Parametric Down-conversion and other single photons sources

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Nov 2, 2013 (5 years and 13 days ago)

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Parametric Down
-
conversion and other
single photons sources

December
2009

Assaf Halevy

Course #
77740
, Dr. Hagai Eisenberg

1




Outline:




Single photon sources




Parametric Down Conversion


inside look




Entanglement from PDC


2

Number of photons in a typical laser beam

3

Each photon carries energy of



For the energy is



A laser beam with power of


Emits



How

can

we

create

single

photons?



Atoms as a single photons source

4

Sodium atoms prepared as

A two level system


System contains few atoms

in each given moment


Laser frequency tuned to the

Energy gap between levels


Coincidence counts recorded

As a function of time


2
nd

order correlation function

5

Antibunching demonstrated


After each emission

The atom has to be stimulated

Again


low probability

For two fold coincidence


Experimental difficulty to

Ensure only one photon

Exists in the system









Imperfect diamond as a single photon source

6

Diamond is an allotrope of carbon


In every diamond some of the carbons are

replaced with Nitrogen and a lattice vacancy



The Nitrogen
-
vacancy pairs are well located

In random points of the lattice

Experimental results

7

8

All measurements presented here

were made on a single NV center!




emission events recorded

From the same center


Key parameter


mean time between

Excitations:


Low power


lower excitation rate


the

System is ready after each excitation to

Emit a photon


High power


bigger probability of the

System to be in an intermediate level



Theoretical model

9

Three level system
-


Intermediate level necessary








Saturation as a function of pump rate K
12

10

Fluorescence from a single molecule

Problem: molecules posses rotational and internal degrees of
freedom, as well as electronic levels


Solution: placing single
Pentacene

molecules in a
p
-
Terphenyl

lattice


Pentacene



consists of
5
Benzene (C
6
H
6
) rings



Experimental results

11



Quantum dot as a single photon source

12










Bulk semiconductors


band gap is fixed


Energy levels in the valence and conduction bands are continuous


Applying stimulus on the bulk can create
excitons



electron hole pairs


When the
exciton

decays


it emits a photon with the fixed band gap energy






Quantum confinement


13

De Broglie wavelength In bulk semiconductor



is much smaller than crystal size


When one or more dimension are at this scale the motion is quantized


This behavior is called Quantum confinement








Quantum dot

14

Consists of tens of semiconductor atoms (up to
50
nm)



Quantum confinement causes energy levels to be discrete



Engineering the quantum dot structure allows control of the band gap



Control over the emission spectrum













Experimental results

15

Finite response time

Of the detector causes

All events in the time

Frame to up
0.5
ns to

Contribute to the value

At causing




Linear optics


the classical description

16



Light frequency is fixed and cannot be changed


Light cannot interact with light






polarization
-

expresses the density of permanent or induced electric


dipole moments in a dielectric material
.



Linear susceptibility


To create new frequencies we need non
-
linear optics

Parametric Down
-
Conversion
-

introduction

Non
-
linear optics

17


Polarization depends on higher powers of the Electric field


Focus on the second order susceptibility:


Applying a field of


results in



Nonlinear process New frequencies generated



Sum frequency generation



(
2
)


3


1


2

L

18


3


1

2

Classically


two wave mixing creates a wave with new frequency


Quantum description: two photons are annihilated, while one is created

-

k
1


k
2

Δ
k=k
3

Wavevector mismatch

Motivation for
Δ
k =
0




Intensity of the resulting wave


19

Parametric Down
-
Conversion

20

Quantum description:
One photon annihilates, two photons created


Interaction Hamiltonian
-



We assume the non depleting pump approximation:






PDC SHG


Energy and momentum conservation: ,



is the polarization mode


Fock representation

21



Our input state is , represent the coherent pump beam


First order approximation of the wave function:


We get



Or




depends also on the interaction time with the crystal


PDC output is linear with pump power

22

Heralded single photon source from PDC

Herald
-

One that gives a sign or indication of something to come


Emission from a two level quantum system can produce

Single photons which do not posses any preferred direction



PDC process is a quantum phenomena in which two photons are emitted in

Defined spatial modes


Measurement of one photon ensures us his twin existence







23

Detection of the signal photon in A triggers measurement in B for
20
ns
resulting in an integer m


