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 were
able 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 light
could 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. Other
experiments 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 to
answer which path light takes we used a Mach-Zehnder interferometer. In a MachZehnder 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 out
which 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.
1
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 set
up. 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 beam
goes through a polarizer and the fringes can be observed by using a camera or a screen.
(Figure 2)
Figure 2. Mach-Zehnder interferometer
2
Procedure and Results
Part I Young’s Double Slit Experiment
We took images of the fringes and single photons observed with double slit set up
with 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 of
magnitude 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.
480
440
400
320
Cross Section
Distance (pixels)
360
280
240
200
160
120
80
40
0
50
100
150
200
0
Gray Value
Figure 3.a
Figure 3.b
Figure 3. Image of the fringes observed with 3 orders of attinuation (left) and its
corresponding cross section (right). With laser power of 1.25µW
3
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 took
several 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 pixels
where the camera detected individual photons. This shows the particle like nature of
light.
After that without changing the order of attinuation we increased the accusition
time 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.
480
440
400
320
Cross section
Distance (pixels)
360
280
240
200
160
120
80
40
140
120
100
80
60
40
20
0
0
Gray Value
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 is
inverted.
4
480
440
400
320
Cross Section
Distance (pixels)
360
280
240
200
160
120
80
40
0
50
100
150
200
0
Grey Value
Figure 5.a
Figure 5.b
Figure 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-Zehnder
interferometer. 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 for
others 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 the
fringes 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 degrees
Figure6. 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.
5
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 Mach
Zehnder 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
480
440
400
360
320
280
240
200
160
Distance (pixels)
Distance (pixels)
Figure 7.a
120
80
0
160
140
120
100
80
60
40
20
0
40
480
440
400
360
320
280
240
200
160
80
120
0
Gray scale
140
120
100
80
60
40
20
0
40
Grey Scale
Cross Section
Figure 7.b
Figure7 Cross section of Mach Zehnder intereferometer data with polarizer angle of zero
degrees (a) and sixty degrees (b).
6
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-Zehnder
interferometer 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 path
information 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
7