Discussion and Applications of Single and Entangled Photon Sources
David Cruz, Nelson Lee
University of Rochester Institute of Optics
October 21, 2013
Abstract:
The formalism of quantum optics says, the state of a member in an entangled pair
must be described relative to the other and these states change instantly. This accepted
property in nature could be seen through experiments described in the subsequent
sections. Opposition however, arose concerning the validity of quantum entanglement
after John Bell proposed the "local hypothesis" with hidden variables. Nevertheless,
applications arise in the communications industry in an attempt to secure sensitive
information and basic notions of quantum entanglement applications can be described
thus, in terms of a sender, a message and a recipient. This paper introduces the concept of
single and entangled photon sources and their role in modern day applications such as
quantum communication and information. We will provide a basis of understanding on
how these sources are achieved, the theory and method behind single and entangled
photon generation and how they can be used.
Keywords: quantum optics, single photon source, entangled photon source, quantum
entanglement,
1
The ability to efficiently produce single and entangled photons gives promise to
the technologies and applications, such as quantum information and quantum
communications, which rely on photons at this level. A single photon source produces
photons that are all separated in time, exhibiting antibunching characteristics [2]. In the
“Quantum and Nano Optics” course at the University of Rochester, students have learned
two methods of producing single photon sources. One method involves attenuating a
laser light source down to a single photon level using optical filters. Attenuation is
determined by calculating how many orders of filtration are needed to achieve a desired
transmittance. In order to do this you would need to know the desired distance, power
and wavelength of the light source to find how many photons per meter are produced.
This is a good approximation for single photon sources, however this method does not
produce true single, antibunched photons.
To produce true single photons we use single emitters. Examples of this include
dye molecules, quantum dots, nano-diamonds, and single-walled carbon nanotubes to
name a few. A laser beam is tightly focused onto a sample with a low concentration of
these emitters in order to excite an electron. The return of this electron from the excited
state to the ground state results in the release of a single antibunched photon
Figure 1: Electron Excitation Leading to Single Photon Emitted [3]
2
The University of Rochester Optics 453 course has involved students using quantum dots
Figure 1. Probability distribution for the number of photons: (a) For mean photon number 1 in coherent state; (b) For mean photon
for single
emittance.
A confocal
fluorescent microscope was used to stage and to
number
0.1 inphoton
coherent state;
(c) For Fock
state.
In
1956,a beam
Hanbury
and Twiss
existence
of correlation
the outputs
two photoelectric
focus
onBrown
the sample
of observed
quantumthedots;
and using
either between
a Hanbury
Brownof and
detectors illuminated by light from a thermal source9-10. In these experiments, using a beamsplitter, they measured
Twiss set
up, orvarying
an EM-CCD
camera,
wereThey
ablefound
to observe
the(bosons)
presence
ofbe in bunches.
intensity
correlation,
the delay between
the we
two arms.
that photons
tend to
This intensity interferometer (in difference with the ordinary amplitude interferometers) is now called a Hanbury Brown
fluorescence
antibunching [4]. In order to determine if these sources are indeed emitting
and
Twiss interferometer.
single
antibunched
photons
need
at theoptics,
second-order
correlation
function,
One
of the
first experiments
whichwe
started
the to
eralook
of quantum
was Kimble,
Dagenais and
Mandel’s (University
of Rochester) first observation of photon antibunching in 197711 which means separation
of
all
photons in time. In
(2)
which
was first photon
proposed
by Hanbury
Brown in
and
Twiss.fluorescence
This function,
, expressed
these
experiments,
antibunching
was observed
resonance
from g
sodium
atoms. by
4
the following
equation:
Photon
antibunching
can be expressed by the value of the second-order correlation function g(2):
g(2)
where
I ( )I ( t
I( ) I(t
is the light intensity , and t + are time intervals, and
(1)
,
(1)
is time averaging. In practice, g(2) can be defined
from
measurements
coincidence
counts,
and intensities
and antibunched
I2 in each arm light
of a Hanbury-Brown
Where
I(τ) is lightofintensity,
τ and
t+τ c(t),
are time
intervals.I1 For
g(2)(0)  1; and Twiss
interferometer: g(2) (t) = c(t)/I1I2
where is the time resolution, and and T is the total acquisition time.
g(2)
(τ) = 1. [2]
For max
antibunched light g(2)(0) < 1, in ideal case g(2)(0) = 0, g(2)max (t) = 1. For coherent light g(2)(t) = 1 for all values of t
including t = 0. For bunched light g(2)(0) > 1 and g(2)(0) > g(2)(t).
