Advanced Physics Laboratory Report Tsakiridou

One-photon One-Slit and Two-Slit Diffraction Experiments

Androniki Tsakiridou

Smith College, Department of Physics, Northampton, MA 01610

(Dated: May 14, 2012)

Abstract

The Young single and double slit experiments offer very useful insights in the characteristic

dimensions of the apparatus, as well as the dual nature of light. The TeachSpin c Two SlitInterference, One Photon at a Time apparatus was used to collect the data used in this report.

Single and double slit diffraction patterns at wavelengths of 670nm (red laser light source) and

541nm (green bulb light source) are compared to determine quantitatively the differences in the

diffraction patterns, and the key dimensional values of the slits that produced these patterns. The

curve fits determined that the double slit separation was 400.5um, and the slits width was within

the range 84.6 98.6um with nominal values of 406.4um and 85um respectively. Using the greenbulb light source at very low intensity, it was also determined that at the central maximum of a

double slit, a single photon travels through the apparatus only 0.005% of the time. In addition,

some statistics conducted on the frequency and the time interval of individual photons clarify that

Poisson statistics govern light emission, and the mean time interval between photon arrivals is

tmean = 1.1288 1.200msec.

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I. INTRODUCTION

Light is a very particular matter that displays characteristics of a wave or particles

depending on the circumstances. When light is incident on an aperture, the relation between

the wavelength and the slit(s) width and slit separation determines whether light behaves

either as a wave or as a particle. When the slit width is significantly larger than the

wavelength of light, light behaves as in Figure 1. However, when the slit(s) separation and

slit width become comparable to the wavelength, light behaves as a wave instead, as in

Figure 2.

FIG. 1. Light behaving as particles.4

FIG. 2. Light behaving as a wave.5

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When light is incident to a double slit, it behaves similarly in the individual slits, but

producing two waves, one at every slit. A little distance after the slits, the two waves meet

and interfere constructively and destructively depending on the distance from the aperture,

as in Figure 3. Consequently, a detector set at a certain distance away from the slits will

observe a pattern very different from the single slit diffraction pattern, where a uniform

curve similar to a Gaussian distribution is observed. In more detail, a pattern of brighter

fringes followed by dark fringes that are separated by a characteristic distance substitutes

the single slit curve.

FIG. 3. Light passing through a double slit, and its diffraction patten.7

By studying the behavior of light of different wavelengths in the same apparatus, a lot

of information can be deduced for characteristic dimensions of the apparatus, such as the

width of the slit, and the distance between the two slits in the case of a double slit.

Also, by reducing the light wavelength to the green light range (495-570nm), the amount

of photons passing through can be greatly reduced, and only one photon can travel at a

time. Having one photon pass the slits at any point of time, and still observing a wavelike

behavior can demonstrate the dual nature of light, where even a single particle can travel

through both slits at once and interfere with itself.

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II. METHODS

The TeachSpin c Two Slit Interference, One Photon at a Time apparatus was used tocollect all data. Figure 4 shows such typical device and Figure 5 provides a schematic of the

apparatus individual components. The source was be alternated between a 670nm red laser

light source and a typical bulb light source with a green filter minimizing the wavelengths

range emitted from 541nm to 551nm with a varying intensity. The first single slit allowed

for a thin band of light to pass and go through the double slit about 0.50m later. The slit

blocker right after the double slit allowed light from both slits or just one to continue its

journey. Consequently, as the detector slit travels along the width of the tube about 0.50m

after the double slit, it detects a pattern of either the double or the single slit diffraction,

depending on the position of the slit blocker. All slits had nominal width = 85um, and

the double slit had nominal slit separation of d = 406.4um.2

FIG. 4. The TeachSpin c Two-Slit Interference, One-Photon-at-a-Time apparatus.8

FIG. 5. A schematic of the individual components of the TeachSpin c Two-Slit Interference, One-Photon-at-a-Time apparatus.8

There are two detectors, a photodiode and a photomultiplier module (PMT). The photo-

diode detects the voltage at the detector, and works very effectively with the red laser light

source. However, the green light bulb source produces light of much smaller wavelength, and

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the photodiode cannot produce an accurate enough pattern. The PMT detects the arrival of

individual photons, and is a very sensitive device. Detecting red laser light photons exceeds

its manufacturing limits, but it detects green light photons much more effectively than the

photodiode.

The PMT is a high vacuum device that detects individual photons. The photons are

incident on a photocathode material, such as a multi alkali that produces electrons as a result

of the photoelectric effect. These electrons are multiplied by an electron multiplier through

secondary emission and finally reach the anode. When an electron reaches the anode, a sharp

current pulse is produced and recorded, making it possible to measure individual photon

arrivals.

The PMT operates at a variable high voltage. Before starting to conduct experiments,

the optimal high voltage range that eliminates the background noise needs to be determined.

A usual method is to measure the ratio of photons arriving with the slit open and closed at

different high voltage values that is unique for every apparatus. The optimal high voltage

for the apparatus used for this experiment was determined at 4.1 units, as shown in Figure

6.

