Figure 5: Comparative Photon Counts Demonstrate the Quantum Paradox

With the discriminator level fixed, both the count rate for dark current (photomultiplier shutter closed) and the count rate for "green" photons can be measured as a function of photomultiplier high-voltage. While the dark current pattern is linear, the low intensity signal saturates. Interpreting these graphs leads to an understanding of how a photomultiplier works and to how to set the operating and threshold voltages.

* Perform Two-Slit Interference with Single Photon Source and Detector
* Recreate Young's Two-Slit Measurement of the Wavelength of Light
* Make Visual Observations of Two-Slit Interference
* Explore Photon Counting Optimization
* Compare and Contrast Two-Slit and Single-Slit Interference
* Amplitude Modulation of Laser Source for Lock-In Detection
* Wave-Particle Duality, in the Student's Hands

With Two-Slit Interference, One Photon at a Time, TeachSpin has built an apparatus that allows students to encounter wave-particle duality with photons, the quanta of light. With this instrument, students perform the seminal two-slit interference experiment with light, even at the limit of light intensities so low that they can record the arrival of individual photons at the detector. That raises the apparent paradox which has motivated the concept of duality: in the very interference experiment which makes possible the measurement of wavelength, one observes the arrival of light energy in particle-like quanta, individual photon events. How is it possible for light to propagate as if it were a wave and yet to be detected as if it were a particle? This paradox is the central theme in Richard Feynman's introduction to the fundamentals of quantum mechanics:

"We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery. We cannot make the mystery go away by explaining how it works . . . In telling you how it works we will have told you about the basic peculiarities of all quantum mechanics."

It is the purpose of this apparatus to make the phenomenon of light interference as concrete as possible, and to give students the hands-on familiarity which will allow them to confront duality in precise and operational terms. When they have finished, students might not fully understand the mechanism of duality - Feynman asserts that nobody really does - but they will certainly have had direct experience of the phenomenon itself. They will have confronted the essential quantum paradox.

The Collaboration:
You couldn’t take Dr. Jonathan Reichert’s Modern Physics course at SUNY Buffalo without reading and rereading his hero Richard Feynman’s description of “a phenomenon which . . contains the only mystery.”

It is no “mystery” then that when David Van Baak mentioned the “Two Slit Interference, One Photon at a Time” he had developed for his students, TeachSpin immediately asked him to collaborate on adding one to our catalog. As Feynman observed, this phenomenon “appears peculiar and mysterious to everyone – both to the novice and to the experienced physicist.” To Feynman, the idea of photon interference was so important that the discussion appears in two places in his Lectures On Physics; Volume 1, Chapter 37 and Volume III, Chapter I.

We have no doubt that every physics student and Ph.D. physicist has shared Feynman’s fascination with this “peculiar and mysterious” phenomenon. It is exciting to be able to make a hands-on version available to pique the curiosity of our current students.

Pulse Counter/Interval Timer.

## EXPERIMENTS

CREATING A SINGLE PHOTON SOURCE

As anyone who has ever used a light dimmer can attest, decreasing the light output of a given incandescent bulb shifts the spectrum toward the longer, red wavelengths. By placing a narrow band green filter in front of a standard light bulb, students use this "obvious" phenomenon to create a source of single photons.

The system is opened, the laser turned off and the bulb lifted into place. The double slit, slit blocker, and detector slit are removed. Now a very narrow band green filter is slid into place in front of the bulb. As the bulb intensity is turned down, the color spectrum shifts to the red, the light intensity in the green region drops dramatically and one photon at a time passes through the single slit. (This works better than neutral density filters.)

The top is now put on and secured which allows the photomultiplier to be activated. The shutter which keeps the light from the entering the photomultiplier is still kept in place. The bulb intensity is set to about half of maximum.

OPTIMIZING THE PHOTON COUNTING UNIT

In the photomultiplier both the high-voltage (operating voltage) and the pulse-height discriminator threshold voltage must be properly selected to optimize the operation of the photon counting unit. They must be set so that the photomultiplier will optimally count green photons and optimally reject the dark current. (This can be done by the instructor or can be an opportunity for students to learn how to use a photomultiplier for proper photon counting.)

## INSTRUMENT

To See Two-Slit Interference, One Photon at a Time in action go to the 6:20 mark in this video provided by Terry Klopcic of Kenyon College Physics Department. The Two Slit's Cricket is being used to make photon arrivals audible.

This video features Professor Ben Schumacher.

