color centers in diamond - eth z...color centers in diamond slides and material courtesy of: joerg...

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Color Centers in Diamond

Slides and material courtesy of: Joerg Wrachtrup, Ronald Hanson, Lilly Childress, and Christian Degen as indicated 6-Apr-17Andreas Wallraff, Quantum Device Lab 3

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Reading: Papers, Reviews, Other Material

6-Apr-17Andreas Wallraff, Quantum Device Lab 4

Reviews:• NV centers (long): M. W. Doherty, N. B. Manson, P.

Delaney, F. Jelezko, J. Wrachtrup, and L. C. Hollenberg, The nitrogen-vacancy colour centre in diamond, Physics Reports 528, 1-45 (2013). (http://www.sciencedirect.com/science/article/pii/S0370157313000562)

• NV centers (less long): F. Jelezko, and J. Wrachtrup, Single defect centres in diamond: A review, Phys. Stat. Sol. (a) 203, 3207 (2006). (http://dx.doi.org/10.1002/pssa.200671403)

• Quantum sensing: C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, arXiv:1611.02427(2016). (https://arxiv.org/abs/1611.02427)

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NE8b (Nickel, Nitrogen)

550 600 650 700 750 8000

10

20

Fluo

resc

ence

, a.u

.Wavelength, nm

ZPL (N-V)-

ZPL (N-V)0

Science 276, 2012-2014 (1997) Phys. Rev. Lett. 94, 180602 (2005)

500 550 600 6500

2

4

6

8

Inte

nsity

(a.u

.)

Wavelength (nm)

6C• Carbon• 4 valence electrons• sp3 hybridization

OV

o

TR12 (interstitial Carbon)PRB 72, 035214 2005

The Dopants

Slide material: Joerg Wrachtrup, Stuttgart

standard diamond lattice


7N• Nitrogen• 5 valence electrons

NV (Nitrogen, Vacancy)

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1

2

k21

CB

Opt

ical

tra

nsiti

on

Fluo

resc

ence

Level Scheme of Color Centers


VB

Properties:• Large band gap Eg = 5.4 eV• Defects form inter-gap states


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10nm ND

QD

Shielding by the Diamond Lattice Provides Photostability


⇒ Oxidation

⇒ ionization

⇒ perfect stability

molecule


Phot

o-lu

min

esce

nce

coun

ts

||

1

2

k21

Opt

ical

tra

nsiti

on

Fluo

resc

ence

Level Structure of Color Centers


1-10

• Electron spin states are spectroscopically resolvable

• Defect behaves as a single atom, trapped in the diamond lattice

• Level structure similar to trapped ions or atoms

⇒ Diamond provides a solid state ion trap ⇒ Experimental power similar to trapped

particles, but much easier to transform into certain applications, e.g. sensing and quantum networks

CB

VB


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The NV Center


• Joint defect consisting of• Vacancy• Neighboring substitutional N

• Negatively charged (NV-)

• Six electron (= two hole) system

3E

3A

0

-11

2.87 GHz

637nm1.95 eV470 THz


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The NV Center


637nm

3E

1A

3A

02.87 GHz

t=300ns

-11

Features:• Initialization:

Optical spin polarization of the ground state (« Laser cooling »)

• Coherence:Narrow lines, T2 = 1 ms, linewidth of ground state levels 1 kHz.

• Readout:Optical detection of the spin state


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The NV Center


637nm

3E

1A

3A

02.87 GHz bright

dark-11






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Experimental Setup for Optical Spin Readout


Confocal microscope with microwave access

MW wire

Phot

on c

ount

rate

(Hz)

Image of implanted diamond


||MW

1 mm

Slide material: Christian Degen, ETHZ


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10µm

Wiring up NV Centers

Slide material: Ronald Hanson, TU Delft

high-fidelity spin control via magnetic resonance

dc Stark tuning:

deterministically placed silicon immersion lens (SIL)

CVD diamonds grown by Element6


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Spin-Resolved Optical Excitation (T < 10K)

Early work by Stuttgart, Harvard, HP LabsSlide material: Ronald Hanson, TU Delft

from 470 THz transition


637nm

3E

1A

3A

02.87 GHz

t=300ns

-11

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Initialization and Readout by Resonant Excitation

Nature 477, 574 (2011)Slide material: Ronald Hanson, TU Delft

Initialization

fidelity > 99.7%

Single-Shot Readout

at the time at TU Delft:

best fidelity F ≈ 98%

ms=0<n>=8.5

ms=±1<n>=0.06


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Optically Detected Magnetic Resonance

Gruber et al, Science (1997)Balasubramanian et al, Nature (2008) Schirhagl et al, ARPC (2014)Slide material: Christian Degen, ETHZ

GHz2.6 2.8 3.0 3.2

B = 0

2.8 mT

5.8 mT

8.3 mTγ = 28 GHz/T

⟩|𝟎𝟎

⟩|±𝟏𝟏

2γB

Inte

nsity

⟩|−𝟏𝟏 ⟩|+𝟏𝟏

Experimental Sequence:• Set magnetic field• Initialize optically• Apply microwave with controlled

frequency and amplitude• Read out optically


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Manipulating a Single Spin


|0>

|-1>|1>

PulsedMicrowave

Experimental sequence:

τ

Laserprepare

Laserread out

Fluorescenceintensity

τ0 1−10 −+ i

2π π

• Pulsed sequence consisting of laser cooling, spin manipulation by pulsed microwaves and detection

• Signal is <1photon/repetition => many repetitions• Similar to ion trap, but experimentally easier

single qubit gates: microwave pulses


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NV Center: Intermediate Summary


637nm

3E

1A

3A

2.87 GHz

t=300ns

τ0 1−10 −+ i

2π π

⟩1|

⟩0|






• Single qubit gates: Microwave pulses

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Three Approaches to Coupling NV Centers


