Polarization Correlation of Entangled Gamma Rays
William Barnes, Cole Hubacz
Physics Department, University of Massachusetts, Amherst, 01003
May 15, 2007
We study the polarization correlation of back-to-back 0.511 MeV gamma ray pairs that emerge
entangled from positronium decay, where the photons carry a restriction on their relative
direction of polarization. A pair of Compton polarimeters, sensitive to the polarization of each
photon, is used to determine the scattering cross sections for two macroscopic configurations
(polarimeters are perpendicular or antiparallel to each other). Klein-Nishina cross sections
predict the asymmetrical perpendicular-to-antiparallel cross section ratio of 2.84, an effect that
would not be present without entanglement [1]. We measure a ratio of 2.51 ± 03, verifying the
predicted asymmetry.
PACS numbers: 03.65.Ud, 32.80.Cy, 36.10.Dr, 61.80.Ed
1. INTRODUCTION
Quantum entanglement is a side effect of quantum mechanics that has yet to be fully understood,
yet its relevance to modern science is rapidly taking root. Briefly stated, entanglement is the
phenomenon where two distinct objects, such as photons or electrons, are able to perform
instantaneous “communication” with one another, uninhibited by the usual restrictions of
classical mechanics and special relativity [2]. Communication between entangled objects occurs
as an experimenter attempts to measure the physical state of either one of the objects. Upon
measurement of one object, he can immediately conclude the status of the second object,
regardless of their geographic separation.
In this experiment, two photons emerge entangled from positronium decay, where the relative
photon polarization directions are predicted from quantum mechanics. Compton polarimeters are
used to measure the direction of polarization of each photon, where a series of NIM electronics,
peak detection hardware, and data acquisition software is used to interpret the information
coming from the polarimeters. To observe the effect of entanglement, measurements are repeated
for two orientations of the apparatus; the polarimeters may be aligned in a perpendicular or
antiparallel fashion. For each orientation, the polarimeters should register events in unequal
numbers, an effect that would not be present without quantum entanglement.
2. SODIUM IN FOIL PRODUCES ENTANGLED PHOTONS
The natural question is, “How does one produce entangled photons in the laboratory?” In this
experiment, we begin with a radioactive sodium (22Na) source, which tends to spontaneously
decay into excited neon (22Ne*) via the reaction 22Na → 22Ne* + + + νe. Noting there are three
daughter products in this decay, we know that the energy carried away by the neutrino and the
beta particle will occupy a continuum of distributions, not discrete values. For the beta-decay of
22Na
the endpoint energy (or highest allowed energy) is 0.545 MeV [1]. For a detailed view of
the collimated sodium source, see Figure 1.
Surrounding the sodium source is a layer of aluminum foil, roughly 1 / 32" , which is known to
contain many free electrons. The emitted beta particle will interact with the electrons until it
nearly comes to rest, which in turn bonds with a free electron, forming positronium (of zero net
charge). At this point, the positronium is subject to the effects of hyperfine splitting, which in
turn forces the positronium into one of two channels. Roughly 75% of all +e- pairs will form
orthopositronium (carries total spin S=1), which decays into three photons, each carrying away
a random fraction of the total energy. In this experiment, the three-photon decay of
orthopositronium is largely ignored. The remaining 25% of all +e- pairs will form
parapositronium (carries total spin S=0), which decays into only two photons (gamma rays).
Due to the zero-spin nature of this decay, we know that the photons emerge with equal energies
of 0.511 MeV in a back-to-back fashion. Because the photons as a pair must obey conservation
laws regardless of their separation, measurements on one photon must imply something about the
other photon. The two photons are said to be entangled.
3. WAVE FUNCTION OF ENTANGLED PHOTONS
The detectors in this experiment are sensitive to photon polarization, so it is necessary to develop
an understanding photon polarization using quantum mechanics. Since the photons are emitted
back-to-back and are indeed on a straight line in the ±z direction, we conclude that all electric
field (polarization) vectors lie in the xy plane. From relatively straightforward helicity and parity
arguments, we write the wave function for the two entangled photons*:
 1,2 
1
2

x
(1) y (2)   y (1) x (2)

(Equation 1)
Similar considerations allow us to rewrite the wave function with a particular focus on the
photon polarization:
 1,2 
i  
x1 y 2  y1 x2 
2
(Equation 2)
* For a more complete derivation of Equation 1 and Equation 2, please see the Appendix to
reference [1].
Equation 2 carries a strong implication that finally justifies the use of Compton polarimeters in
this experiment. The electric polarization vectors for the two photons must be at right angles to
each other.
4. COMPTON POLARIMETERS
The Compton polarimeter consists of two primary components (There is one polarimeter for
each gamma ray). A half-inch thick aluminum plate, roughly 45o, with the z-axis, is meant to
serve as a Compton scattering target. The original gamma ray will scatter with some new energy,
causing electrons within the aluminum to recoil appropriately. This process is well characterized
by the Compton scattering formula:
1 1
1
1  cos  
 
