Studying Photon Number Distribution of

NV-Centre Emission in Nano-Diamond

W. Schmunk1 M. Gramegna3 G. Brida3 I. P. Degiovanni3

M. Genovese3 H. Hofer1 S. Kück1 L. Lolli3 M. G. A. Paris4

S. Peters1 M. Rajteri3, A. M. Racu, A. Ruschhaupt2 E. Taralli3 P. Traina3

1Physikalisch-Technische Bundesanstalt, Germany

2Istituto Nationale di Ricerca Metrologica, Italy

3Universita degli Studi di Milano, Italy

4Leibniz Universität Hannover, Germany

Motivation

Application of single photon sources …

Quantum physics

Quantum computing

Quantum Key Distribution

Biomedical physics

Efficiency calibration of single photon detectors

Motivation

Why photon number distribution is of interest?

e.g.

• quantum key distribution:

multiphoton events vulnerable to attacks

• efficiency calibration of single photon detectors

photon statistics affects result of calibration

Single Photon Detector Calibration

Signal Number of photons

hn I1

hn

I2

I1 < I2 hn

“click” SPAD

hn “click” SPAD

Only one “click” per time

Analogue detector Digital detector

1E-3 0.01 0.1 10.15

0.20

0.25

0.30

thermal radiation

laser radiation

Fock state radiation

2/

1-Wert

2/

1

<n>

Single Photon Detector Calibration

W. Schmunk, M. Rodenberger, S.Peters, H. Hofer, S. Kück, Radiometric Calibration of Single Photon Detectors by a Single Photon

Source based on NV-centers in diamond, J. Mod. Opt. 58, 1252 (2011)

Introduction

Several methods have been developed to analyze unknown

photon statistics, e.g.:

• photon number resolving detector, e.g. transition edge

sensor (TES)

• “on/off-measurements”

• detector tree

• …

Here:

• NV-centre emission is studied

• results compared to the g(2)(0)-values obtained by

Hanbury-Brown & Twiss (HBT)-measurements

The Nitrogen-Defect (N/V) Center in Diamond

high photo stability at room temperature

bright emission: up to 106 photons per second detected

short decay time 8 ns - 30 ns

broad luminescence spectrum

NV-defects in nano diamonds: minimization of optical

limitations caused by the high refractive index of diamond

600 800 10000.0

0.2

0.4

0.6

0.8

1.0

NV center

Inte

nsity (

a.u

.)

Wavelength (nm)

Nano-diamonds with NV-centres on Si substrate

Quantum Communication Victoria, Australia

HBT Interferometer Measurements

Hanbury-Brown Twiss

Interferometer

TNN

Ng C

21

2 )(

ng

tI

tItItg

11)0(

)((

)()()(

)2(

2

2

Second order correlation

function

Number of single

photon emitters

HBT Interferometer Measurements

excitation: pulsed laser @532 nm, 743 kHz

emission: spectral filtering: (694 37) nm

Centre 1: g(2)(0) = 0.53 ± 0.02 Centre 2: g(2)(0) = 0.06 ± 0.03

Hanbury-Brown-Twiss set up → g(2)(t)

0.0 500.0n 1.0µ 1.5µ 2.0µ0

2

4

6

8

10

12

Co

incid

en

ce

s (

cp

s)

Time (s)

0 500n 1µ 2µ0

200

400

600

800

1000

1200

Co

incid

en

ce

s (

cp

s)

Time (s)

Photon Number Resolving Detector at INRIM

Operation temperature Tc = 130 mK

Sharp superconducting phase transition T ~ hn = 1 mK

Optical fibre coupling (9 µm core)

M.Rajteri et. al. Metrologia 46, 2009, 283 - 287

Transition edge sensor (TES):

Sensitive calorimeter measuring pulse energy

Foto: G.Brida Tc T

R

T

h

→ E

TES Signal

Pulse amplitude ~ n/wavelength

Time constants

electrical rise time ~ 5.2 µs

thermal response time ~ 32 µs

Energy resolution

E = 0.41 eV @ 690 nm

Amplitude (mV)

occu

ren

ce

1

2

3

4 5

Experiment

Fit

TES – Measurement Results

0.00 0.02 0.04 0.06 0.08 0.10

101

103

105

107

1

Counts

Amplitude (V)

0

0.00 0.04 0.08 0.12

101

103

105

107

1

2

Co

un

ts

Amplitude (V)

