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
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