-- Main.thern007 - 15 May 2015

Young's Double Slit Experiment with Quantum Eraser

By: Joel Therneau & David Schoder

Advisor: Clement Pryke & Kurt Wick

Date Submitted: May 14, 2015

Abstract

We observed the particle/wave duality of single photons using a double slit experiment. An incandescent bulb passing light through a band-pass filter and a single slit creates a horizontal plane wave incident upon a double slit. A photomultiplier tube (PMT) translating across the diffraction envelope recorded the resulting photon self- interference pattern. Polarizers were then used to mark the photon passing through the slits, providing which-path information and eliminating photon self-interference. Finally, the addition of another polarizer destroyed the which-path information and partially restored the photon self-interference pattern.

Introduction

The particle/wave duality of light has historically been a rich source of confusion amongst physicists, with both the particle and wave "picture" being successfully used to describe the physics underlying light phenomena[1]. The double slit experiment provides an excellent backdrop to explore the particle and wave characteristics of light, and explore interesting "thought pictures" about how to best explain the results. In this experiment, the wave-like nature of light is demonstrated by observing the interference pattern that light produces when going through a double slit. The particle picture is then explored by attempting to determine which slit the photon passes through, which has the curious effect of destroying the interference pattern. The interference then re-emerges when this which-path information is destroyed prior to photon detection.

Theory

When light passes through a double slit, each slit like acts like a wave source, with amplitudes adding constructively or destructively due to the path length difference between different wave crests. The path length difference is dependent on the length between the slit location and the detection apparatus, L, the distance between the slits, d, and the wavelength of the light, <a href="%ATTACHURL%/lambda.gif">

</a> . The distance between destructive interferences is given by [3]:

where x is the horizontal distance on the detection plane where the photon is detected. Figure 1 below demonstrates this effect.

Light travelling through a single slit creates a diffraction pattern governed by the following equation [3]:

where a is the slit width and the position and x is the distance on the detection plane. When this light passes through a double slit the equation becomes a product of the single slit diffraction equation and a double-slit interference term [3]:

In the above equation the cosine term governs the interference pattern introduced by the double slit, with d being the distance between each slit. Both of these formulas can be related to the number of strikes registered in a PMT as it is translated across the diffraction envelope.

Experimental Setup

Results

The data in Figures 8 through 11 was taken with the light intensity such that only one photon is in the system at any given time. It can also be seen that “dark count” has been reduced by a factor of 20 from its rate in Figure 7. This was achieved by simply cooling the PMT with dry ice. The condition of reducing the light intensity to this single photon regime is complicated by the fact that photons cannot be thought of strictly as a particle. This leaves open the possibility that two photons could overlap and possibly interact with one another. If we treat a photon as a quantum mechanical wave packet, the most natural analog to “photon length” is the uncertainty in its time multiplied by the speed of light. A purely monochromatic photon would have an exact energy given by E=hc/λ. The photons used in this experiment are certainly not purely monochromatic, but, due to the band-pass filter, have an uncertainty in wavelength Δλ=10 nm. From this, the uncertainty in energy is

Applying this to the time energy uncertainty relationship, we arrive at

Plugging in for ∆E and solving for ∆t

With λ_1=551 nm and λ_2=561 nm, plugging in and multiplying by the speed of light, we arrive at a lower bound wave packet length of 2.5 µm.

It can be calculated how long a photon would have to be to be overlapping in our experiment. If we assume the photons are evenly spaced in time, by calculating the number of photons emerging from the double slit per second and dividing the speed of light by this number, the total distance between photons is

Simply integrating over the central diffraction envelope and dividing the speed of light by that number will not work. This approach is wrong for three reasons. First, integrating over the central diffraction envelope only accounts for 88 percent of photons entering the system. This can be shown by dividing the integral over the central hump by the integral over all space. Second, the PMT’s entrance slit does not envelop the entire diffraction envelope. Figure 12 illustrates. Third, the quantum efficiency of an average photomultiplier is around 20 percent [5]. Taking all this into consideration, the distance between photons was calculated to be roughly 4 km. This is many orders of magnitudes larger than the estimated length of a photon. Therefore, it is reasonable to assume that single photons are self-interfering.