Dilyana Mihaylova Lab 2-Report

8/17/2019 Dilyana Mihaylova Lab 2-Report

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Lab II Young’s double slit experiment By Dilyana Mihaylova

Abstract

The purpose of this lab was to study the wave particle duality of light by

conducting several experiments. We conducted several double slit experiments using

Young’s double slit experiment set up and we also used a Mach-Zehnder interferometer

to show the effects of “which path” information on interference experiments. We wereable to show the wave particle duality of light and we were unable to observe any

interference from the Mach-Zehnder interferometer unless we used an analyser polarizer

to erase this \which path" information.

Background Information

One of the biggest questions in physics was the nature of light. Weather lightcould be described by waves or particles. Young’s double slit experiment consists of

observing light as it goes through two slits at a certain distance from each other. The light

that passes through each slit creates an interference pattern through constructive and

destructive interference. This experiment proved the wave nature of light. Otherexperiments such as the photoelectric effect showed the particle properties of light. In this

lab we observed both the wave like and particle like nature of light by sending a single

photon at a time through two slits. We were still able to observe the fringes. In order toanswer which path light takes we used a Mach-Zehnder interferometer. In a Mach-

Zehnder interferometer light from a source is split up, send through two different arms

and re-combined, created similar fringe pattern as Young’s double slit experiment. By polarizing light so that the two light beams are orthogonal to each other we can find outwhich path light takes. However by doing this the interference pattern will be destroyed

and if the “which path” information is erased, the fringe pattern can be recovered.


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Experimental Setup

The Young double slit setup includes a laser beam from a 633nm, 5mW HeNe

laser which goes through a pinhole and a lens. After that light goes through two slits,each of which was 10microns, and they are 90 microns apart. The fringes behind the

double slit can be observed on a screen or a camera. We used an EMCCD camera.(Figure 1) There was also a stand in front of the double slit where we could place

attenuators. The beam splitter was used to send light from the HeNe laser to the other setup. We used an image software ImageJ to plot the cross-section of the images we took.

Figure 1. Young’s Double split experimental set up

The Mach-Zehnder interferometer setup uses the same HeNe laser as an

excitation source. The light goes through a linear polarizer with 45 degree output polarization and polarizing beam splitter. After that the light travels through two separate

arms and is connected again through a non polarizing beam splitter. Then the laser beamgoes through a polarizer and the fringes can be observed by using a camera or a screen.

(Figure 2)

Figure 2. Mach-Zehnder interferometer


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Procedure and Results

Part I Young’s Double Slit Experiment

We took images of the fringes and single photons observed with double slit set upwith the EMCCD camera.

Using the known relationships:

N /s (number of photons per second) = P*λ/h*c

N/m (number of photons per meter) = P*λ/h*c2

Where P is the power of the laser, λ is the wavelength, h is Planck’s constant and c is the

speed of light we were able to calculate the additional filters needed in order to attenuated

the laser light from the single photon level.

First we looked at the fringes from light that was not attenuated to a single photon

level (Figure 3). The image shows the fringe pattern for attenuation of 3 orders ofmagnitude and its corresponding cross section. The fringes observed, show the wave property of light. There is no maximum in the center of the fringes because the slits are

carved in a lithographic plate and the light reflected from it interferes to distort the

pattern.

Figure 3.a Figure 3.bFigure 3. Image of the fringes observed with 3 orders of attinuation (left) and its

corresponding cross section (right). With laser power of 1.25µW

C r o s s S e c t i o n

0 5 0

1 0 0

1 5 0

2 0 0

0

4 0

8 0

1 2 0

1 6 0

2 0 0

2 4 0

2 8 0

3 2 0

3 6 0

4 0 0

4 4 0

4 8 0

D i s t a n c e ( p i x e l s )

G r a y V a l u e


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After we observed the fringes for the unattinuated laser light we added more

filters infront of the double slit until we had attinuation of seven orders of magnituted

which was the calculated necessary attinuation on order to have single photons. We tookseveral images for different camera accumulation times. All images were taken with

maximum gain.First we took an image with accumulation time .1s. (Figure 4.a) We were not able

to observe fringes but after the image was color inverted you can observe dark pixelswhere the camera detected individual photons. This shows the particle like nature of

light.