Once the single-slit and double-slit curves from both the red laser light and the green

bulb light were recorded, they were analyzed using the theoretical formulas. In more detail,

the double-slit curves were fit using Equations (1), (2), with A as a constant.

V = A () (cos)2 (sin

)2 (1)

where

=pid

sin (2a)

=pia

sin. (2b)

with d= slit separation, and a=slit width.1

Respectively, the single-slit curves were fit using Equation (3), with B as a constant.1

V () = B (sin(pia/)pia/

sin)2 (3)

.

For the green light source data, the double-slit curve needed to be additionally normalized

because the background noise was greater with greater measurements. In order to remove

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FIG. 6. PMT noise ratio at different voltage values.

the background noise, a curve fitting the minimums at the dark fringes was created and was

subtracted from the recorded values, leaving the dark fringes close to 0 counts/second.

For the statistics part of the experiment, data were taken at the maximum point of the

double-slit interference pattern, recording the frequency of photons arriving at the PMT in

a 104 time sample. Presenting the data in the inverse way, the time interval between photon

arrivals for a sample of 105 photons was also recorded, providing useful insight to the nature

of light emission.

III. RED LASER LIGHT SINGLE-SLIT AND DOUBLE-SLIT DIFFRACTION

RESULTS

The first experiment was conducted using the red laser light source and the photodiode

detector. Measurements were taken every 0.05um to ensure that all variation was captured.

The nominal light wavelength was 670nm5nm producing a maximum voltage of 0.65V forthe double slit diffraction pattern, and 0.18V for the single slit diffraction pattern. The ratio

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between the highest bright fringe and the adjacent dark fringes was r1 = 440 and r2 = 139

respectively. The uncertainty for both the single-slit and the double-slit measurements were

determined using the statistical standard deviation of the data set.

Fitting of the single-slit data was achieved using the pre-existing single slit curve fit in

Logger Pro. The best fit wavelength was determined at = 670nm, and the best fit slit

width at = 98.5um. Respectively, fitting of the double-slit data was achieved using the

pre-existing double slit curve fit in Logger Pro. The best fit wavelength was determined

again at = 670nm, the best fit slit width at = 88.6um, and the best fit slit separation

at d = 400.5um, as shown in Figure 7.

FIG. 7. 670nm single-slit and double-slit diffraction patterns analysis.

Although the single-slit best fit stayed within the error range of the data, the double-slit

best fit fitted quite accurately only the data after the central maximum. The data before

the central maximum appear to be slightly shifted. This phenomenon could be justified by

the possibility that the recorded central maximum was close to, but not the real maximum,

or that the detector had an offset created by the detector slit.

The best fit predictions of the wavelength, the slit width and separation are fairly close

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to the nominal values, as shown in Table I.

Nominal Values Best Fit Values

Wavelength (nm) 670 5 670Slit Width (um) 85 88.6 - 98.6

Slit Separation (um) 406.4 400.5

TABLE I. Comparison of nominal and best fit characteristic values for red laser light data.

IV. GREEN LIGHT SINGLE-SLIT AND DOUBLE-SLIT DIFFRACTION RE-

SULTS

The second experiment was conducted using the green laser light source and the PMT

detector. Measurements were taken every 0.10um to ensure that all variation was captured.

The nominal light wavelength was within the range 541nm 551nm producing a maximumphoton count of 771photons

secondfor the double slit diffraction pattern, and a maximum photon

count of 274photonssecond

for the single slit diffraction pattern. The ratio between the highest

bright fringe and the adjacent dark fringes was r1 = 8.03 and r2 = 8.86 respectively. The

uncertainty for both the single-slit and the double-slit measurements were recorded along

with the actual measurements.

Fitting of the single-slit and double-slit data was achieved similarly to the red laser light

data. The best fit wavelength was determined at = 541nm for both the single-slit and the

double-slit data. The best fit slit width was determined at = 84.6um for the single-slit

data, and at = 88.6um for the double-slit data. The best fit slit separation was determined

at d = 400.5um, the same as for the red laser light data. All information is also displayed

in Figure 8.

Similarly to the red laser light data, although the single-slit best fit stayed within the

error range of the data, the double-slit best fit fitted quite accurately only the data after the

central maximum, and the data before the central maximum appear to be slightly shifted.

This phenomenon could be justified with the same arguments: there is the possibility that

the recorded central maximum was close to, but not the real maximum, or that the detector

had an offset created by the detector slit that has not been accounted for.

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FIG. 8. 541nm single-slit and double-slit diffraction patterns analysis.

The best fit predictions of the wavelength, the slit width and separation are fairly close

to the nominal values, as shown in Table II.

Nominal Values Best Fit Values

Wavelength (nm) 541 551 541Slit Width (um) 85 84.6 - 88.6

Slit Separation (um) 406.4 400.5

TABLE II. Comparison of nominal and best fit characteristic values for green light data.

