Discussion and Applications of Single and Entangled Photon Sources
David Cruz, Nelson Lee
University of Rochester Institute of Optics
October 21, 2013, revised December 4, 2013
Abstract:
Single photon sources; such as quantum dots, nano-diamonds, and carbon
nanotubes; and polarization entangled photons, are important in the field of quantum
optics; more specifically for the roles they play in quantum encryption and quantum
information. One of the obstacles with this technology is being able to efficiently produce
single photons with antibunching characteristics. If this can be accomplished quantum
communication would be very secure. New experiments are also showing that direct
communication between entangled photons is impossible. If two particles cannot be
factored into single particle states they are said to be entangled. If a measurement is
performed on one particle, this will give you reliable information about the second
particle regardless of how far apart they are. Creation of polarization entangled photons
was done using spontaneous parametric down conversion by BBO crystals. With that
being said, quantum entanglement is rare and difficult to observe.
Keywords: quantum optics, single photon source, entangled photon source, quantum
entanglement,
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 between
photons, power and wavelength of the light source to find how many photons per meter
1
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 a single emitter. The return of this electron from the
excited state to the ground state results in the release of a single antibunched photon
magnitude attenuation is required. Such a highly attenuated beam is a very good approximation for a single-photon
source, and some modern quantum-cryptography systems are based on propagating a faint, 1.55- m laser beam in optical
fibers. Even wave-particle duality of photons in faint classical beams are observed starting from the first experiments of
Vavilov and Brumberg in the 1930s 8. But in quantum cryptography systems, faint beams of laser or classical light are
vulnerable to a beam-splitter attack by Eve, because such beams sometimes have doublets and triplets of photons as
mentioned earlier. Figure 1, (a) shows the probability (Poisson distribution) for finding only one photon, no photons at
all, and two, three and four photons together in a coherent light beam when the mean photon number equals 1. With
light attenuation to the mean photon number 0.1, in 9 cases there will be no photons et al., and only in one case a single
photon will appear [Figure 1, (b)]. For quantum cryptography a photon number state, the so-called Fock state [Figure 1,
(c)], is preferred with mean photon number 1 with probability for one photon equal 1. For further reading see books2,3
Figure 1: Electron Excitation Leading to Single Photon Emitted [3]
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 we were
able
to observe
fluorescence
antibunching
[4]. toInbe in bunches.
intensity
correlation,
varying
the delay
betweenthe
thepresence
two arms. of
They
found that photons
(bosons) tend
This intensity interferometer (in difference with the ordinary amplitude interferometers) is now called a Hanbury Brown
order
to determine
if these sources are indeed emitting single antibunched photons we
and
Twiss
interferometer.
needof to
at the second-order
correlation
function,
was Dagenais
first proposed
by (University
One
the look
first experiments
which started the
era of quantum
optics, which
was Kimble,
and Mandel’s
11
of Rochester) first observation of photon antibunching
in
1977
which
means
separation
of
all
photons
in time. In
Hanbury
Brownphoton
and Twiss.
This function,
g(2)in
, expressed
by the following
equation:
these
experiments,
antibunching
was observed
resonance fluorescence
from sodium
atoms.
Photon antibunching4 can be expressed by the value of the second-order correlation function g(2):
g(2)
I ( )I ( t
I( ) I(t
,
(1)
(1)
Where I(τ)
is light
intensity,
and
time
intervals.
g(2)(0) g(2)1;can be defined
where
is the
light intensity
, τand
t +t+τ
areare
time
intervals,
and Foris antibunched
time averaging.light
In practice,
from
measurements
g(2)max
(τ) = 1. [2] of coincidence counts, c(t), and intensities I1 and I2 in each arm of a Hanbury-Brown and Twiss
interferometer: g(2) (t) = c(t)/I1I2
where is the time resolution, and and T is the total acquisition time.
For 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
2
including t = 0. For bunched light g(2)(0) > 1 and g(2)(0) > g(2)(t).
In a modern experimental implementation, single (antibunched) photons are produced by focusing a laser beam tightly
into a sample area containing a very low concentration of emitters, so that only a single emitter becomes excited (See
Since the discovery of the "spooky action from a distance", quantum
entanglement has been able to be reproduced experimentally, and holds much promise for
the advancement of securer communication or sends a message that can't be intercepted.
Polarization 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 BBO crystals are nonlinear optical crystals with a broad phase
matching range and transparency region [5]. Spontaneous parametric 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 set up
includes a pump laser, two BBO crystals, quartz plate, two avalanche photodiodes
(APDs), a collecting system, interference filters, two polarizers (See figure below) [6],
and a computer card counter/timer.
Polarizer
BBO
Crystal
Mirror
APD
APD
Polarizer
Quartz
Plate
Pump
Laser
Figure 2: Experimental Setup to Produce Quantum Entanglement
Polarization 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]
3
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].
An application of quantum entanglement deals with quantum cryptography. In
1991, Artur Ekert proposed a quantum key distribution protocol that can be made using
quantum states.
properties.
The structure of the quantum key distribution depended on two
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.
4
Contributions:
Nelson Lee wrote the Abstract and the section regarding entangled photons.
David Cruz wrote the section regarding single emitters, and also applied corrections and
rewrote the Abstract for resubmission.
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