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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
6-Apr-17Andreas Wallraff, Quantum Device Lab 5
7N• Nitrogen• 5 valence electrons
NV (Nitrogen, Vacancy)
||
1
2
k21
CB
Opt
ical
tra
nsiti
on
Fluo
resc
ence
Level Scheme of Color Centers
Slide material: Joerg Wrachtrup, Stuttgart
VB
Properties:• Large band gap Eg = 5.4 eV• Defects form inter-gap states
6-Apr-17Andreas Wallraff, Quantum Device Lab 6
||
10nm ND
QD
Shielding by the Diamond Lattice Provides Photostability
Slide material: Joerg Wrachtrup, Stuttgart
⇒ Oxidation
⇒ ionization
⇒ perfect stability
molecule
6-Apr-17Andreas Wallraff, Quantum Device Lab 7
Phot
o-lu
min
esce
nce
coun
ts
||
1
2
k21
Opt
ical
tra
nsiti
on
Fluo
resc
ence
Level Structure of Color Centers
Slide material: Joerg Wrachtrup, Stuttgart
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
6-Apr-17Andreas Wallraff, Quantum Device Lab 8
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The NV Center
Slide material: Joerg Wrachtrup, Stuttgart
• 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
6-Apr-17Andreas Wallraff, Quantum Device Lab 10
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The NV Center
Slide material: Joerg Wrachtrup, Stuttgart
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
6-Apr-17Andreas Wallraff, Quantum Device Lab 11
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The NV Center
Slide material: Joerg Wrachtrup, Stuttgart
637nm
3E
1A
3A
02.87 GHz bright
dark-11
6-Apr-17Andreas Wallraff, Quantum Device Lab 12
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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Experimental Setup for Optical Spin Readout
Slide material: Joerg Wrachtrup, Stuttgart
Confocal microscope with microwave access
MW wire
Phot
on c
ount
rate
(Hz)
Image of implanted diamond
6-Apr-17Andreas Wallraff, Quantum Device Lab 13
||MW
1 mm
Slide material: Christian Degen, ETHZ
6-Apr-17Andreas Wallraff, Quantum Device Lab 14
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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
6-Apr-17Andreas Wallraff, Quantum Device Lab 15
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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
6-Apr-17Andreas Wallraff, Quantum Device Lab 18
637nm
3E
1A
3A
02.87 GHz
t=300ns
-11
||
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
6-Apr-17Andreas Wallraff, Quantum Device Lab 19
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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
6-Apr-17Andreas Wallraff, Quantum Device Lab 20
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Manipulating a Single Spin
Slide material: Joerg Wrachtrup, Stuttgart
|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
6-Apr-17Andreas Wallraff, Quantum Device Lab 44
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NV Center: Intermediate Summary
Slide material: Joerg Wrachtrup, Stuttgart
637nm
3E
1A
3A
2.87 GHz
t=300ns
τ0 1−10 −+ i
2π π
⟩1|
⟩0|
6-Apr-17Andreas Wallraff, Quantum Device Lab 52
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
• Single qubit gates: Microwave pulses
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Three Approaches to Coupling NV Centers
Slide material: Joerg Wrachtrup, Stuttgart
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
6-Apr-17Andreas Wallraff, Quantum Device Lab 53
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Coupling by Dipolar Interaction
Slide material: Joerg Wrachtrup, Stuttgart
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
6-Apr-17Andreas Wallraff, Quantum Device Lab 54
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:
6-Apr-17Andreas Wallraff, Quantum Device Lab 55
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Single spin readout
Coherent interactionLength scale ∼some10 nm,
Magnetic Dipole Coupled Spin Arrays
Slide material: Joerg Wrachtrup, Stuttgart
STED on NV: 10nm resolution: Hell et al., Nat. Phot. (2009)
T2 limitCoupling vs. distance:
6-Apr-17Andreas Wallraff, Quantum Device Lab 56
• Distance dependence of dipole coupling scales as d-3
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Take Pure (CVD) Diamond and Implant Nitrogen!
Slide material: Joerg Wrachtrup, Stuttgart
*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
6-Apr-17Andreas Wallraff, Quantum Device Lab 57
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Two Defect CentersElectron spin ground state:
5nm
0
1+
1−
6-Apr-17Andreas Wallraff, Quantum Device Lab 60
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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
6-Apr-17Andreas Wallraff, Quantum Device Lab 61
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
6-Apr-17Andreas Wallraff, Quantum Device Lab 62
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Φ+= 12(| ⟩+ + +| ⟩− − )
Fidelity Φ+: 0.67(theoretically: 0.9)
decoupling
Bell State: Density Matrix Tomography
6-Apr-17Andreas Wallraff, Quantum Device Lab 64
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Three Approaches to Coupling NV Centers
Slide material: Joerg Wrachtrup, Stuttgart
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
6-Apr-17Andreas Wallraff, Quantum Device Lab 73
|| 6-Apr-17Andreas Wallraff, Quantum Device Lab
Coupling Nearby 13C Nuclei
Slide material: Joerg Wrachtrup, Stuttgart
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
|| 6-Apr-17Andreas Wallraff, Quantum Device Lab
Creation of Entangled States
Slide material: Joerg Wrachtrup, Stuttgart
• 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
|| 6-Apr-17Andreas Wallraff, Quantum Device Lab
Different development: QND readout of nuclear spins
Slide material: Joerg Wrachtrup, Stuttgart
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
|| 6-Apr-17Andreas Wallraff, Quantum Device Lab
QND Readout of a Single Nuclear Spin
Slide material: Joerg Wrachtrup, Stuttgart
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
||
Three Approaches to Coupling NV Centers
Slide material: Joerg Wrachtrup, Stuttgart
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
6-Apr-17Andreas Wallraff, Quantum Device Lab 82
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