Young's Double Slit Experiment

Benjamin Buscher, Alison Cheng

University of Minnesota - School of Physics and Astronomy

Minneapolis, MN 55455

Introduction

Photons exhibit both wave and particle-like behavior under varying conditions. It is well known that when light is incident upon a double slit, it exhibits an interference pattern contained within a diffraction envelope that resembles that of a classical wave. When light is isolated into a single photon, the wave model of a photon breaks down and the photon is expected to follow the behavior of a classical particle. However, as a single photon travels through a double slit, it still exhibits wave-like behavior as seen by an interference pattern probability distribution of where along a screen it will be projected and detected. This seems to violate the principles of locality and causality because it would mean that as a single particle, the photon goes through both slits and interferes with itself. Quantum mechanics explains this behavior using Schrodinger’s wave function which governs the probability that a photon will be in a certain position in space-time and would allow for wave-like behavior from a single observable photon.

The quantum-mechanical behavior becomes even more pronounced when “which-way” mutually perpendicular polarized filters are inserted after the double slits. Any single photon wave component emanating from one of the slits is polarized perpendicular to the wave component emanating from the other slit. From this, it is possible to infer at the detector which slit the photon would have traveled down by checking the polarization state of the photon. However, in Rueckner and Peidle’s similar experiment, the self-interference pattern with the perpendicular polarizers is replaced by that of a particle through a single slit1. With the introduction of a third filter polarized at 45 degrees with respect to the other two, the self-interference pattern is restored. This third filter is called a quantum eraser, because its presence removes the information necessary to distinguish which slit the photon traveled down.

In this experiment, we attempted to test the single photon self interference phenomenon, the dissolution of the interference pattern under the presence of which-way polarizers, the restoration of the interference pattern with the addition of a quantum eraser. In addition, we explored the effects of a single polarizing filter covering only one of the two slits.

Theory

Young’s double-slit experiment uses a continuous beam of photons to produce the double-slit interference pattern. When the photon passes through the double slit, it will exhibit a wave interference pattern due to path length differences between the contributions of each slit which is dependent upon the wavelength of the light being used λ, the distance between the slits d, and the length between the slits and the viewing screen L.

The distance between fringes is given by:

For photons going through a single slit, the slit width yields a diffraction envelope spreading out the probability distribution of where along the screen the photon will strike. The intensity of photons reaching the screen as a function from the central peak intensity is shown in equation [2], where w is the slit width, L is the distance between the double slit screen and the detector screen, and x is the distance from the central peak of the diffraction pattern on detector screen.

Light incident on the double slit produces an interference pattern contained within the envelope of the diffraction pattern, which is expressed by

For a photon emission rate R along any directed length D in time window τ, the Poisson probability distribution for x photons to be present is given by

The probability that a given time window has more than one photon present is then

Our criteria for critical photon emission rate is thusly

Setup and Apparatus

The experimental setup consisted of a standard #47 light bulb with a nominal voltage of 6.3 volts DC, 0.15 Amperes, and 0.94 Watts, contained within a centrally bored out and candle soot darkened aluminum rod stock serving to restrict and collimate the light. At the other end of the aluminum rod, a (545+/-5)nm THORLABS band pass filter transmitted our target wavelength photons through a 0.16mm by 3mm single slit screen a distance r from the light bulb to further collimate and attenuate the light source. The emitted photon beam was directed to a double slit screen, positioned a distance d from the light source which transmitted the photons to a photomultiplier tube affixed to a translational stage at a distance D from the light source

The detection screen consisted of a Hammatsu H6240-01 photomultiplier tube with a 0.02mm single slit opening. The detector was connected to a computer and affixed to a Thorlabs MTS50-Z8 translational stage. LabView software was modified and written to record 10 seconds of photons at 0.1mm increments along the 50mm range of the translational stage. All position and photon count data collected was saved to CSV data files in numbered batches along with the particular parameters of the given data run such as light bulb current and the distances between optical components. The entire apparatus was contained within a light tight black box with coaxial data and power connections. To further limit the influence of outside light, black canvas and black electrical tape were used to further cover and seal any sources of light contamination. Data was collected across four conditional setups.

Condition 1: Condition 2:

Condition 3: Condition 4:

Results

Conclusion

We were unable to attain data at voltages low enough to ensure single photon events through the double slits. Data collection at applied voltages less than the critical photon rate was confounded by two primary factors: 1.) the magnitude of the dark current fluctuation noise relative to the peak intensity of the observed pattern, 2.) the inability to produce a clear interference pattern at any voltage or intensity until the introduction of a single slit screen in front of the light source and band pass filter.

The single slit in front of the rod and band pass filter served to restrict the range of angles from which photons might impinge upon the double slit: this had the benefit of making the light incident on the double slit qualitatively more like a plane wave. It was found empirically that the single slit in front of the light source was essential in order to attain full depth of the interference pattern inside the diffraction envelope. It is possible but not understood or explored in this paper that the combination of the aluminum collimating rod stock and band pass filter may act to disperse and widen the angular path of photons from the light source as they are directed towards the double slit screen, resulting in a smearing of the interference pattern at the detector screen. The single slit in front of the band pass filter and collimating rod is believed to limit this influence.

The dark noise fluctuation current was significant relative to the peak photon intensities we detected. Due to the shortage of time once the single slit screen solution was found, we were unable to take data containing larger sampling periods or by using methods to cool the photomultiplier tube to reduce the impact of the dark current noise. While our results are not from single photon detections, the data collected across the four conditions agrees with the expectations for single photon behavior and it is believed that by addressing the dark current fluctuations via the method of cooling the PMT at a constant temperature and taking position intensity readings over longer sampling periods will produce successful results.

References

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