0

TES: g(2)(0) = 0.5 ± 0.1

HBT: g(2)(0) = 0.53 ± 0.02

TES: g(2)(0) = 0.0 + 0.1

HBT: g(2)(0) = 0.06 ± 0.03

g(2)(0)-values: TES results agree with values measured by the HBT

Centre 1 Centre 2

n n

n nn

nP

nPPng

2

2

)2(

)(

)()0(

‘On/Off’ Photon Statistic Reconstruction

Partial reconstruction of photon statistics by varying detection efficiency

‘No-click’ probability p0 for a binary detector of detection efficiency n

hit by a quantum optical field with density matrix :

nnp n

n||)1()(0 nn

diagonal elements

of the density matrix

Photon number distribution and g(2)(0)-value can be obtained by:

• Maximum Likelihood estimation

• least square fit

‘On/Off’ Measurements

n

n

nn n

nf

,0)(

n0,n : number of "no-click" events

nn : total number of runs

variable detection efficiency

Information on the photon number distribution is gained from the ratio:

SPAD

n n

Neutral density filters

SPS Pulsed

mode

Trigger

‘On/Off’ Measurement Results

• Low efficiency of the optical detection set up (~ 3 % – 4 %)

• Low signal to noise ratio → high order photon component has a high error

• High zero photon component

0.0 0.2 0.4 0.6 0.8 1.00.95

0.96

0.97

0.98

0.99

1.00

Fre

que

ncy

f n(n)