After that without changing the order of attinuation we increased the accusitiontime to 1 second and took another image. Once again we were able to observe faint

fringes (Figure 5.a) This supports the wave theory of light. Figures 4 and 5 together show

the wave particle duality of light.

Figure 4.a Figure 4.b

Image of attinuated laser light with 7orders of magnitute attinuation taken for .1s (left)

with its corresponding cross section (right) . Note that the EMCCD camera image isinverted.

C r o s s s e c t i o n

0 2 0

4 0

6 0

8 0

1 0 0

1 2 0

1 4 0

0

4 0

8 0

1 2 0

1 6 0

2 0 0

2 4 0

2 8 0

3 2 0

3 6 0

4 0 0

4 4 0

4 8 0

D i s t a n c e ( p i x e l s )

G r a y V a l u e


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Figure 5.a Figure 5.bFigure 5. Inverted image of attinuated laser light with 7 orders of magnitute attinuation

and 1second accumulation (left) with corresponding cross section (right)

Part II Mach-Zehnder experiment

We also took images with the EMCCD camera of the output of the Mach-Zehnderinterferometer. First we took images with different orders of magnitude attenuation and

with different acquisition levels. In order to show the properties of “which way

information” we took 36 images while rotating the polarizer by ten degrees starting from

zero. For some polarizer angle we were able to take a clear image of the fringes while forothers the images are very blurry. For angles where we can not observe the fringes we

have “which path information” which means that we know which path the photons chose.

This demonstrates the particle nature of light. For angles where we can observe thefringes we see the wave nature of light but at the same time we do not know which path

the photons took.

a. zero degrees b. sixty degrees c. eighty degrees d. 170 degreesFigure6. Fringe visibility for different angle of polarization. For zero degrees (a) there are

no fringes so we know “which path information”. For sixty degrees we can see clear

fringes (b). The power of the laser was 6µW.

C r o s s S e c t i o

n

0 5 0

1 0 0

1 5 0

2 0 0

0

4 0

8 0

1 2 0

1 6 0

2 0 0

2 4 0

2 8 0

3 2 0

3 6 0

4 0 0

4 4 0

4 8 0

D i s t a n c e ( p i x

e l s )

G r e y V a l u e


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We also aligned the Mach Zehnder interferometer by removing the two mirrors

and two beam splitters. After that we placed them back in the set up and tried to align

them in such a manner so that when the two beams are recombined at the second beamsplitter they overlap completely and create and interference pattern both at close and

far distances.

Part 3 Calculating the fringe visibility

The fringe visibility can be calculated using the cross section of the images taken

with the EMCCD camera and using the formula

where N refers to the maximum and minimum of the gray scale. For example in the MachZehnder interferometer at polarizer angle of zero degrees will have a no definite fringe

visibility while at a polarizer angle of sixty degrees there is a fringe visibility of 58% and

the periodic structure of the fringes is much more noticeable (Figure 7.b)

Cross Section

0

20

40

60

80

100

120

140

0 4 0

8 0

1 2 0

1 6 0

2 0 0

2 4 0

2 8 0

3 2 0

3 6 0

4 0 0

4 4 0

4 8 0

Distance (pixels)

G r e y S c a l e

Cross Section

0

20

40

60

80

100

120

140

160

0 4 0

8 0

1

2 0

1

6 0

2

0 0

2

4 0

2

8 0

3

2 0

3

6 0

4

0 0

4

4 0

4

8 0

Distance (pixels)

G r a y s c a l e

Figure 7.a Figure 7.b

Figure7 Cross section of Mach Zehnder intereferometer data with polarizer angle of zerodegrees (a) and sixty degrees (b).


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Conclusion

In this lab we used Young’s double slit experiment with attenuated laser light to

show that light behaves both as a particle and a wave. We also used a Mach-Zehnderinterferometer to study the effects of which path information. We were able to observe

the disappearance of the fringes for angles of the polarizer at which the which pathinformation is present. We were also able to calculate the fringe visibility by using the

cross sections of the different images.

References

1. M. B. Schneider and I. A. LaPuma, “A simple experiment for discussion of quantum interference and which-way measurement,” American Journal of Physics, vol. 70, no. 3, p.

266, 2002.

2. Chitraleema Chakraborty, “ Nature of photon: Particle or a wave?” 12, 4, 2012

Dilyana Mihaylova Lab 2-Report

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