Figure 1: Schematic Diagram of U-Channel

TeachSpin's Two-Slit Interference, One Photon at a Time allows students to confront the "mystery" of wave-particale duality by comparing the results of visual, photodiode and photomultiplier observations of interference patterns generated by the same optical path. With the system open, they can use a white card placed at the far end of the U-channel to make naked-eye qualitative observations of an interference pattern cast by the laser. Closing the system, they can use a photodiode to make quantitative measurements of light intensity as a function of position for the interference pattern they have just been looking at. Most dramatically, they can explore, quantitatively, the relative rate of photon arrival as a function of position across the same region. (see figure 1 above).

QUALITATIVE OBSERVATIONS AND CALIBRATION OF THE MICROMETERS

With the system opened and using the laser, the student adjusts the single and double slits to make sure they are properly aligned. A viewing card placed just behind the double slit/slit blocker assembly shows a pair of thin red lines of laser light. Now the reading on the micrometer for both slits blocked, only left slit open, both slits open, and only right slit open can be determined.

In subdued light, interference patterns can easily be seen on a small white card placed in front of the detector slit. While learning to use the slit blocker, they can easily see distinct differences between the interference patterns from single and from double slits. These observations are essential for a clear appreciation of the sets of measurements taken when the cover is closed and the apparatus appears more like a "black-box."

MEASURING LIGHT INTENSITY AS A FUNCTION OF POSITION

With the laser on, the system is closed up and the photodiode placed in the optical path. The photodiode is connected to a voltmeter through a current-to-voltage converter. The student moves the detector slit across the face of the photodiode and records the output voltage (which is proportional to the light intensity) as a function of micrometer reading. Here, we want the student to get a quantitative record of what was observed visually.

In Figure 2 to the right we show the data obtained in this realization of Young's classic experiment. The lines are drawn merely to guide the eye.

The instrument consists of a black anodized aluminum U-Channel, a little over a meter in length, with a light tight removable cover. At one end, the student can select either of two light sources: a 670 nm, 1mW laser or a small flashlight bulb. The detection system at the opposite end is either a photodiode or a complete photon counting module.

Just in front of the light source is a single entrance slit. With either the laser or bulb illuminating this slit, the central maximum of the slit's diffraction pattern is aligned to cover a double slit assembly about 40 cm down the U-channel. Just past the double slit, a moveable "slit blocker" can be manipulated manually using a micrometer mounted on the outside of the U-channel. Using the slit blocker, students can compare the patterns created by the double slit to those created by either of the single slits. Three double slit assemblies, each of distinct slit spacing, are included.

At the far end of the U-channel is a moveable single slit, the detector slit. It, too, is attached to a translational stage actuated by a micrometer. Students move the detector slit across the interference pattern in front of either the photodiode or cathode of a photomultiplier to make quantitative measurements of either the light intensity or photon arrival rate as a function of position.

The black box with the brass front panel contains a complete photon counting module, as well as a photodiode detector connected a current-to-voltage converter. The box is supplied with a special flange and a light shutter. The photodiode is mounted on the outside of the shutter so that it is in the light path when the shutter is closed, and removed from the light path when the shutter is opened to let the light pass to the photomultiplier.

As in all TeachSpin apparatus, students are encouraged to explore the effect of changing a wide variety of parameters. In this instrument, the photomultiplier's high voltage supply and pulse-height discriminator level are both controlled and monitored from the front panel. It is also possible to inject a test pulse to calibrate the charge-sensitive preamplifier.

The entire photon-counting module can be detached from the U-channel and operated independently (requiring only a 15 volt regulated DC supply). This unit is thus available for other applications in the teaching or research laboratory, such as low intensity spectroscopy or photon correlation experiments.

The single-photon light source consists of a #47 flashlight bulb connected to a variable voltage-regulated power supply. The bulb is housed in a black plastic tube with a removable narrow-band green interference filter at the output end. A schematic is shown below.

Although flashlight bulbs such as this one generate about 1016 photons per second in ordinary use, operation at reduced power not only lowers the total production rate of photons, it also shifts the distribution toward longer wave length, thereby markedly reducing the production rate of "green" photons. The result is a thermal source of randomly produced photons, capable of giving a photon even rate at the detector in the range of 10^
1 - 10^5 per second. Thus, it is easy to take data in the "one photon at a time" regime in which the average waiting time for the next photon event vastly exceeds the time-of-flight for a photon through the apparatus.