Since
the discovery
of the "spooky
action fromphotons
afar", are
quantum
entanglement
In a modern
experimental
implementation,
single (antibunched)
produced
by focusing a has
laser beam tightly
into a sample area containing a very low concentration of emitters, so that only a single emitter becomes excited (See
been able
beemits
reproduced
experimentally,
and holds
much promise
the3advancement
Figure
2). It to
then
only one photon
at a time because
of fluorescence
lifetime.for
Figure
shows a commonly observed
photon “antibunching histogram” from such a single emitter.
of securer communication or sends a message that can't be intercepted.
Polarized entangled states of two photons can be obtained by using "spontaneous
parametric down conversion" in two type I phase matching BBO crystals. Beta Barium
Borate
or 2.BBO
crystals
are nonlinear
opticallaser
crystals
with a broad
phase
matching
Left
: Figure
Excitation
of a single
emitter by a focused
beam. Right:Figure
3. Typical
histogram
of the range
number of second
photons that appear at a definite time interval t after the first photon in each photon sequence c(t).
and transparency region [5]. Spontaneous down conversion or SPDC is the process in
which the nonlinear crystal is used to split photons into pairs of photons (signal and idler
photon). The pair of photons must have the same energy and momentum as the original
photon and are phase matched with correlated polarizations. The use of SPDC and BBO
crystals result in quantum entangled pairs. The whole set up includes a pump laser, BBO
crystal, quartz plate, two avalanche photodiodes (APDs) and two polarizers (See figure
below) [6].
3
Polarizer
BBO
Crystal
Mirror
APD
APD
Polarizer
Quartz
Plate
Pump
Laser
Figure 2: Clauser-Horne-Shimony-Holt Inequality (CHSH) to produce
quantum entanglement
Polarized entangled photons can be represented by the mathematically,
, where H is the horizontal polarized photon and V is the
vertical polarized photon. The subscript "s" stands for the "signal" photon and the "i"
subscript stands for the "idler" photon. Δ is the phase difference of the photons that result
after the down converted polarizations (See figure below). [7]
John Bell showed "locality principle" with hidden variables violates quantum mechanics
principles. This can be seen in the above experiment for arbitrary angles of the polarizer
[2].
Figure 3: Type I Spontaneous parametric down conversions. Left image is the down conversion of horizontal
photon. Right image is the down conversion of the vertical photon.
The result recorded by APDs and coincidences are detected by a counter card inside the
computer. John Bell showed "locality principle" with hidden variables violates quantum
mechanics principles. This can be seen in the above experiment for arbitrary angles of the
polarizer [6].
4
An application of quantum entanglement deals with quantum cryptography. In
1991, Artur Ekert proposed a quantum key distribution that can be made using quantum
states. The structure of the quantum key distribution depended on two properties. One is
that the quantum states are perfectly correlated or have 100% probability that if sender
and the recipient measure the outcomes to measure if the photon has horizontal or vertical
polarization, their conclusions will be the same. The second property is that any attempt
to intercept the message results in the destruction of the correlation in a way that the
sender and recipient can detect.
References:
1. http://www.nature.com/news/quantum-teleportation-achieved-over-record-distances1.11163
2. Lukishova, Svetlana. Lab 3 lecture 1, Web. Fall 2013.
http://www.optics.rochester.edu/workgroups/lukishova/QuantumOpticsLab/homepage/SP
S_Lecture_1.pdf
3. “University of Tokyo, Fujitsu and NEC Succeed in Quantum Cryptographic Key
Distribution from Single-Photon Emitter at World-Record Distance of 50 km” University
of Tokyo Fujitsu Laboratories Ltd. NEC Corporation. September 2010.
http://www.fujitsu.com/global/news/pr/archives/month/2010/20100910-02.html
4. Lukishova, Svetlana. Lab 3-4 Manual. Web. Fall 2013
http://www.optics.rochester.edu/workgroups/lukishova/QuantumOpticsLab/homepage/op
t253_labs_3_4_manual_08.pdf
5. http://eksmaoptics.com/nonlinear-and-laser-crystals/nonlinear-crystals/beta-bariumborate-bbo-crystals/
6.
http://www.optics.rochester.edu/workgroups/lukishova/QuantumOpticsLab/homepage/En
tangl_Bell_Inequal_OPT_253_10_28_09.pdf
7. SPS_Proceed_SPIE_Lukishova_revised
5