f19electronpositron

Abstract

This experiment measured coincident correlations in photons with entangled spin states produced from the annihilations of positrons with opposite spin state electrons. The spin polarization differences were measured by using Compton scattering’s angular correlation with the polarization of the scattering ray. The data from two separate trials gave differing results. The data from trial 1 resulted in a factor of 0.6 times the theoretical model with the following goodness-of-fit parameters for that reduced fit, reduced chi squared value of 2.0 and PTE=0.07. The data from trial 2, which was fit directly to the model, resulted in a reduced chi squared value of 2.5 and the probability to exceed PTE=0.02.

Introduction

The first mention of quantum entanglement was by Schroedinger. In a seminal paper from 1935, he recognized how crucial it was to quantum mechanics. [1]. Einstein is quoted referring to entanglement as "spooky action at a distance". [2] Entanglement is the process of knowing some characteristic of one particle based on a characteristic of an entangled particle. One characteristic that can be measured for observing evidence of entanglement is spin of coupled photons. This experiment looked at the coupled nature of two photons spin states as a method for observing evidence of entanglement. Entanglement is theorized to have many large applications such as quantum computing [3], quantum cryptography[4], and many more.

Through electron-positron annihilation, two photons with entangled spin polarization states are produced. The intention of this experiment was to study those coupled photons by measuring their coincident events in detectors positioned to measure the polarization differences. Particularly, the methods used to explore this quantum electrodynamics phenomenon are explicitly non-optics based and provide a unique perspective to the theory; a theory that provides a glimpse at the fundamental mechanics of these elementary particles. The model predicts that due to their coupled nature, there should be more coincident events for photons with opposite spin polarization states. If proven correct, the predictive power afforded by the insight could be advantageous for future experiments.

Theory

As an irradiated material decays by positron emission, the positions quickly find opposite spin state electrons and annihilate with them. Constrained by conservation laws, the annihilations produce two 511 keV gamma-rays that propagate away from the annihilation site in opposite directions and with opposite spin polarization states. Unlike the spin states of the particles, opposite spin for photons means that they must be orthogonal. The spin states of the two newly created photons exhibit entanglement behavior described by the following wave equation shown below.

When the photons with entangled spin states undergo Compton scattering, they gain an azimuthal scattering angle phi as a function of the polarization. That scattering behavior is described by the Klein-Nishina equation

where theta is the standard Compton scattering angle. The Klein-Nishina equation can be reduced to the following ratio after integration and azimuthal angle substitution.

The ratio can then be converted to an energy dependent equation by the Compton equation for the free electron, given that the annihilation photon energies are significantly greater than the bound electron energy. The equation is

The incident energy formed through the annihilation of the positron and electron comes from their rest masses and is equal to the product of the mass and squared speed of light. For this experiment, the Compton equation reduces to

Experimental Setup

Calibration:

To understand the voltage energy relationship of each detector, they each needed to be characterized. This was accomplished by comparing detector outputs with sources of various known energy spectra. The sources used were Ba-133, peaks 356keV and 81keV, and Na-22 with 511keV. The decay spectra are as follows;

The conversion factor was determined from the slope of a fit line. Shown below is the fit for detector 3.

Apparatus:

The two 10 uCi sources rested vertically at the center of a lead collimator, shown below. The chamber of the collimator in which the sources resided was machined to closely accommodate the plastic enclosures for those sources.

In order to measure azimuthal angle differences of 90 degrees, the detectors were arranged in the following way.

The signals from the detectors passed through amplifiers and were then fed in two locations. The first was sent directly to an oscilloscope. The second location was a set of discriminators. From the discriminators, the signal passed through logic gates with an output pulse when detector 1&3||2&3 are true. The logic pulse acted as a trigger for the collection of data sent directly to the scope. A schematic is shown below.

The actual setup is shown here.

Results

The data was collected from the scope by a LabView script as counts per voltage. Using the conversion factor, the data was changed to counts per energy. Then, the newly formed energy arrays were placed in a histogram with the bounds of [0 520] keV and a step size of 20 keV. An example of the histogram comparison is shown here.

The experimental ratio was determined by dividing counts for Det 90 by Det 0 for each bin. The range of angles allowable reduced the energies of interest to [270 380]. The data was fit according to the theoretical model. The results of the first trial can be seen below. The ratio magnitude was found to be 0.6 times the model, but the trend adhered closely to expectations.

The results of trial 2 without an extreme outlier can be seen below. This trial appeared to follow the theoretical model without an outlier.

Conclusion

Two trials of varying apparatus configurations were used to explore the spin states of coupled photons produced in positron-electron annihilation events. For a given duration, the total counts for opposite and same spin state photons coincident on specifically placed detectors were gathered. The ratio of counts for opposite over same spin state gamma-rays was calculated and compared to theory. The two trials differed regarding the ratio magnitudes, but agreed in trend. The data in trial 2 adhered closely to the predicted model, while the data for trial 1 followed only the trend and had a reduced magnitude.

By following the trend, the data in both trials support the angular arguments of the theory. Relative to the respective ratios at the boundaries, E'=0 & E'=511 keV, the data tended to behave as the model predicted. Despite the promising trend, the discrepancies between the trials offers no definitive answer regarding the counts' magnitude differences, but there is no reason to mistrust the theory at this stage. More data must be collected to determine which trial, if either, have repeatable results.

Acknowledgements

Thanks to the University of Minnesota for the use of the equipment and facilities, Kurt Wick for his knowledge and assistance, Roger for his guidance and role as adviser, and Kevin for his willingness to solve problems and answer questions.

References

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