Laboratory 2: Single Photon Interference
David Cruz, Nelson Lee, Natalie Pastuszka
University of Rochester Institute of Optics
September 25, 2013
Abstract:
The main focus of this laboratory experiment was to demonstrate the wave-particle duality of light by observing single photon interference. To accomplish this, a red He-Ne laser (632.8 nm wavelength, approximately 5 mW power) was attenuated to produce single photons which were sent through an interferometer onto a detector. The first part of the experiment demonstrated wave-particle duality by sending the attenuated beam through a Young’s double slit interferometer and observing the presence of interference patterns detected by an EM-CCD camera. The second part of this experiment involved using a Mach-Zehnder interferometer to determine how “which path” information affects interference by splitting the beam through two different polarized paths and observing the appearance and disappearance of fringes.
Introduction and Background:
Light is comprised of massless particles known as photons. Though these photons are characterized as particles, they exhibit the properties and behavior of waves as well. This phenomenon is known as wave-particle duality. The main goal of this experiment is to demonstrate how these particles interfere with theirselvesin the same way that waves would. One method will be using a Young’s double slit interferometer and observing interference on a single photon level to show wave-particle duality. The other method uses a Mach-Zehnder interferometer to observe howhaving “which-path” information affects interference fringes by performing a measurement and collapsing the photon’s wave function, thereby causing it to behave like a particle.
In Young’s double slit experiment, a beam is incident on a screen with two slits. On a single photon level one would, in theory, expect to be able to know which slit the particle goes through. The result would be only two intensity patterns on the detector. However, this is not the case. Instead what we see is a series of light and dark fringes.
Figure 1: Young’s Double Slit Experiment Demonstrating the Wave-Particle Duality of Photons
This is due to the absence of “which-path” information. By blocking off one of the slits, thereby knowing the exact path, we would not see fringes. We observed these interference patterns using an EM-CCD camera, and these fringes are more visible towards the center of the detector and become less intense as the particles go farther from the central position.
Figure 2: Interference Pattern Observed in Young’s Double Slit Interferometer
Mathematically, to define a contrast of the interference pattern we introduce the following equation for fringe visibility:
Fringe Visibility = I max – I min
Where Imaxand Imin represent the maximum and minimum intensities of the wave. This relation is observed in the data that was collected and automatically calculated in the software.
In the second portion of the experiment, a Mach-Zehnder interferometer was used to split the beam, polarize each path vertically or horizontally, recombine the beam, and use a polarizer to erase “which-path” information. This was done on a beam with a large diameter which can be seen with the naked eye. The same effect was observed on a single photon level using the EM-CCD camera. Depending on the angle of the final polarizer, the knowledge of “which-path” information was destroyed and restored and the disappearance and reappearance of interference fringes was observed.
Experimental Setup:
I. Young's Double Slit Experimental Setup
The end goal of the experiment was to show the nature of particles as being in accord with the concept of wave-particle duality. A 5mW He-Ne laser with a 633nm wavelength supplied the light used in both experiments. Light coming from beam needed to be attenuated so 4 orders of magnitude neutral density filters were used; however, due to classical photon statistics, we did not achieve antibunching. The attenuated light was sent through slits that were 10μm wide and 90μm apart. An EM-CCD camera(observation screen) was used to observe the interference patterns that we would expect from waves. See the setup below.
II. Single Photon Interference with Mach-Zehnder Interferometer Experimental Setup
To achieve single photon interference, we used a Mach-Zehnder interferometer (See figure below). To allow for the "which-way" information needed to observe wave-like behavior, we set two polarizers (A and B) positioned at 45 degrees. Again, the neutral density filters were used to attenuate the beam to average about 1 photon per meter. The light splits into two separate arms after polarizing beam splitter A and then reunited using a non polarizing beam splitter. The fringes were then observed using the EM-CCD camera.
Procedure:
I. Young's Double Slit
Alignment and Preparation
Align the beam in order for light to pass through the slits and for the interference patterns to be captured by the camera.
Once the apparatus is properly aligned, the laser should be reduced to a single photon level using neutral density filters.
Capturing Interference Pattern
Adjust visual settings using ImageJ software in order to process the interference patterns.
II. Single Photon Interference with Mach-Zehnder Interferometer
Alignment and Preparation
To align the Mach-Zehnder interferometer, light (bright spots) that should be coming into the camera should overlap in both the far and near field. The resulting beam should then be aligned with the camera.
After alignment, neutral density filters should be used to reduce the beam to a single photon level.
Polarizer B should be rotated between 0 and 360 degrees (relative) and the resulting intensity and visibility should be recorded.
Capturing Interference Pattern
Once the apparatus is properly aligned and angle is adjusted, use settings on camera (ie. gain, accumulations and exposure time) in order acquire the best image to see interference patterns.