Photons Magnetic dipolar coupling Use nuclear spin qubits

Cirac, Zoller, Lukin `06

• Proper levels and transitionsManson, Hemmer, Santori

• Transfer limited photons:Batalov et al. PRL 08

• But: bad coupling efficiency

3coherent 2d T∝

• Magnetic dipoles

14N

C

V

C

C

• Couple NV to surrounding nuclei

• Couple nuclei via NV

• Read out single nuclei


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Coupling by Dipolar Interaction


ground state energy levels:

NV A

NV B

⟩1|⟩0|

⟩1|

⟩0|

coupling energy

Idea: • NV B interacts with the magnetic dipole of the electron spin of NV A• Depending on the state NV A, NV B has another resonance frequency


NV B

NV A

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Spin Hamiltonian: Coupled Spins

Slide material: Lieven vanderSypen, TU Delft

Typical values forJ depending on distance between spins• from kHz up to few 10 MHz for electron spins• up to few 100 Hz for nuclear spins

Ising coupling term

solid (dashed) lines are (un)coupled levels

J > 0: antiferro mag.

J < 0: ferro-mag.

16 configurations

Example with 5 nuclear spins:


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Single spin readout

Coherent interactionLength scale ∼some10 nm,

Magnetic Dipole Coupled Spin Arrays


STED on NV: 10nm resolution: Hell et al., Nat. Phot. (2009)

T2 limitCoupling vs. distance:


• Distance dependence of dipole coupling scales as d-3

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Take Pure (CVD) Diamond and Implant Nitrogen!


*Element Six Ltd., UK

N+ ions

1,1µm

surface

depth ~ 200 nm FWHM

105 N104 N103 N

N+ ions, 2MeV

10µm

Annealingat 900°C

Success chance 1% to have two coherently interacting dimers


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Two Defect CentersElectron spin ground state:

5nm

0

1+

1−


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Dipolar Coupling: Switching of Spin B

NVA

0

0

NVB

0

1+

1−

NVA

Initial state F≥85%

mw mw

Ramsey fringe on NVA

0 10 20 30 40 50 60-0,5

0,0

I PL [a

.u.]

evolution time Τ [µs]

NVB

π/2 π/2


NVA NVB

0 10 20 30 40 50 60-0,5

0,0

I PL [a

.u.]

evolution time Τ [µs]

Switchable interaction! Coupling between defect: 0,5,10,20 kHz

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Controlled-NOT for Spin-Spin Coupling Before AfterA B A B↑ ↑ ↑ ↑↑ ↓ ↓ ↓↓ ↑ ↓ ↑↓ ↓ ↑ ↓

” flip A if B ↓”

if spin B is ↑

YA90 XA

90Delay1/2JAB

xy

z

xy

z

xy

z

xy

z

z z z

if spin B is ↓x

yx

yx

yx

y

z

| 0 ⟩

| 1 ⟩

| 0 ⟩ + i | 1 ⟩√2

| 0 ⟩ + | 1 ⟩√2

time

A target bitB control bit

wait

different rotation direction depending on control bit


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Φ+= 12(| ⟩+ + +| ⟩− − )

Fidelity Φ+: 0.67(theoretically: 0.9)

decoupling

Bell State: Density Matrix Tomography


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3coherent 2d T∝


14N

C

V

C

C





|| 6-Apr-17Andreas Wallraff, Quantum Device Lab

Coupling Nearby 13C Nuclei


14N

13C

V

13C

Flip NV conditioned on nuclear state

Flip nuclei conditioned on NV and nuclear state

• 12C has no nuclear spin (I = 0) and magnetic moment

• 13C nuclear spins (I = ½, 1.1 % abundance) create magnetic field at NV

• CNOT gate is implemented by selective microwave transition(flip nucleus if other nucleus is in |0>)

Splitting of electron spin spectrum:

74


Creation of Entangled States


• Creation of entangled states possible

P. Neumann et.al., Science 320, 1326 (2008)• Scaling up to four nuclear spins

straightforward• Combination of electron and nuclear

spin states for quantum register• Scaling to 10-20 spins presumably

possible

1100

Flip NV conditioned on nuclear state

Flip nuclei conditioned on NV and nuclear state

75


Different development: QND readout of nuclear spins


Readout of single quantum systems• Standard readout

• <1 photon per run limited by photon shot noise (at best)• Example: fluorescence detection of single NV

• Single shot readout• determine spin state in a single run but destroy the

system or its quantum state• requires >1 photon per run limited by quantum shot

noise• Example: Photon detection in Photomultiplier

• Quantum non demolition (QND) readout• >1 photon per run and preservation of the system and

its spin state• Projective measurement• Example: Microwave photons in circuit QED

10 + 0

76


QND Readout of a Single Nuclear Spin


14N

C

V

C

C

n-spinstate|Ψ⟩

e-spin

correlaten- and e-spin

measuree-spin

esr π

time

laser

79

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Repetitive QND measurements reveal quantum jumps of a single nuclear spin (in diamond at room temperature)

6-Apr-17Andreas Wallraff, Quantum Device Lab

Observing Flips of a Single Nuclear Spin

P.Neumann et.al., Science 329, p.542 (2010) 80

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Photon counting histogram of time trace

Two almost perfect Poissonians Threshold for state discrimination

– Fidelity from overlap 99%– Fidelity to detect given state 92%

thre

shol

d

6-Apr-17Andreas Wallraff, Quantum Device Lab

Fidelity of Spin State Detection

Slide material: Joerg Wrachtrup, Stuttgart 81

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3coherent 2d T∝


14N

C

V

C

C





color centers in diamond - eth z...color centers in diamond slides and material courtesy of: joerg...

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