Spin state tomography of a single electron spin in a diamond with a single photonfor entanglement swapping
Naeko Niikura, Hideo Kosaka
Yokohama National University

Motivation

We demonstrate optical preparation and readout of electron spin coherence in a single NV center in diamond for quantum repeater.

Quantum information communication

Quantum repeater Fundamentally secure communications
 Communication distance is : 200km (present)→ >1000km (future) A quantum repeater is requiredNV center in diamondEntanglement swapping

emissionabsorption

N : Nitrogen
V : Vacancy[1]electron……

memoryAliceEntanglement detection……

memory[3]

BobBell measurement

entanglement

photonMost important function for quantum repeaters

 Long coherence time (T2e>0.6s at 77K, T2n>1s at RT) [4],[5],[6] Single electron/nuclear spin manipulation [7] Optical Initialization & readout of electron spins [7][1] E. Togan et al., Nature 466, 730 (2010)[2] H. Bernien et al., Nature 497, 86 (2013)

Objectives

Approach

Experimental setup

Excitation to spin-orbit entangled stateMicrowave resonance

1. Microwave spin coherence generation

PCOptical resonance
10ES

3. Photon-spin entanglement detection

EX e

4. Optical spin state tomography

Nonresonantexcitation
532nm(Green)Heralded by single photon click
5. Photon-to-nuclear spin state transfer
Via quantum teleportation

l

1 e

A1 e

EY e

Via spin-orbit entanglementl

1 e  E 

E2 e
E1 e

0.9

10MHz

0.8

2860

2870

0eeee

Polarization ofreadout









  XY





 i   i    D  i    A

 i   i    A  i    DV|  ›MW(Photon polarization state)(Electron spin state)

HMW switch

Multiphoton

EySingle
photon470.4790

Single-photon
Counter (APD)
Monochromater

T=5K

MW offMW on

Ex
E1 E22A2

A1

470.475

470.480

470.4853us

Microwave(Spin pumping)

180ns

Red light 1(Spin preparation)

180ns

Red light 2(Spin readout)

10ns

Gate
(photon count)

Polarization ofreadout

0.7
0.6
0.5
0.4
0.3
0.2
0.1



1



F+z = 97%2| + ›ph10|  ›ph8

Spin state readout

Coherent
population trapping64204590

135

180

HDVAH



ee

Spin state preparation by photon

D 180

1.200E49800

7600

- 135

5400

3200

A90



45D01000+04590135180

D

+A

-D

Polarization angle of writing light (deg.)① Arbitrary spin state preparation by light② Excitation to A2 state by light③ Observing luminescence of PSB photon→Spin state readout

Arbitrary spin state generation andreadout by light are demonstrated.

4. Optical spin state tomography
YF+z = 97%

VDA      i    i  

i+zi

1
0.9

0.8
0.7
0.6

0.8

0.5
0.4
0.3
0.2

0.5

0.1
00.1

F-z = 96%

Crystal orientation (100)laser

10ns|A2

H

0.70.6iF-y = 99%

0.4
0.3

F-x = 98%-x-y0.2

0H1VH

F-x = 98%

Realpart

TypeⅡa（Nitrogen percentage < 5ppb）

Spin state writing and readout with light

121
0.9

0.8

0

Diamond (CVD)PSB photon
0.9Sample

φ25um
Copper wire

2. Optical arbitrary spin state preparation

The luminescence of PSB photon is observedin near V polarization. Therefore, it
demonstrated that spin state prepared by
MW is    . (Ref. left table)

Two-photon
interferometer

Spectrum
Analyzer

Pulse width

Green laser(Spin initialization)

140

Phonon Side Band (PSB)
photonAmplifier

Pulse sequence

X

1



Z



Preparedspin stateii

EO modulator

Bloch sphere representation

D

470.4789

3. Photon-spin entanglement detectionV

EO modulator

Polarization angle of readout light (deg.)① Coherent spin state preparation by microwave② Excitation to A2 state by light③ Observing luminescence of PSB photon→Spin state readout

Conditional probability

Bloch sphere

Ae

0s

Polarization ofwriting| + ›MW+

 H

Poincare sphere

AO modulator

Light frequency (THz)4Linear polarization

It is possible to read electron spin state prepared by microwave orlight by observing the luminescence of PSB photon.