Considering the central maximum at the double-slit set up, 771photonssecond

are measured to

arrive at the PMT. Since the PMT has an efficiency of 5%, as mentioned in the manual, the

actual number of photons arriving at the PMT is 15, 420photonssecond

. Consequently, there is a

photon arriving at the PMT every tmeasurement =1

15420= 64, 850ns. Because photons travel

at speed c=3 108ms

, they arrive at the PMT about every tarrival=1

3108 ' 3ns. Finally, onlytarrival

tmeasurement= 3ns

64850ns= 4.623 103% of the time there is an e arriving at the PMT when the

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slits are set for maximum photons arrival. Since the probability of one e travelling in the

device is less than 0.005% of the time, the probability of more than one e traveling at the

same time is negligible. Therefore, when the source used is the green light bulb, there is only

one photon passing at a time from the double slit. Still, the expected double-slit diffraction

pattern is observed; even a single photon behaves as a wave that propagates through both

slits at once and interferes with itself after the aperture to produce the typical pattern.

V. STATISTICS OF INDIVIDUAL PHOTON ARRIVALS

Findings from the previous section suggest that it is highly unlikely that more than one

photon travel through the device at a time. More statistical experiments were conducted

in order to gain more insight on how frequently photons arrive at the PMT. Collecting a

data sample of 104 seconds at the central maximum of the double slit set up, the variation

of photonssecond

arrival was recorded, as shown in Figure 9. The distribution appears random, and

photons arrive at tmean = 1.1160 1.1468msec.Recording the results in a different manner, the time intervals between photon arrivals are

shown in Figure 10, instead of the photonssecond

arrival rate. The time intervals display an expo-

nential behavior, a pattern similar to radioactive decay, with tmean = 1.1288 1.200msec.The common point with radioactive decay and photons emitted through the light bulb is

that both events depend on constant factors such as tmean and t1/2, and are irrelevant to

time since the beginning of the event, suggesting a Poisson distribution behavior.3

One of the characteristics of Poisson distribution is that small sample intervals display an

exponential behavior. For this experiment, the sample interval was m = 1, and the behavior

is clearly exponential. As the sample intervals increase, the distribution changes to a skewed

one, and for even larger sample intervals, it is very similar to a gaussian, similarly to Figure

9. Overall, both methods of data collection offer very close tmean values, as shown in

Table III.

tmean (msec) t (msec)

Frequency of photon arrivals 1.1160 1.1468Time interval of photon arrivals 1.1288 1.1200

TABLE III. Comparison of mean time interval obtained through both experiments

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FIG. 9. Frequency of photon arrivals.

VI. CONCLUSIONS AND FUTURE WORK

In total, this experiment was successful in showcasing the wave nature of light. The red

laser light and green bulb light sources experiments were both quite successful in finding a

best fit for the light wavelength, the slit widths, and the slit separation, as shown in Table I,

and Table II. The slight shift of the fit observed in all experiments can be justified by an

offset created by the detector slit. Future work based on these experiments could include

testing different double slits and comparing the different diffraction patterns. Also, the

results could be analyzed in different ways, i.e. fixing the fitted slit width and separation

from the red laser light data when taking measurements using the green light source, in

order to find a fit for the green light wavelength.

The green light diffraction results also showcase how light behaves when it passes through

an aperture one-photon-at-a-time, when a single photon behaves as a wave and produces

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FIG. 10. Time interval of photon arrivals.

the single or double interference pattern, depending on the set up.

Finally, the statistics provide useful insight on the mean time intervals between photon

arrivals, as well as the nature of light emission, as it behaves according to Poisson statistics.

Some future work could include taking data at bigger sample intervals, e.g. m = 2 100,and comparing the resulting tmean.

ACKNOWLEDGMENTS

I would like to thank the many people who helped and supported me in the completion

of the Advanced Physics Laboratory course.

Thank you to Professor Nathanael Fortune who helped me set up and align the equipment,

with data logging and processing, as well as the special accommodations made through the

course just for me, and have allowed me to finish the required work.

Thank you to Professor Doreen Weinberger for her help when some communication and

personal issues rose, and with data processing for the first section of this experiment.

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Finally, thank you to Dean Erika Laquer who granted me an extension to finish working

for this course completing all requirements.

[email protected]

1 A. C. Melissinos, J. Napolitano, Experiments in Modern Physics, 2nd. ed. (Elsevier, Oxford,

UK, 2003).

2 TeachSpin, Two-slit interference, one photon at a time The Essential Quantum Para-

dox,(TeachSpin. Inc., Buffalo, NY, United States, 2004).

3 H. D. Young, Statistical Treatment of Experimental Data, 1st. ed. (McGraw-Hill, United States,

1962).

4 http://innovativescience.blogspot.com/2011/02/diffraction.html, retrieved on May 10, 2012

5 http://www.universetoday.com/89409/diffraction-of-light/, retrieved on May 10, 2012

6 http://abyss.uoregon.edu/ js/ast122/lectures/lec04.html, retrieved on May 10, 2012

7 http://abyss.uoregon.edu/ js/ast122/lectures/lec04.html, retrieved on May 10, 2012

8 http://www.teachspin.com/brochures/Two%20Slit.pdf, retrieved on May 10, 2012

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