If m occurs N(m) times in N cycles then


If every down
-
converted photon is detected (quantum efficiency
1
) and no

dark counts then


In the experiment:


Signal to noise ratio is
1
/
5

Quantum efficiency is small



Defining the probability to produce n Idler photons

24

Accounting for probability to detect m background

Photons



If is small for then also



In this case we can invert the equation and get M

Linear equations in






Methods for achieving phase matching condition

25

Temperature tuning: refractive index changes with temperature
-

LiNbO
3


Quasi phase
-
matching: Periodically poling of the nonlinearity
-

LiTaO
3



Angle tuning: the use of birefringence


BBO, BiBO

Phase matching condition:
Δ
k =
0

Normal materials


In a degenerate collinear case
:


Impossible because of dispersion

K
Signal

K
Idler

K
Pump

26

Δ
k =
0

Achieved with Birefringence

Index of refraction in anisotropic crystals depends on polarization

2
n
e
(
2

)

= n
e
(

)


+ n
o
(

)
possible!



How to do it?

27

The index ellipsoid


a measure for crystal symmetry

Ѳ

Ф

n
slow

n
fast

k
pump

n
z

n
x

n
y

For every propagation direction there are
2
normal modes of polarization

Δ
k =
0
Achieved with Birefringence

28

PDC processes



Collinear Non
-
Collinear






Type I


PDC products posses same polarization



Type II


PDC products posses orthogonal polarization


29

K
Signal

K
Idler

K
Pump

K
Signal

K
Idler

K
Pump

Scheme of non
-
collinear type II PDC process

Nonlinear


crystal

Pump

beam

H polarized

V polarized

Momentum and Energy conservation:

1

2

K
Signal

K
Idler

K
Pump

30

Degenerate case
-

Signal and Idler with the
same wavelength


Experimental setup

Rep. rate


76
MHZ

Pulse duration

Low noise


Camera

Band pass filter


Low pass filter

Dichroic mirror

Ti:Sapphire laser

Crystal

31

Residual pump

Why pulsed laser?

31

1
. Knowledge of the arrival times of the down
-
converted


photons within the pulse duration


2
. Improved probability of higher order events





Broadband spectrum of the pump beam and the PDC photons

Pulsed laser drawback

Angular dependency in the pump beam propagation direction

32

Comparing simulation to experimental results with BBO

33

Experiment

Simulation

Polarization of the down
-
converted circles

Vertical polarization

Horizontal polarization

34

Quantum entanglement

Separable state

Entangled state

Entangled photons states are essential
for quantum optics experiments

35

Generated Wave function

Polarization entangled state

The photons are labeled by their spatial mode and their polarization

36

1

2

:
References

M. Fox, Quantum optics


An
inroduction
, Oxford university press (
2006
)


H.J. Kimble et al., “Photon
antibunching

in resonance fluorescence”, Phys. Rev.
Lett
.
39
,
691
-

695
(
1977
)



T.
Basche

et al., “Photon antibunching in the
flouescence

of a single dye molecule trapped in a solid”, Phys. Rev.
Lett
.
7
,
1516
-
1519
(
1992
)


K.
Kurtseifer

et al., “Stable solid
-
state source of single photons”, Phys. Rev.
Lett

85
(
2000
)
290
-
293



P.
Michler

et al. ,”A quantum dot single photon turnstile device, Science
290 2282
-
2285
(
2000
)


(
R.W Boyd, Nonlinear optics,
2
nd

edition , Elsevier (
2003


M. Rubin et al., “Theory of two
-
photon entanglement in type
-
II optical parametric down
-
conversion”, Phys. Rev. A
50
5122
-
5133
(
1994
)


C. Hong and L. Mandel, “Experimental realization of a localized one
-
photon state”, Phys. Rev.
Lett
.
56
,
58
-
60
(
1986
)



P. G. Kwiat et al., “New high intensity source of polarization
-
entangled photon pairs,” Phys. Rev.
Lett
.
75
,
4337
-
4341
(
1995
)









37