Quantum Entanglement
Greg Balonek, James Corsetti, Anthony J. Visconti, Zachary DeSantis, Kenneth McKay
University of Rochester, Institute of Optics,
Rochester, NY 14627
ABSTRACT
Entanglement is the property of a quantum mechanical system wherein a physical characteristic of one particle
depends on that of another. In this lab, we obtain a polarization-entangled state of two photons through measuring the
coincidence counts between two single photon detectors. We verify that the particles were in fact entangled by
calculating the visibility of the coincidence counts measurements as the polarization angles were varied. Although we
do not calculate the S-parameter to verify a violation of Bell’s inequality, all of our visibility calculations are above
0.71, which indicates that the two photon’s polarizations are in fact entangled.
INTRODUCTION
travels a longer distance than does a vertical photon in the BBO
pair before being down converted. This path difference accounts
for an additional phase term on the horizontal ‘ket’ of the
quantum wave function. The down converted entangled photon
pair is of very low intensity because most of the light passes
directly through the BBO crystals. The photons are detected by a
pair of single-photon counting avalanche photodiodes (APDs)
after passing through 10 nm bandpass filters. Polarizers were
placed in front of each APD so that the polarization state of
photons could be selected and count rates measured. Data from
the APDs is collected using a LabView interface on a computer
with a counter-timer board inside.1 Below is an optical schematic
of the experimental setup.
If two particles are entangled, then their wave functions
cannot be separated. There is some shared physical characteristic
that the two particles possess, for example polarization, spin or
momentum. This lab investigates two photons with entangled
polarizations. Therefore, if there is a disturbance or measurement
made on one particle, the state of the other particle is also
affected. This quantum mechanical principle holds regardless of
how far apart these two particles are. Classical mechanics cannot
explain the phenomenon and furthermore; if the quantum
mechanical system is entangled, then Bell’s classical inequality will
be violated.1
EXPERIMENTAL PROCEDURE
A 100 mW pump argon ion laser with a wavelength λ = 363.8
nm and with vertical polarization is used to generate entangled
photons. The light passes through a quartz plate which induces a
phase difference between the two polarization components. Next
the light passes through a pair of orthogonal BBO crystals. The
incident light is oriented 45º with respect to the crystal pair. The
photons are down-converted, that is, they are converted to light at
λ = 727.6 nm. The BBO crystals convert horizontal light into two
vertical photons and convert vertical light into two horizontal
photons. The two output photons have opposite angles with
respect to the optical axis, but can be oriented at any angle
Optical Schematic of Quantum Entanglement Setup1
azimuthally about the optical axis. Therefore we describe the
Photons incident on APD B are historically called signal photons
output of the BBO crystals as a ‘cone’ of light illustrated below.
and photons incident on APD A are historically called idler
photons. Count rates for individual and coincidence photons are
measured as the orientation of the polarizers with respect to the
BBO and with respect to each other are changed. The
coincidence count is when a signal and idler photon hit their
respective APD within a 26 ns time span.
Polarization entangled photon pairs1
RESULTS
Note that the horizontal and vertical output cones are
overlapping because the input light is 45º polarized. Half the time
the photons are converted to a horizontally polarized pair and
half the time a vertically polarized pair. Also, a horizontal photon
The data results from the laboratory are found in Figures 1-2 and
Table 2. Figure 1 below illustrates the sine squared dependence of
the coincidence count rate on the relative angle between the two
polarizers. Two curves are plotted. The blue curve represents
1
measurements made with the polarizer for APD A at 0º with
respect to the BBO pair as the polarizer for APD B was varied
from 0º to 360º. The yellow curve represents measurements made
with the polarizer for APD A at 90º with respect to the BBO pair
as the polarizer for APD B was again varied from 0º to 360º.
Curve
A: 0 deg
A: 90 deg
Visibility
0.76
0.74
Table 1.
Note that the visibility for both curves is above 0.71, which
implies that we have achieved polarization-entangled photons.
DISCUSSION QUESTIONS
Two particles are considered entangled when their wave functions
are linked so that one object can no longer be described without
mention of the other. Any measurement performed on one
particle will change the state of the other. Mathematically, this
means that the wave functions cannot be factored. In this
particular lab, entangled photons are produced with two
perpendicular BBO crystals through a process called spontaneous
parametric down-conversion. Spontaneous parametric downconversion is the process where a high energy photon is split into
two other photons at half the energy. To prove that the photons
were entangled, a violation of Bell’s inequalities was measured to
illustrate non-classical behavior. Simply, a sine squared
dependence with a visibility greater than the classical limit was
shown for the relationship between coincidence counts and
polarizer angle. The maximum coincidence counts occurred when
the difference in angle between the two polarizers was 90 degrees.
The minimum occurred when the difference in the angle was a
multiple of 180 degrees. The count rate of single photons did not
change with angle. The sine squared dependence matches with
the equations derived in section 4 for the probability of
coincidence.
Figure 1: Coincidence count vs. polarization angle
Note that the coincidence count for the blue curve varies as sine
squared with respect to the polarization angle of APD B.
Subtracting the 90º offset of the yellow curve would also yield
sine squared dependence. Below is a plot of the single count for
APD B as the polarization angle is varied. The individual photon
count does not vary over angle, whereas the coincidence count
does. Also we made measurements of maximum and minimum of
similar curves at polarizer A settings 45º and 135º we obtained
fringe visibility of 0.896 and 0.914 respectively.
REFERENCES
1. “Entanglement and Bell’s Inequalities.” Dr. Svetlana
Lukishova. University of Rochester, Institute of Optics. Fall 2008.
Figure 2: Single count vs. polarization angle
From the coincidence count measurements in Figure 1, the
visibility is calculated in Table 1 below.
2