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Measuring the Behavior of Single Photons in a Mach-Zehnder Interferometer with a Quantum Eraser
Ben Francis, Robert Schubert-Sponsel
University of Minnesota-Twin Cities
School of Physics and Astronomy
Minneapolis, MN 55455
Abstract
We demonstrate the existence of single photons and build a Mach-Zehnder interferometer with a quantum eraser. An anticorrelation parameter of αABB’ = 0.000 ± 0.003 was recorded, showing the presence of single photons, while the quantum eraser was not able to be completed. The interesting effects of quantized light, superposition, and information destruction are explored.
Introduction
When a photon enters a Mach-Zehnder interferometer and is given two possible paths to follow after being transmitted or reflected through a beamsplitter, it takes a superposition of these paths. Observing the path of the photon causes this superposition to collapse and the photon to take a single path. [1] If there is an interference pattern created by the superposition of both paths, such as in the Mach-Zehnder interferometer, the pattern will disappear with the collapse.
In order for these phenomena to be explored using quantum mechanics, it must be shown that the light used is composed of single photons.This demonstration of single photons relies upon the correlation and anticorrelation of detectors in two different experimental setups, a correlation experiment and an anticorrelation experiment.
In the first experiment, a pair of correlated photons is created by spontaneous parametric down-conversion through a
β-barium borate (BBO) crystal (see Fig. 1a).
(a) (b)
Fig. 1. (a) The correlation experiment to detect correlated photons from the BBO crystal. (b) The anticorrelation experiment to show anticorrelated photons from a beam splitter. (Original Figure)
In the second experiment (Fig. 1b), one correlated photon is sent to detector A and the other is sent through a beam splitter leading to either detector B or B’. Showing anticorrelation between B and B’ demonstrates that a single photon is going to either detectors B or B’.
The photons previously sent through the beam splitter are sent into a Mach-Zehnder interferometer (see Fig. 2). The interferometer has two possible paths for the photon and the photon takes a superposition of both paths and interferes with itself.
Fig. 2. Mach-Zehnder Interferometer and polarizers with parts labeled. (Original Figure)
By introducing two polarizers, one at 0° and one at 90°, we distinguish which path a photon takes. The superposition then collapses as the photon “chooses” one discrete path, as opposed to the superposition of both. Finally, we put a second pair of 45° polarizers between the detectors and the second beam splitter, the “quantum eraser”, and the interference returns.
Theory
The experiment utilizes detectors which send signals to a coincidence counting module (CCM), which gives the rate at which photons are hitting the detectors. The CCM determines each detector’s rate of counts per second, RA, RB and RB’.
If an event happens at both detector A and B within a certain time window, it is defined as a coincidence. In order to define this coincidence, the CCM defines the coincidence window as τ. The rate at which these coincidences occur is defined as RAB. In addition, an anticorrelation parameter, 𝛼, can be calculated [2]:
(1)
The setup from Fig. 1b is used to show anticorrelated detectors. The anticorrelation parameter for all three detectors is [2]:
(2)
Showing 𝛼ABB’<<1 in the anticorrelation experiment demonstrates that a semiclassical explanation of light is insufficient and single photons must exist in the experiment.
The established single photons are sent into the interferometer, still using detector A to determine when to look at detectors B and B’. An interference pattern from the second beam splitter can be seen by adjusting the position of one of the mirrors to change the path length difference of the two paths. Because nothing is in place to measure the path which the photon takes, this is called the “untagged” arrangement.
If two polarizers are placed in each path immediately before the second beam splitter, one at 90° and one at 0°, each photon will be “tagged” by a new polarization. Distinguishing the photon's path collapses the superposition to one discrete path. There will not be interference and adjusting the path length difference will have no effect on the rates of B and B’.
The final third setup results in the polarization information of the photons being “erased”. This occurs when two polarizers oriented at 45° are put between the second beam splitter and both B and B’ detectors, while still keeping the previous 90° and 0° polarizers. This 45° polarizer acts on photons with 90° or 0° polarization in the same way, so that we can no longer tell which path the photon takes. Because by the time the photon reaches the detectors no measurement of photon’s path occurs, the photon's superposition does not collapse and the interference pattern returns.
Results
The setup is followed from the MXP single photon interference experiment webpage in accordance with Fig. 1a, 1b, and 2. Measurements are taken with a coincidence window of 10 ns, 20 ns, 40 ns, and 60 ns as an average over 25 s. The results from the correlation experiment are shown in Table I:
Table I. α values from the correlation experiment.
The results from the anticorrelation experiment are shown in Table II:
Table II. α values from the anticorrelation experiment.
The high αAB values from the correlation experiment show that the apparatus is dealing largely with single photons from the BBO crystal, as opposed to accidental photons such as background photons from the room, dark noise from electronics, or photon bunching from the laser. Quantized photons are demonstrated from the near zero values of αABB’
Troubleshooting
The interferometer half of the experiment was not able to be completed. Although the experimental setup is described in detail by the MXP single photon interference experiment webpage, upon reaching the white light interference step we encountered large difficulties. In this step, interference patterns are needed from both the HeNe laser and a white light to ensure interference will occur with the correlated photons. We discovered some additional methods that will help this process in the future.
