Single Photon Interference

quantum nature of light - wave-particle duality - probability - double slit experiment

What it shows:
In this demonstration we perform the double-slit interference experiment with extremely dim light. Rather than the usual screen, the arrival of individual photons is registered and stored electronically. This alone is evidence for the graininess or particle nature of light. However, we take the experiment one step further and show that even when the light intensity is reduced down to several photons/sec, the audience can see the familiar Young's double-slit interference pattern build up over a period of time as the arrival and position of each photon is stored on an electronic screen. This addresses the question (and dilemma) of how can single photons interfere with photons that have already gone through the apparatus in the past, or with those that will go through in the future, or with themselves. Finally, the slit arrangement is such that it is possible to know which of the two slits the photons are passing through. In that case the Young's double-slit interference pattern does not manifest itself.

How it works:
The geometry of the experiment is simple. The ubiquitous HeNe laser serves as the coherent light source which illuminates a double-slit slide. The resulting interference pattern is projected directly into a video camera sans lens. What is unusual about the apparatus is of course the extreme light sensitivity of the video camera and a homemade electronic interface that turns the analog storage oscilloscope into a "storage TV monitor." The general layout is illustrated below.



The polarized light from the laser is attenuated by two rotatable Polaroid filters which allow one to adjust the intensity down to barely visible. The beam is further attenuated by a 26 µ pinhole (fitted into the endcap of a 4" O.D. PVC pipe) which also serves as a spatial filter. A disk inside the pipe holds the double-slit slide 1 - an O-ring prevents any stray light from getting around the disk into the camera. A light-tight seal between the PVC pipe and video camera is provided by simply stuffing black cloth between the extension tube (on the end of the camera) and the pipe. The entire apparatus is light-tight enough to be used with lecture hall lights on.

The low light level camera is a COHU 4400 series camera. 2   It's vidicon has two stages of highly sensitive optical image intensifiers so that (according to the manufacturer) a "usable picture is produced with only 2×10-6 lumens/ft2 " (or fc). 3   It is sensitive enough to respond to single photons of light with a quantum efficiency of about 0.1%. 4   The distance between the source and detector is 1.25 meters so, from a particle point of view, a photon exists for about 4 hsec in the apparatus. Since a typical accumulation rate of 5 photons/sec translates to an actual rate of 5000 per second, the average number of photons present at any instant is ≈ 2×10-5; thus there is less than one photon present at any time, even at accumulation rates several tens of thousands times higher than what is observed in the demonstration experiment.

The composite video output signal is processed by an "Oscilloscope-TV Converter" 5   which generates linear sawtooth waveforms (ramps) locked to the horizontal and vertical video sync pulses. The ramps are fed to an oscilloscope 6   in the X-Y mode and generate a TV raster on the screen. The composite video signal is amplified and inverted (by one of the scope's vertical amps) and sent to the "ext Z-axis in." This modulates the beam and produces the image. Some video signal processing is necessary to remove internal "ion events" in the camera that produce very bright flashes on the image. 7   A single channel analyzer (SCA) 8   is invoked to remove these events and generates a clean TTL logic signal to modulate the beam. Details and circuit diagrams are presented after the Comments section. Another video camera aimed at the oscilloscope screen allows the audience to view the interference pattern.

The experiment is performed by turning on the laser and adjusting the polarizer (closest to the pinhole) so that the familiar double-slit interference pattern is seen on the oscilloscope screen. Even at this relatively high intensity, the intensity is low enough so that it is evident that one is seeing the simultaneous sum of individual events -- the evidence being a very grainy shimmering image. One can then slowly decrease the light intensity by rotating the polarizer until the interference pattern is no longer recognizable -- only single flashes of light appear on the screen at a rate one can almost count. At this point the scope is switched to the storage mode 9   and the single flashes of light are stored "live." By integrating the events in this manner for approximately a minute, the image of the double-slit interference pattern is built up in real time. If desired, the total photon count can be monitored on a scaler.