overall

efficiency

detector

efficiency

Efficiency n

experimental data

different ND filters

‘On/Off’ Measurements Results

0 1 2 310

-9

10-7

10-5

10-3

10-1

Pn

Photons0 1 2 3

10-9

10-7

10-5

10-3

10-1

Pn

Photons

“On/Off”: g(2)(0) = 0.5 0.1

TES: g(2)(0) = 0.5 ± 0.1

HBT: g(2)(0) = 0.53 ± 0.02

“On/Off”: g(2)(0) = 0.02 0.05

TES: g(2)(0) = 0.0 + 0.1

HBT: g(2)(0) = 0.06 ± 0.03

n n

n nn

nP

nPPng

2

2

)2(

)(

)()0(

Centre 1 Centre 2

Summary

Photon number distribution of NV-centre emission …

measured by TES detector and ‘On/Off’ measurements

results exhibit high zero photon components

→ low overall efficiency of the used single photon source

g(2)(0)-value calculated from photon number distribution

compared to HBT interferometer values

→ good agreement for TES- and “On/Off”-results

Further ‘On/Off’ measurements will be performed for

brighter NV-centres

→ to study the applicability of the method for determination

of the photon statistics of single photon sources in general

Single Photon Detector Calibration

‘On/Off’ Measurements

n

n

nn n

nf

,0)(

n0,n : number of "no-click" events

nn : total number of runs

variable detection efficiency

Information on the photon number distribution is gained from the ratio

SPS On/Off

dichr.BS

SF

Laser 532 nm

f =740 kHzrep

100 xNA = 0.9

dichr.BS

SF

Laser 532 nm

f =740 kHzrep

100 xNA = 0.9

Filter

=700 38 nmNotch 532 nm

xyzpiezo

scanner

MMF

FC

FC

SMF532 nm

MMF

SPAD

Lasersync

start

TCSPC

stop

ND

Delay generator

gateFC FC

L

SPS On/Off

dichr.BS

SF

Laser 532 nm

f =740 kHzrep

100 xNA = 0.9

Filter

=700 38 nmNotch 532 nm

dichr.BS

SF

Laser 532 nm

f =740 kHzrep

100 xNA = 0.9

Filter

=700 38 nmNotch 532 nm

xyzpiezo

scanner

MMF

FC

FC

SMF532 nm

MMF

SPAD

Lasersync

start

TCSPC

stop

ND

Delay generator

gateFC FC

L

SPS On/Off

dichr.BS

SF

Laser 532 nm

f =740 kHzrep

100 xNA = 0.9

Filter

=700 38 nmNotch 532 nm

dichr.BS

SF

Laser 532 nm

f =740 kHzrep

100 xNA = 0.9

Filter

=700 38 nmNotch 532 nm

xyzpiezo

scanner

MMF

FC

FC

SMF532 nm

MMF

SPAD

Lasersync

start

TCSPC

stop

ND

Delay generator

gateFC FC

L

SPS On/Off

dichr.BS

SF

Laser 532 nm

f =740 kHzrep

100 xNA = 0.9

Filter

=700 38 nmNotch 532 nm

dichr.BS

SF

Laser 532 nm

f =740 kHzrep

100 xNA = 0.9

Filter

=700 38 nmNotch 532 nm

xyzpiezo

scanner

MMF

FC

FC

SMF532 nm

MMF

SPAD

Lasersync

start

TCSPC

stop

ND

Delay generator

gateFC FC

L

SPS On/Off

dichr.BS

SF

Laser 532 nm

f =740 kHzrep

100 xNA = 0.9

Filter

=700 38 nmNotch 532 nm

xyzpiezo

scanner

MMF

FC

FC

SMF532 nm

MMF

SPAD

Lasersync

dichr.BS

SF

Laser 532 nm

f =740 kHzrep

100 xNA = 0.9

Filter

=700 38 nmNotch 532 nm

xyzpiezo

scanner

MMF

FC

FC

SMF532 nm

MMF

SPAD

Lasersync

start

TCSPC

stop

ND

Delay generator

gateFC FC

L

SPS On/Off

dichr.BS

SF

Laser 532 nm

f =740 kHzrep

100 xNA = 0.9

Filter

=700 38 nmNotch 532 nm

xyzpiezo

scanner

MMF

FC

FC

SMF532 nm

MMF

SPAD

Lasersync

dichr.BS

SF

Laser 532 nm

f =740 kHzrep

100 xNA = 0.9

Filter

=700 38 nmNotch 532 nm

xyzpiezo

scanner

MMF

FC

FC

SMF532 nm

MMF

SPAD

Lasersync

start

TCSPC

stop

ND

Delay generator

gateFC FC

L

SPS On/Off

dichr.BS

SF

Laser 532 nm

f =740 kHzrep

100 xNA = 0.9

Filter

=700 38 nmNotch 532 nm

xyzpiezo

scanner

MMF

FC

FC

SMF532 nm

MMF

SPAD

Lasersync

dichr.BS

SF

Laser 532 nm

f =740 kHzrep

100 xNA = 0.9

Filter

=700 38 nmNotch 532 nm

xyzpiezo

scanner

MMF

FC

FC

SMF532 nm

MMF

SPAD

Lasersync

start

TCSPC

stop

ND

Delay generator

gateFC FC

L

SPS On/Off

dichr.BS

SF

Laser 532 nm

f =740 kHzrep

100 xNA = 0.9

Filter

=700 38 nmNotch 532 nm

xyzpiezo

scanner

MMF

FC

FC

SMF532 nm

MMF

SPAD

Lasersync start

TCSPCstop

ND

Delay generator

gate

FC FC

L

dichr.BS

SF

Laser 532 nm

f =740 kHzrep

100 xNA = 0.9

Filter

=700 38 nmNotch 532 nm

xyzpiezo

scanner

MMF

FC

FC

SMF532 nm

MMF

SPAD

Lasersync

start

TCSPC

stop

ND

Delay generator

gateFC FC

L

SPS On/Off

dichr.BS

SF

Laser 532 nm

f =740 kHzrep

100 xNA = 0.9

Filter

=700 38 nmNotch 532 nm

xyzpiezo

scanner

MMF

FC

FC

SMF532 nm

MMF

SPAD

Lasersync start

TCSPCstop

ND

Delay generator

gate

FC FC

L

[1] Zambra et al. PRL 95, 063602 (2005)

Photon Statistics Reconstruction by

On/Off measurements

0.0 0.2 0.4 0.6 0.8 1.00.95

0.96

0.97

0.98

0.99

1.00

Fre

que

ncy

f n(n)

overall

efficiency

detector

efficiency

Efficiency n

experimental data

different ND filters

… based on constrained Log-likelihood probability function

Maximum-likelihood estimation

Fraction of ‘no-click’ events

Diagonal elements

of the density matrix

nnnp

pfL

N

n

K

||)(

)(log

10

0

1

n

n

n

Zambra G. et. al. PRL, 2005, 063602

Optical fiber

ITES

Electronics &

data aquisition

INRIM: TES module

20 µm x 20 µm

TES – Transition Edge Detector

Nano-diamonds with NV-centres

Quantum Communication Victoria, Australia