Microwave(2.88GHz)

16|  ›pheV



470.4788

StrainSpin state preparation by MW   H

Red light 2（637nm）

Spin state readout with lightDegenerate470.4787

Excitation to A2 state, where orbit and spin areentangled, was observed by magneto-optical doubleresonance.

Spin state readout

Red light 1（637nm）

0Light frequency (THz)with microwave and red light| + ›ph

Green laser（532nm）

Multi
photonSpin-orbit entangled statee

Polarization ofwriting②Spin pump2

6

470.470|A2

4

1. Microwave spin coherence generation

Preparedspin state

Pulse generator~Lifetime limit

8PSB photon30MHz

0Photon count (K/s)

Z  

62890

with MW + red lightzero field splitting(～2.88GHz)

MWPhoton-spin correlation
A2   2880

10

1 e

Experimental results④ReadMagneto-optical double resonanceNon-radiative decay

with only red light③prepare0.7

resonant
excitation～637nm(Red)

initialize①Initialize

Ex

8

Microwave frequency (MHz)GSMW offwith red light

Photon count (K/s)

A2 e  E 

Photon count (K/s)

Via coherent population trapping

1.0

Photon count (a.u.)

2. Optical arbitrary spin state preparation

with MW

Photon countquantum statetransfer[3] N. Mizuochi et al., Nature Photonics 6, 299 (2012)[4] G. Balasubramanian et al., Nat. Mater. 8, 383 (2009)[5] M. V. G. Dutt et al., Science 316, 1312 (2007)[6] P. C. Maurer et al., Science 336, 1283 (2012)[7] A. Gruber et al., Science 27, 276 (1997)

Polarization angle of readout light (deg.)entangled photon pair[2]2VDF+x = 92%

1A

F-y = 99%

D2A

F+y = 93%

0.5

i

F+x = 92%

1+y+xF+y = 93%-10-1-0.5-z-1Imagpart
0.50.25+10-0.25

Definition of fidelity

F-z = 96%-0.5

F  Tr(ideal  meas 

Photon-spin entanglement detection via spin-orbit entanglement is demonstrated with F>92%.

c matrix representation

Spin measurement process tomography

 spin   cij i  photon j (i : Pauli operators)

Real part

Real part

0.5
0.25

0.25

00.40Z0

Y-0.2I X Y ZI

X

-0.25

00000000Z

Y-0.5Z-flip process00:  spin   z  photon z01

Via coherent population trapping0.250

-0.25

0.2I X

YI
Z
Error processes

X

By misalignment & stain| -ph|e -0.25| -ph|e-0.5| ph|e-0.5| -ph|e| +ph|e+| ph|e| +ph|e| +ph|e| +ph|e+| -ph|e| ph|e| +ph|e| +ph|e| -ph|e| -ph|e| -ph|e0

1 0ˆ
M
2 0001
1001
1000
 A2 A20
0

2. Optical arbitrary spin state preparation(Entanglement
measurement

Tr Mˆ  ˆ photon  ˆ spin

eClassicalmessage

1. Photon-to-nuclear spin state transfer
Via quantum teleportation~10km

2. Demonstration of entanglement swapping

PhotonElectron~100us0.5

1. Microwave spin coherence generation

Ent. Swapping
pe

0.5

0.8
0.6

Seedentanglement

Ent. swapping

Imaginary part

Imaginary part

1Outlookp

F=95%

0
0c 0
0Conclusions

timeSpin preparation process tomography

3. Photon-spin entanglement detection
Via spin-orbit entanglement (F>90%)



4. Optical spin state tomography
Heralded by single photon click

Acknowledgements
This work was supported by FIRST, NICT, Grant-in-Aid for Scientific Research (A)-JSPS (No.
24244044), and DYCE-MEXT (No. 23104701). We thank Joerg Wrachtrup, Norikazu Mizuochi,
Kae Nemoto and Burkhard Scharfenberger for their collaboration and discussions.