Before conducting the white light interference it is critical that the HeNe laser, which represents the location of the B/B’ photons, be arranged exactly in the center of each beam splitter and mirror. When white light is put through the interferometer, you can see a shadow of the beam splitter if you put a card where the detectors will go. If the HeNe does not enter the shadow of the beam splitter, it will be impossible to align the interferometer so interference is seen in a detector. We had to entirely realign after discovering that ours did not.
Alignment of the interferometer for HeNe interference is the best way to get it close to the very elusive white light interference. The best way to reliably do this is the same process of mirror walking. Use the two mirrors to get the two points from the HeNE on top of each other on a target close to the interferometer. Then use the beamsplitter to get the points on top of each other on a larger far away point. Repeat until there is a good interference pattern with very large fringes.
Creating the white light interference is the most time consuming and difficult step of the experiment. There are eight degrees of freedom among the second beamsplitter and the two mirrors in the interferometer that need to be adjusted to achieve this. Only when all eight are near perfect in alignment is any interference seen.
We found no general strategy for this, although the range necessary is exceedingly small so the adjustments should have incredible finesse. When you are close, the pattern grows frills or bumps at its top on the spectroscopy graph. Once these become recognizable, it is advised to move only one knob at a time, always maximizing the pattern achieved. They must be adjusted further until they are discrete fringes, even if there are many of them (see Fig. 4).
These multiple fringes show what the single fringe interference pattern will look like; the lower bound of the fringes are what singe fringe destructive interference would look like and the top what constructive would look like. The goal is to lower the amount of fringes without losing the intensity difference between fringes, so that a dark fringe has 70% to 80% of the intensity of a bright fringe. Adjusting the mirrors increases the intensity of the interference and adjusting the beam splitter and linear mount of Mirror 1 lower the number of fringes. In this way, eventually the end result will be one fringe. The process of beginning with the standard intensity spectrum of the flashlight is shown in Fig. 3:
Fig. 3. The standard spectrometer graph of the flashlight.
An extreme example of seeing many fringes is shown in Fig. 6:
Fig. 4: The spectrometer graph showing many fringes.
After adjustments, Fig. 5 (a-c) shows the process of lowering the number of fringes while maintaining the intensity difference between bright and dark fringes.
Fig. 5. (a, left) Lowering the number of peaks in the pattern to three. (b, center) Lowering the number of peaks to two. (c, right) Regaining the intensity and sharpness of the two peaks.
Finally one peak is achieved, where the difference between the maximum and minimum is between 70% to 80% of the total, as shown in Fig. 6:
Fig. 6. One fringe, where the black overlay corresponds to the maximum, bright fringe and the red the minimum, dark fringe.
This was achieved twice. However, other variables required restarting the process. After the first success, we realized that the mirrors were not at the same height, resulting in one providing more light than the other in the interference pattern. In this way, a destructive interference pattern could not be fully achieved (as can be seen in the diagrams). After the second calibration, it was realized that the HeNe laser was not aligned properly with the white light interference. The HeNe represents the alignment of the correlated photons, so the white light interference had to be moved. For future experiments, it is advised to ensure that these additional variables are properly set up before the white light interference is focused on.
Conclusion
This experiment sought out to demonstrate the existence of single photons and the effects of a quantum eraser in a Mach-Zehnder interferometer. The first of these goals was confirmed by two experiments. First, a correlation experiment resulted in an anticorrelation parameter of αAB = 634.2 ± 8.9. Second, an anticorrelation experiment resulted in an anticorrelation parameter of αABB’ = 0.000 ± 0.003. These can only be explained by the use of single photons in the apparatus and excludes explanations using a semiclassical theory of light. The quantum eraser was not completed and remains a goal for future experiments. However, the effects of a quantum eraser are able to be discussed as quantum mechanical due to this confirmation of the use of single photons.
References
[1] Griffiths, “Introduction to Quantum Mechanics”, 2nd Edition, Pearson Prentice Hall. (2005): 106.
[2] Pearson, Brett J., and David P. Jackson. "A Hands-on Introduction to Single Photons and Quantum Mechanics for Undergraduates." American Journal of Physics 78.5 (2010): 475, 478, 472, 476, 476.
[3] Power Technology Incorperated, “GPD(405-50) 405nm 1-50mW Blue Laser Diode Module”, <http://www.powertechnology.com/index.php/gpd-405-50.html>.
[4] Shih, Yanhua , "Entangled biphoton source - property and preparation". Reports on Progress in Physics. (2003): 66.
[5] Thorn, J.J.; Neel, M.S.; Donato, V.W.; Bergreen, G.S.; Davies, R.E.; Beck, M. (2004). "Observing the quantum behavior of light in an undergraduate laboratory" (PDF). American Journal of Physics. 72 (9): 1210–1219.
[6] Wilson, Buffa, Lou, “Physics”, 6th Edition, Pearson Prentice Hall. (2007): 777.
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