S17_Young'sDoubleSlit

Young’s Double-slit Experiment with Single Photons and a Quantum Eraser

Chiou Yang Tan & Xin Zhi Tan

University Of Minnesota - School of Physics and Astronomy

Introduction

Imagine that a lot of balls are thrown through two windows, one at a time; it will only hit two area on the wall behind the windows. However, when we repeat the same experiment with photons, the photons will form interference pattern. [1] This phenomenon implies that the photon are interfering with itself, and for a single photon to interfere with itself, it must passes through both slit at the same time. Hence, it will be interesting to look at which slit does the photons go through. When we try to observe which path does the photons take, the wave function of the photons will collapsed into a single definite state, so the interference pattern will be destroyed. In this experiment, a which-path marker, which is a pair of mutually perpendicular polarizers, was used to obtain the which-path information by marking the photons with their polarization. [2] Then, a quantum eraser, which is a polarizer that held 45 degree with respect to the which-path marker, was used to remove the which-path information and restore the interference pattern. [3]

Theory

For a single photon light source, a photon itself will not produce an interference pattern; instead it will be detected at some location on the screen. Only by accumulating many photon detection events, there will be areas with higher photon detection rate than the others, and the pattern produced resemble interference pattern. This situation is counterintuitive because the photons pass through the slits one at a time and we should expect the pattern produced is similar as the ball scenario as mentioned earlier. This situation suggests that the photon interferes with itself as some sort of wave when it passes through both slits to produce interference pattern, except that the peaks of this pattern are regions where there are more chances that the photon will be detected. In quantum mechanics, this wave-like property of the photon can be described by a wave function. [4]

If we treat the areas at which there are no photon hits as destructive interference and the areas where there are many photons hit as constructive interference, we can describe this pattern by Young’s double-slit intensity equation, which is

(1)

where all the relevant parameters are shown in figure below.

Figure 1. Typical setup for a Young's Double-slit experiment. (Original figure)

Equation (1) only works when the double-slit is driven by a single point source of light. In reality, the entrance slit has a finite slit width, 𝑏; for it to act like a point source, the distance between the entrance slit and the double-slit, 𝐿𝑠𝑜𝑢𝑟𝑐𝑒 , must fulfill the coherence condition,

(2)

When the coherence condition for a point source is not fulfilled, [5] shows that the interference term in equation (1) has to be modified to describe this pattern,

(3)

Experimental Setup

An incandescent light bulb was used as the light source along with a bandpass filter that attenuated all light outside 546 ± 5 nm, giving us an approximation of monochromatic light. A H6240-01 photomultiplier tube (PMT) was used to count the photon that hit at the position of interest. The effective detection area PMT is about 2 cm, therefore a 20 micron single slit was placed in front of it, allowing us to record the photon counts at a particular location. The PMT was placed on a Thorlab translation stage, allowing us to move the PMT to desirable location. The process of collecting photon counts and the movement the PMT was facilitated by a LabVIEW program.

The whole setup was placed inside a dark box so that the PMT only measures the photons from the dim light source. Dry ice was also used to cool the PMT to reduce thermal noise produced by it.

Figure 2. The setup for the double-slit experiment. (Original figure)

Figure 3. The setup for the which-path experiment. The which-path marker marks the photons by

its polarization. In other words, the photon that passed through the "top" slit will have 90 degree

polarization, while the photon that passed through the "bottom" slit will have 90 degree polarization.

Therefore, the information of which slit does the photons go though exists. (Original figure)

Figure 4. The setup for quantum eraser experiment. With the quantum eraser, no matter which slit the photons

take, they will have the same polarization at the end. Hence, the which-path information was erased. (Original figure)

Single photon Calibration

The detection of an individual photon can be treated as an independent random event, which can be described by Poisson distribution. The probability of finding 𝑛 photons with the rate of photon emission 𝑅 at time interval 𝜏 can be describe by

[6] (4)

To ensure that we are dealing with single photon, we restrict the photon emission rate such that, from double-slit to PMT, the probability of having two photons must be much lower than the probability of having only one photon, which is

(5)

where the time interval 𝜏 is the duration of photon travel from double-slit to PMT. This particular value of 𝜏 was chosen because we were only concerned about those photons that passed through the double-slit.

Before the experiment was started, the PMT was placed right behind the double-slit to measure the photons count, without the 20 micron single slit, to make sure that criteria above was fulfilled.

Result

For all the result shown below, data fitting was done using Least Square Fit to find the value of 𝐼0 from equation (1) or 𝐴 from equation (3) depending on experiment.

Figure 5. Data taken with V = 3.98 V and entrance slit’s width, 𝑏=52.6±0.3 μm.

Data above was subtracted by a value of 12.3±0.2 counts/s as dark count.

The observed pattern agrees with the theoretical fit with a reduced 𝜒² of 2.11.

Figure 6. Data taken with V = 5.80 V and entrance slit’s width, 𝑏=79.4±0.5 μm. The voltage and

entrance slit's width were increased since the pattern was not obvious due to the decrease in intensity.

Data above was subtracted by a value of 11.1±0.2 counts/s as dark count. The observed pattern agrees

with the theoretical fit with a reduced 𝜒² of 3.06.

Figure 7. Data taken with V = 5.80 V and entrance slit’s width, 𝑏2=79.4±0.5 μm. Data above

was subtracted by a value of 7.3±0.2 counts/s as dark count.

The reason the interference pattern of quantum eraser was not as well-defined as the interference pattern in double-slit is yet to be determined. However, our guess was that this is due to the imperfection of polarizer. Future groups could use polarizers of different transmission rate to determine whether this is the cause of it.

Conclusion

From our result, it shows that photon exhibits the behavior of wave. In the double-slit and quantum eraser experiment, although most of the time only one photon passed through the double-slit, interference pattern still persists. For the case of which-path experiment, the interference pattern was destroyed and only showed diffraction pattern, which matches our prediction. In quantum eraser experiment, the interference pattern was restored but not as well-defined as the one in the double-slit experiment.

Reference

[1] Stephen Hawking, Leonard Mlodinow. “The Grand Design” Bantam Books Trade Paperbacks (2010)

[2] Justin Winkler. “Single Photon Interference”. (2010)

[3] Wolfgang Rueckner and Joseph Peidle. “Young’s double-slit experiment with single photons and quantum eraser.” Am. J. Phys. 81, 951 (2013)

[4] Eisberg, Robert, and Robert Resnick. "The Wave-Particle Duality." Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles. (2nd ed.). John Wiley & Sons, (1985).

[5] Hecht, Eugene. Optics – Fourth Edition, Addison-Wesley Publishing Company, Inc. (2002)

[6] Samuel W. Hasinoff. “Photon, Poisson noise”