2 Lab Report
Carlin Gettliffe
Abstract: In this lab we investigated the wave-particle duality of light. We verified lights wave properties by conducting both a double slit experiment and constructing a Mach-Zehnder interferometer. In each case we recorded interference patterns at both high intensities and single photon levels. By building up interference
patterns gradually over time, we demonstrated that single photons can indeed interfere with themselves. The interference patterns we observed provide direct evidence that light can behave both as a particle and a wave.
1. INTRODUCTION AND THEORETICAL BACKGROUND: The wave-particle duality of light is one of the basic tenets of quantum mechanics. Stated simply, wave-particle duality means that in certain conditions light will behave as a wave, while in others it will behave as a particle. Any direct
measurement of light collapses the wave function and results in particle behavior. When light is allowed to travel uninhibited, however, we observe wave-like properties. These wave-like properties are evident even in the case of single photons, which can interfere with themselves. In this lab we repeated the classic Youngs Double Slit Experiment. We also built a Mach-Zehnder interferometer. Youngs Double Slit Experiment serves as a basic way of demonstrating the wave property of light. In any situation where coherent light is split into two paths and subsequently recombined, we would expect to see interference (as long as no direct measurements of the light are performed along the way). Additionally, when light passing through the two slits is attenuated to the single photon level we would expect to still observe an interference pattern being built up over time. This is a result of single photon interference. The implication of single photon interference is that as experimenters we can only think of photons as particles when they arrive at specific points of interaction. As long as no measurement has been performed, light behaves as a wave, even at single photon intensity levels. In the Mach-Zehnder interferometer
experiment, this fact can also be clearly observed. As soon as which path information is destroyed, we observe an interference pattern. If we preserve which path information
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(meaning we know where an individual photon has been), no interference pattern can be observed because we have already verified lights particle nature. In this lab we used a 633nm He-Ne laser as a light source. In order to attenuate the beam to single photon levels we used a series of filters to bring the laser intensity down to an average of 1 photon/300 meters. A cooled CCD camera was used as a detector. This experiment provided verification of a fundamental prediction of quantum mechanics: wave-particle duality.
2. PROCEDURE
FIG 1. Mach-Zehnder Interferometer
FIG 2. Youngs Double Slit Experiment
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1. We measured the laser intensity to be 0.27uW. Since we were using a 633nm He-Ne laser, the power per photon was calculated to be 3.14x10-19 J. Thus, at 0.27uW the number of photons arriving at the detector was 8.5x1011 photons/second. A spacing of 300 meters between photons corresponds to a rate of 1x106 photons/second. Thus we needed attenuation of roughly 10-6 in order to reach the desired average interphoton spacing. This was accomplished using neutral density filters. 2. We placed a double slit in the path of the laser and positioned the CCD camera to collect light passing through the two slits (See FIG 2). 3. We captured images of double slit interference at high intensity levels. 4. We placed neutral density filters in front of the laser source to achieve our desired photon spacing of 1 photon/300 meters. 5. We captured images of the two slit interference pattern for various exposure times in order to show that the high intensity interference pattern is identical to a low intensity interference pattern gradually accumulated over time (i.e. a collection of single photons). 6. We then built a Mach-Zehnder interferometer (shown in FIG. 1) and directed the beam from the interferometer towards the CCD camera using two mirrors. 7. A polarizing beam splitter was used to split the light into two paths, each with opposite polarization. After redirecting the light with mirrors, the light was
recombined using another beam splitter (FIG 1). 8. In order to align the Mach-Zehnder interferometer we first carefully aligned the individual components in order to ensure that the laser beam was close to level throughout the interferometer. We recombined the split beams using a beam splitter. Further alignment was achieved by tilting/rotating the beamsplitter slightly in order to get the two beams to closely overlap. 9. We used the CCD Camera to capture images of the recombined beams both with a 45 degree polarizer at the exit of the interferometer and without any polarizer at all. 10. We captured images of the interference pattern from the Mach-Zehnder interferometer at both high intensity and single photon levels to show that the interference pattern is preserved even when photons are passing through the system
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one at a time, and that high intensity patterns are similar to low intensity patterns built up over time. This demonstrates wave-particle duality.
RESULTS AND ANALYSIS Our results confirmed that interference patterns can be built up gradually from single photon interference. In FIG 3 it is possible see to double slit interference first in a well defined interference pattern (image 1) and then in gradually more fuzzy interference patterns (images 2-4). Image 4 clearly shows that light was arriving at the CCD in the form of particles (we can see individual dark pixels), and yet an interference pattern was still present. This is a clear demonstration of wave-particle duality. The intensity patterns corresponding to images 2-4 all show the intensity variations characteristic of a double slit arrangement. The visibility of the double slit interference patterns can be calculated using the simple equation (max-min)/(max+min) x 100. In FIG 4, the visibility of the Image 2 is very close to 100%, but decreases with increasingly short exposure times. The visibility of Image 3 is about 60%, and the visibility of Image 4 is approximately 25%. Our results clearly indicate that visibility increases with greater exposure times. Our preliminary results from the Mach-Zehnder interferometer confirmed that when which-path information is preserved no interference pattern is present. In the two images from FIG 5 the only thing that was changed was the presence of a polarizer. When a polarizer was present we observed interference fringes because all which-path information was destroyed (the wave function was not broken down). As long as no polarizer is present the path that a photon took is encoded into its polarization state. Thus, it is not free to take both paths and cannot interfere with itself. As soon as another polarizer is introduced at the exit of the system, the information about which path the photon took is destroyed because it has a new polarization. In FIG 6 it is evident that the same single photon interference that was observed in the double slit experiment is present in the Mach-Zehnder interferometer experiment. By capturing a series of images with different exposure times, we observed the way an interference pattern gradually builds up as photons pass through the system and interfere with themselves. 4
Image 1
Image 2
Image 3
Image 4
Attenuation Image 1 Image 2 Image 3 Image 4 None 0.16 9.4 x 10 1.2 x 10
-6 -6
Acquisition Time (s) 0.3 0.3 1 3
Gain None None 255 255
FIG 3. Double slit interference patterns. 5
Image 2 - corresponding intensity pattern.
Image 3 - corresponding intensity pattern.
Image 4 - corresponding intensity pattern.
FIG 4. Intensity cross sections of double slit interference patterns.
Which-path information destroyed (with polarizer)
Which-path information preserved (no polarizer)
FIG 5. Images from Mach-Zehnder interferometer with and without polarizer.
We observed that without a polarizer no interference pattern was observed because light exiting the interferometer contained which-path information. When the 45 degree polarizer was placed at the exit of the interferometer an interference pattern was observed. 6
Image 1
Image 2
Image 3
Image 4
Image 5
Image 6
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FIG 6. Images from Mach-Zehnder interferometer at varying exposure times.
Attenuation Image 1 Image 2 Image 3 Image 4 Image 5 Image 6 3.0 x 10 3.0 x 10 3.0 x 10
-6 -6 -6
Acquisition Time (s) 1 2 5 10 25 ~5
3.0 x 10-6 3.0 x 10
-6
3.7 x 10-5
FIG 6 CONTINUED.
DISCUSSION AND CONCLUSION The d...