S16_Young'sDoubleSlit

Introduction

Long has light been a subject of debate throughout the study of physics. Perhaps the most famous of these debates was centered about one of its intrinsic properties, the question of whether light was a particle or wave. Scientific greats from Newton to Einstein have pondered this question, and in providing their theories, have allowed a deeper understanding of it. Today, it is well-known that light is both a particle and a wave, the property that created the need for this experiment to be conducted in the first place. This experiment, Young's double slit experiment performed in the quantum mechanical limit, is of interest not only as a counterpart to the original, but as an exploration of the strange, seemingly impossible nature of quantum mechanics. For example, single photons incident upon the double slits will interfere with just themselves, not other photons, despite that action going against most people's intuition. However, with the appropriate application of the laws of quantum mechanics, predictions can be made about a photon's behavior when passing through the slits. Specifically, this so-called photon self-interference was expected to result in an interference pattern. This interference pattern was then thought to be destroyed through the use of which-path polarizers, and then subsequently brought back by the implementation of a quantum eraser.

Theory

Light incident upon the double slits will create a variable intensity pattern on a screen a distance L away from the slits. This intensity pattern is made up of the superposition of a diffraction pattern and an interference pattern. The interference pattern expected to be observed through photon self-interference has the same distribution as that of the classical limit, and thus is expected to be (Derived in [1]):

where lambda is the wavelength of the incident photon, y is the distance along the screen, a the slit width,and d is the distance between the slits.

Figure 1. The typical double slit geometrical setup. (Reprinted from [2])

In order to obtain a more accurate model, the fact that an aperture of finite width was used to collimate means that the light did not come from a point source, and thus the coherence of the light must be accounted for. Thus this

interference for finite source is given as (Derived in [3]):

where b is the width of the aperture and A is a constant.

In order for photon self-interference to occur, the components of a photon's wave function must be closer than the magnitude of the coherence length, as it is a measure of the uncertainty of distance. This

coherence length of light is given as(Derived in [3]):

where this lambda is the central wavelength let through by the band-pass filter.

Finally, as an auxiliary variable to help explain the obtained data, visibility was investigated as well. It causes the bottom of the interference pattern to raise up from zero and approach the maximum value, depending on the value of the visibility. The equation for visibility is (Derived in [3]):

Apparatus

The light was supplied through the use of an incandescent light bulb. The light was selected around a central wavelength of 546 nm by the band-pass filter. From there, it was collimated by the aperture opening and traveled onward to the double slits. Data was taken through the use of a Hamamatsu 6240-01 photomultiplier tube mounted upon a translational stage. This PMT's sensor acted as the screen to which the light traveled from the slits.

Below is the set up from the basic double slit experiment. Light intensity was reduced to the point that only a single photon passed through the double slits at a given point in time. From this, the interference pattern for a source of finite width was expected to be viewed.

Next, the which-path markers were added in. These were simply mutually orthogonal polarizers. These were expected to have the affect of destroying the interference pattern.

Finally, a quantum eraser was added to the set up in addition to the which-path markers. The quantum eraser used was just another polarizer at an orientation 45 degrees between the which-path markers. This set up was expected to bring back the interference pattern, albeit with a lower intensity than before.

Results

Below is the image of the interference pattern given by the basic set up of the double slits.

As is apparent upon inspection, the it fits the model well in terms of general shape and intensity, but not accurately enough in order to say that it fit within the uncertainty. Regardless, it is thought that interference

really did occur with this set up,despite it's inconsistency with the theory.

Next, the data for the destroyed intensity pattern is presented.

In a similar fashion, this data too fit the model to a certain degree, but differed at some key points. For example, the period of the model and actual data differ, causing us to once again be unable

to say that the prediction matched the results within the uncertainty. Regardless, it is still thought that the which-path markers successfully destroyed any interference pattern and left us with just a diffraction pattern, as expected.

Below is the final data set, that for the intensity pattern after the addition of the quantum eraser.

As is apparent, this data set matches the prediction the least. The points themselves appear to be just a single slit pattern. Only when many points are brought together in a moving average does one see

any semblance of the expected interference pattern. Essentially, the reconstruction of the intensity pattern was not viewed.

Conclusion

Despite the vast differences between the collected data and the predicted results, it is thought that the theory was still correct. Because of the similarities between the data and the model in the first and second set ups, it is thought that perhaps some sort of unaccounted-for factor caused our data to differ so much. One such explanation could possibly be that the slits and PMT were offset by an angle. This could possibly explain the lopsided data set in the basic interference pattern.

References

• 1. A.P. French, Vibrations and Waves, W. W. Norton & Company Inc., 1971.

  2. Sen-ben Liao, Peter Dourmashkin and John W. Belcher, Interference and Diffraction, Physics 8.02 Electricity and Magnetism Course Notes, Massachusetts Institute of Technology, 2004. http://web.mit.edu/viz/EM/visualizations/coursenotes/modules/guide14.pdf

  3. Hecht, E., and A. Zajac, Optics, Addison-Wesley Publishing Company, Inc., 1979