resonant) frame

Quantum bit
Qubit, spin-1/2 (NV is spin-1!)

Superposition state"0" ≡ 𝑚𝑠 = 0

𝜓 = 𝛼 0 + 𝛽|1〉"1" ≡ 𝑚𝑠 = −1𝜓

= 𝑒 𝑖𝑖𝜃𝜃
𝑖𝑖
cos 0 + 𝑒 sin |1〉
22

Global phase𝜃𝜃𝜓 = cos 0 + 𝑒 𝑖𝑖 sin |1〉22

𝛼 2+ 𝛽 2=10≤𝜃≤𝜋0 ≤ 𝛾, 𝜙 < 2𝜋0≤𝜃≤𝜋0 ≤ 𝜙 < 2𝜋

Bloch sphere
Qubit, spin-1/2 (NV is spin-1!)"0" ≡ 𝑚𝑠 = 0"1" ≡ 𝑚𝑠 = −112|0〉θ( 0 − 𝑖|1〉)12( 0 + |1〉)

ɸx|1〉

𝜃𝜃𝑖𝑖
𝜓 = cos 0 + 𝑒 sin |1〉2212( 0 − |1〉)y12

( 0 + 𝑖|1〉)

Rabi oscillation
Initialization

Microwave

ReadoutTp

ms = 0π/2-pulse

π-pulsems = −1Quantum coherence

0 ≡ 𝑚𝑠 = 0

Ψ = 𝛼 0 + 𝛽|1〉1 ≡ 𝑚𝑠 = −1

T2: measure of how long a superposition state is preserved

Measurement of T2
Time domain → Decay time constant T2
π/2

Frequency domain → Lorentz width

Decay of the transverse signal
t1/T2MW pulseνeνMeasurement of T2
Time domain → Decay time constant T2
π/2

Frequency domain → Lorentz width

Decay of the transverse signalt

1/T2*MW pulseνeνe+ δν

Inhomogeneous line broadening
Seen to precess at δν in the frame rotating at νe
π/2

yt=0t = τ(−)

νSpin echo
Initialization

ππ/2

τ

Modulation function

π/2τPositive

Sign of phase accumulation
Negative

Phase accumulation
by DC field(angle from the y axis)
π/2

yt=0t = τ(−)

Readoutt = τ(+)

t = 2τ

Coherence time
T2 = 6.2 μsp = 1.26

Stretched exponential decay
2𝜏exp −𝑇2𝑝Near-surface NV center• N+ implantation into 12C (I = 0) layer• dNV = 6.26 nm• B0 = 23.5 mT
AIP Advances 10, 025206 (2020) Misonou et al.

AC magnetometry
CP (N = 4)π/2π

τ/2ππττπτ

π/2

τ/2Modulation function

AC field at fac = 1/2τπBacSensor phase buildup = loss of coherence𝑡𝛾𝐵ac � cos 2𝜋𝑓ac 𝑡 𝑑𝑑0φ = 8τγBac/πNuclear spin sensing• T2 = 6.2 μs @B0 = 23.5 mT• N = 64 (XY16)• (2τ)−1 = 64/(2 x 32 μs) = 1 μs
→ γHB0 = (42.577 kHz/mT) x B0 = 1.00 MHz
AIP Advances 10, 025206 (2020) Misonou et al.

Nuclear spin sensing
𝐶(𝜏) = 𝑓(𝐵rms )𝐵rms =

5𝜋𝜋𝜇0ℎ𝛾H
34𝜋96𝑑NV

Phys. Rev. B 93, 045425 (2016)

••
•
•
•
•

Proton density ρ = 6 x 1028 m−3 (known)dNV = 6.26 nm
Brms ≈ 560 nT
Detection volume (dNV)3 ≈ 0.25 zL (zepto = 10−21)# of proton ρ(dNV)3 ≈ 1500
Thermal pol. (10−7) vs. statistical pol. (1500)0.5 ≈ 39
AIP Advances 10, 025206 (2020) Misonou et al.

Toward single-molecular imaging• Spectral resolution→ Easy to resolve isotopes→ Need to measure J-couplings & chemical shifts (ppm!)→ Limited by sensor/memory lifetimes (T2e/n, T1e/n)• 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 ϕNuclear spin

NV spinToward single-molecular imaging• Spectral resolution→ Easy to resolve isotopes→ Need to measure J-couplings & chemical shifts (ppm!)→ Limited by sensor/memory lifetimes (T2e/n, T1e/n)• 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

Nuclear spin

NV spinAC magnetometry
CP (N = 4)

π/2π

τ/2ππ

τ

τπ

τ

π/2

τ/2

Modulation function

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
α1α3α2α4α5ts = 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•••••[NV] ≈ 3 x 1017 cm−3# of NV ≈ 5 x 109Vdetect ≈ 25 pL# of protons ≈ 2.5 x 1015
RF pulse → FID
See also: Science 357, 67 (2017) Aslam et al. [B0 = 3 T, fe = 87 GHz, T1n = 260 s]
Nature 555, 351 (2018) Glenn et al.

NMR spectroscopy
J-coupling

Chemical shift

See also: Science 357, 67 (2017) Aslam et al. [B0 = 3 T, fe = 87 GHz, T1n = 260 s]
Nature 555, 351 (2018) Glenn et al.

Toward single-molecular imaging• Spectral resolution→ Easy to resolve isotopes→ Need to measure J-couplings & chemical shifts (ppm!)→ Limited by sensor/memory lifetimes (T2e/n, T1e/n)• 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

Nuclear spin

NV spinSummary• Applications to biology, geoscience, condensed matter...
• Tools for single-molecule imaging/structural analysis arebeing developed→ Ultrahigh resolution sensing[1,2,3], resolving chemical
shifts[3,4] & suppression of back action from n-spins[5,6]→ Determination of the position of individual n-spins[7,8,9][1] Science 356, 832 (2017) Schmitt et al. (Ulm)[2] Science 356, 837 (2017) Boss et al. (ETH)[3] Nature 555, 351 (2018) Glenn et al. (Harvard)[4] Science 357, 67 (2017) Aslam et al. (Stuttgart)[5] Nature Commun. 10, 594 (2019) Pfender et al. (Stuttgart)[6] Nature 571, 230 (2019) Cujia et al. (ETH)[7] Phys. Rev. B 98, 121405 (2018) Sasaki et al. (Keio)[8] Phys. Rev. Lett. 121, 170801 (2018) Zopes et al. (ETH)[9] Nature 576, 411 (2019) Abobeih et al. (Delft)