## INTRODUCTION

Figure 4: Photon Counting Data for Single and Double Slit Configurations

A DRAMATIC DEMONSTRATION OF THE "ESSENTIAL QUANTUM PARADOX"

The "essential quantum paradox" can be shown dramatically by a simple experiment. The detector slit is positioned, in turn, at the three empirically determined positions of the -1 minimum, the central maximum, and the +1 minimum of the interference pattern, marked in Figure 4 as P-1, P0, and P+1. Photon count rates are measured for the slit-blocker set to permit light to pass through only one slit, through both slits, or through only the other slit. Data is shown in Figure 5.

At the central maximum, going from one to two sits quadruples not doubles, the count rate. And, contrary to the logic of classical particles, at either minimum, opening a second slit markedly reduces the count rate.

Figure 2. These data can be compared to different theoretical models of the two-slit phenomenon. The simple Fraunhofer model reproduces most of the major features, but the more sophisticated Fresnel integral or Feynman's "sum over paths" can give students greater depth of understanding. Both are carefully discussed in the instructor's manual.

Figure 3: The data shown indicates that a setting near 550 V is optimal.

# TWO-SLIT INTERFERENCE, ONE PHOTON AT A TIME

INTERPRETING THE DATA TO VALIDATE SINGLE PHOTON PRODUCTION

With the photomultiplier shutter open, students use a frequency counter to find the rate at which photons are coming through the single slit. The photomultiplier readings will be around 50 x 103 photons/second. Since photomultiplier is rated at 5% efficiency, the actual photon arrival rate is 20 times greater, 1000x103 or 106 photons/second.

It is here that students must convince themselves that this counting rate indicates the bulb is indeed dim enough so that only one photon at a time reaches the photomultiplier. Here are two possible conceptual arguments, both use the fact that the distance from single slit to detector is close to one meter.
1. Using time of flight measurements: A photon traveling 3x108m/s will navigate the one meter path from single slit to detector in roughly 3 nanoseconds. Our counter indicates a time of flight of 10-6 seconds or 1000 nanoseconds. On average, therefore, there is a photon in flight between the single slit and the photomultiplier for only about 3 ns out of every 1000 ns. This means that for 99.7% of the time, there are "no" photons in flight, while for only 0.3% of the time there is "one" photon in flight in the apparatus. The probability of there being two photons in flight simultaneously is thus negligible. All of the interference effects observed in the apparatus can thus be comfortable ascribed to the behavior of individual photons, coming through the single slit one at a time!

2. Using frequency measurements: The flight path is roughly one meter. If we were to visualize an arrangement such that a new photon would be released only after the one in transit arrived at the photomultiplier then the photons would be 1 meter apart. This would mean that the time between photons would be 1m/3x108m/s. The photon count rate would then be 3 x 108photons per second. The photomultiplier will show around 50 x 103 photons/second. The photomultiplier is rated at 5% efficiency so this means that the actual photon arrival rate is 20 times greater or 1000x103 photons/second. We are getting only 106 photons/sec which means that the photons act as if they are 100 meters apart.

OBSERVING THE RESULT OF SINGLE PHOTON INTERFERENCE

Once students have convinced themselves they will be getting one photon at a time, they close the photomultiplier and reopen the channel. Now they must reinsert the double slit, slit blocker and detector slit, and check their alignment.

The system is again closed and the photomultiplier shutter opened. With the discriminator output connected to a frequency counter, students determine counts in 10 second intervals at various locations of the detector slit. Data for the three possible positions of the slit blocker are shown below. The graph of photon counts vs. detector-slit location for two-slits open reveals the same general interference pattern observed using the laser and photodiode. The slightly closer spacing of the maxima shows that we are now looking at green photons rather than the red ones from the laser.

AN EXTENSION

As always, TeachSpin instruments lend themselves to expanded investigations. By injection of a TTL signal, the diode laser can be modulated so that lock-in detection of the photodiode signal becomes possible. Because of the noise rejection of lock-in detection, sensitive quantitative measurements of the laser-light interference signal can be achieved, even with the U-channel uncovered. TeachSpin's Signal Processor/Lock-In Amplifier is ideal for making these measurements.

Photomultiplier tube: Hamamatsu R 212

Preamplifier-Discriminator: Amptek A-111

Interference Filter: 546 nm, 10 nm FWHM

All Slit Widths: 0.09 mm

Double Slit Separations: 0.35, 0.40, 0.45 mm

Laser (Class II): 670 ± 20 nm<1.0 mW

Universal Power Supply
Input: 110 - 230 VAC, 50 - 60 Hz
Output: 15 V DC

Optical Light Path: 1 meter

Overal Instrument Length: 52 inches