E ' E me c 2
(Equation 3)
The scattering of linearly polarized photons that scatter off of atomic electrons has also been well
studied; a process which is described by the Klein-Nishina formula:
d 1  E '   E E '

 r0    2(sin  cos  ) 2 
d 2  E   E ' E

2
(Equation 4)
At a fixed scattering angle  , the Klein-Nishina formula predicts “linearly polarized photons
will preferentially scatter in a direction perpendicular to the polarization vector of the incident
photon” [1]. On the aluminum plate, incident gamma rays cause the embedded electrons to move
in a linear back-forth motion. The motion of the electrons (assumed to be oscillating in the z
direction) is a source of new radiation, which is emitted in the xy plane in all directions. A
sodium iodide (NaI) detector, heavily shielded in lead, detects the new radiation, and this
constitutes an “event”. For each event, a sodium iodide detector passes its received signal to
NIM electronics. For a detailed view of the apparatus that holds the polarimeters, see Figure 2. It
should be noted that the apparatus was designed in effort to maximize the asymmetry in
perpendicular-to-antiparallel event rate.
5. NIM ELECTRONICS AND DATA ACQUISITION
When either one of the detectors registers an event, there is no guarantee that they have seen a
genuine event. Through the full course of data analysis, we are able to select desired events to a
reasonable extent. The first guard against unwanted events is to require a coincidence between
the two detectors. Simply stated, this means that both detectors must register events roughly
simultaneously (within 10-100 nanoseconds of each other). The justification is as follows: if the
gamma rays from the sodium source are emitted back-to-back at the same time, and given the
apparatus is constructed in a symmetrical fashion, then both detectors should be triggered at
about the same time.
Signal processing is first handled by NIM, or Nuclear Instrument Module electronics (see Figure
3) [3]. Other responsibilities of NIM electronics are to amplify incoming signals, register the
number of raw and coincidence events on digital scalers, and, most importantly, to relay the
signal information a peak detector circuit. The chief role of the peak detector circuit (not shown)
is to receive an analog signal (ultimately from the NaI detectors) and convert it into an elongated
digital pulse. The voltage of the output pulse indicates the energy of the Compton-scattered
photons. When the peak detector relays along a genuine event to a computer, data acquisition
software called LabVIEW performs all of the necessary means to store the data and produce a
real-time histogram of energy levels vs. number of counts.
6. PROCEDURE AND DATA ANALYSIS
With the source in position, choose to have the polarimeters in an antiparallel orientation, and
allow LabVIEW to acquire data and build a histogram for roughly 30 minutes with NO
“filtering”. When complete, two histograms will have been generated, one for each NaI detector.
Ideally, only one energy peak should be visible on each histogram, with background events in
relatively low numbers. Due to the inherent differences between NaI detectors, there will appear
to be a smaller peak somewhere near, or superimposed on, the central peak. Using LabVIEW, set
the data filtering option to omit energy values outside of the central peak, as this greatly reduces
the number of unwanted events. With the filtering markers in place, allow LabVIEW to collect
data for 60 minutes. Using curve-fitting software, estimate the remaining background curve on
each histogram, and subtract it from a curve that fits the original data. The remaining curve is a
good approximation to the actual energy values registered by the NaI detectors over the 60
minute run. Finally, use software to estimate the area under the desired curve. See Figure 4.
Repeat the same procedure when the polarimeters are perpendicular to each other, and obtain the
area under the background-filtered curve for each histogram. Klein-Nishina cross sections
predict the asymmetrical perpendicular-to-antiparallel cross section ratio of 2.84. In the summer
of 2006 when the data of Figure 4 was obtained, the area under the curves was determined to be
2.51 ± 03 (compare to 2.84). If quantum entanglement played no role in this experiment, this
ratio would be an even 1.00.
7. Conclusion
There exist a few unmentioned parameters, such as insufficient lead shielding, in this experiment
that may dilute the asymmetry in our results. However, a result of 2.51 ± 03 clearly demonstrates
that the polarization correlation of back-to-back 0.511 MeV gamma ray pairs that emerge
entangled from positronium decay are indeed entangled.
REFERENCES:
[1] Umass Physics Amherst. Course 440 handout: Quantum Entanglement: The Compton
Polarimeters. May 2007
[2] Einstein, Podolsky, Rosen. Can Quantum-Mechanical Description of Physical Reality be
Considered Complete? May 1935
[3] Umass Physics Amherst. Course 440 handout: Quantum Entanglement Electronics. May
2007
Figure 1: The sodium source in a lead collimator. As evident from the side view, lead shielding
attenuates particles emitted in the lateral direction.
Figure 2: The pair of Compton polarimeters shown with the collimator. Lead shielding acts to
filter background activity. The bottom polarimeter is free to swing in the azimuthal direction.
Figure 3: NIM electronics.
Figure 4: Histograms for the antiparallel orientation of the polarimeters. The vertical axis is
number of event; the horizontal axis is a list of channels numbers proportional to the energy of
each event. Filter markers are visible in red.