Results and Analysis:
I.Young’s Double Slit
Using the EM- CCD camera, we were able to verify the phenomena described in the wave- particle duality theory, where single photons are able to exhibit properties of a wave by producing interference fringes, which can be observed when single photons travel through two slits. Different neutral density filters, exposure times, and accumulations were varied to observe the best possible fringes. To find the order of these neutral density filters we first had to determine power and wavelength of the light source and use these values calculate how many photons per meter were being produced using the following equation:
Once this value is calculated, the order of magnitude gives us how many orders of filtration are needed to achieve a desired transmittance, and in this case single photons.
Figure 5: Interference fringes and analysis under neutral density filter of magnitude 2 at 0.1 second exposure time.
Figure 6: Interference fringes and plot profile under neutral density filter of magnitude 4 at 0.003 second exposure time. There is a slight indication of fringes, but they are not clear at all. The plot profile demonstrates a sinusoidal curve that is less distinguishable and contains a significantly greater amount of noise.
Figure 7: Interference fringes and plot profile under neutral density filter of magnitude 4 at 0.003 second exposure time and 255 gain. The settings for the acquisition of data are the same in both Figure 6 and Figure 7, with the exception that Figure 7 has gain. It is important to note the different in visibility of fringes.
Figure8: Interference fringes and plot profile under neutral density filter of magnitude 6 at 0.01 second exposure time, 255 gain, and accumulation of 90-10.
Figure 9: Interference fringes and plot profile under neutral density filter of magnitude 6 at 1.00 second exposure time, 255 gain, and accumulation of 100-10.
The images of the interference fringes were taken using an EM- CCD camera. The plot profile (left images) of the intensity of the interference fringes through Young’s double slit experiment were obtained through the program ImageJ. The intensity curve that varies over distance represents a sinusoidal function with some distortion that is directly correlated to the images of the fringes. Figures 5, 7, and 9 have the clearest fringes for each neutral density filter of magnitude order 2, 4, and 6, respectively. There is a distinction in the images when the acquisition various settings are altered, as is evident when comparingFigures 8 and 9. Both of the figures have the same order of filters and gain, but were exposed for a different amount of time and with a slightly different accumulation, thus allowing for better clarity of fringes.
II. Mach- Zehnder Interferometer
Depending on the angle of the final polarizer in the Mach- Zehnder interferometer setup, we were able to see fringes at different ranges of visibility.
(a) 150degrees (b) 100 degrees (c) 50 degrees (d) 0 degrees
Figure 10: Images captured by EM- CCD camera of fringe visibility at different angles of polarizer. As the polarizer changed angles by 45degrees with reference to the recombined beam, the fringes would alternate with appearing and disappearing. The interference fringes that have the most distinguished bands of minima and maxima (images (a) and(c)) indicate the absence of the “which- way” path knowledge.
Figure 11: Plot profiles of intensity of images of interference fringes captured by EM- CCD camera. The plot profile on the left represents the intensity profile of the interference pattern when the maxima and minima bands were the clearest. The plot profile on the right is of the interference fringes when the polarizer was rotated by 45 degrees with respect to the recombined beam and the image on the left, thus at an image that did not display fringes.
In Figure 11, both figures represent similarly sinusoidal functions, but are out of phase by 180 degrees with respect to each other. The two plot profiles represent the intensity of the interference fringes at different polarizations of the recombined beams. The plot on the left shows the plot profile when the interference fringes have the most distinguished bands (Figure 10, plot (a)) and the plot on the right displays the intensity profile of the image that was captured when the polarizer was set at 45 degrees to the point where the fringes were most visible (Figure 10, plot (b)). According to the “which- path” theory, because we were able to predict which path the photons would take, no interference fringes were visible. At a point where the polarization was set to an angle which halted our knowledge of path, fringes appeared.
Conclusion:
The results of our experiments clearly demonstrate the manner in which single photons behave. Single photons exhibit behavior customary to both waves and particles, as follows the wave- particle duality theory; single photons create an interference pattern that is explainable only by the nature of waves as was evident in Young’s Double Slit experiment. The Mach-Zehnder setup permitted exploration of “which- path” information as the observance of fringes depended on the angle of the polarizer. By blocking the light through use of the polarizer and thereby knowing the path of the photons, no fringes were visible. In the situation that the angle was rotated to a position where there was no predictability of the photon’s path, interference fringes would appear and confirm the classical quantum properties.
References:
- Lukishova, Svetlana. Lab 2 Manual, Web. Fall 2013.
- “A simple experiment for discussion of quantum interference and which-way measurement”. Schneider, M. B., LaPuma, I.A.
Contributions:
Under the guidance of Dr. Svetlana Lukishova, all members contributed equally during lab to calculate values for ND filters; setup equipment and interferometers; and collect and analyze data.
David Cruz wrote the “Abstract” and “Introduction and Background” sections.
Nelson Lee wrote the “Experimental Setup” and “Procedure” sections.
Natalie Pastuszka wrote the “Results and Analysis” and “Conclusion” sections.