It is also possible to repeat the experiment by "forcing" the photons to go through a particular slit. This is accomplished with a movable razor-blade mask which can be positioned during the course of the experiment so as to allow the light to pass through either slit and not the other, or both slits simultaneously. The slide holder and mask arrangement is shown below. Not shown is a plastic cover that fits over the slide and keeps the razor blade from falling off. A magnet (outside the PVC tube) is used to pull the razor blade back and forth.



For example, by pulling the mask to the right, one can block the light from passing through the left slit, integrate the photon events for 60 seconds, "instantaneously" switch to the other slit (without stopping the experiment) and continue integrating for another 60 seconds. In so doing, one has allowed photons to pass (one-at-a-time) through each of the slits for 60 seconds. From a classical point of view, this is equivalent to the previous experiment (assuming each photon goes through only one slit or the other) except we now know which slit each photon is passing through. Contrary to the classical view, no double-slit interference pattern develops.

Setting it up:
Set up the 7313 oscilloscope as follows:

• vertical mode - left trigger source - left
• The scope does not have an X-Y mode in its time-base module. Replace the time-base plug-in module on the scope with the 7A18 vertical amp module (it must be in the right-most slot). The horizontal ramp is fed to ch 1 of this module, which becomes the horizontal, or X, amp.
• The vertical ramp is fed to ch 1 of the left 7A18 vertical amp, which becomes the vertical, or Y, amp. The composite video signal is amplified by ch 2 of the left amp module, which becomes the Z amp. The trigger should be ch 2 and display ch 1.
• The amp out signal (of ch 2) is fed to the ext Z-axis in (both on the rear of the scope). Invert ch 2 (for a positive image) and adjust the picture brightness with the ch 2 gain.
• Turn the scope's Intensity control all the way down as this improves the contrast greatly.
• If an SCA is interposed, the lower and upper-level discriminators (LLD & ULD) should be set to about 0.2 volt and 1.0 volt, respectively. Since the SCA output is a TTL pulse, the ch 2 gain should be reduced appropriately.

The Oscilloscope-TV Converter needs to be adjusted prior to each use. Do so by feeding it a video signal from one of the regular cameras aimed at an evenly illuminated test pattern. 10   Tweak the "vert adj" and "horiz adj" pots on the Converter to yield a stable, single image on the oscilloscope. The X and Y amplifier gains on the scope can now be set so that the image fills the screen and is geometrically undistorted. 11   The SCA has two outputs and, if desired, the second output can be sent to a scaler to totalize the photon count.

Comments:
Single photon interference experiments are not new. 12   Strictly speaking, we are not detecting single photons of light but rather single photoelectrons, liberated by the light impinging on the detector screen. Nevertheless, the quantum nature of light is evident. The positions of arrival (of the photons) are random but the probabilities of arriving at certain positions are not. This is beautifully born out in the demonstration. Rating ****

Oscilloscope-TV Converter:
A video picture is displayed at a rate of 30 Hz. Each picture is composed of two interlaced frames, drawn sequentially, so that interlacing gives an effective rate of 60 frames/sec. The picture consists of 525 horizontal lines with 262½ lines/frame. Thus the picture is produced at the rate of 15,750 lines/sec -- the inverse of this is 63.5 µsec/line. This establishes the required periods for the horizontal and vertical ramps: 63.5 µsec and 16.67 msec (1/60 sec), respectively. These two ramps, when synchronized and fed to the scope in the X-Y mode, produce a rectangular raster display.

The composite monochrome video signal consists of horizontal and vertical blanking and sync pulses as well as the picture information. The oscilloscope-TV converter must strip the sync pulses from the picture information and separate the horizontal and vertical sync pulses to trigger the ramps. The oscilloscope itself provides for blanking the electron beam by an inversion of the picture signal and uses that signal for the Z-axis (modulation) input.

The following circuit diagram illustrates the oscilloscope-TV converter. The scheme of the circuit is to (1) amplify and separate the synchronizing pulses from the video signal and cancel noise, (2) sort the horizontal and vertical pulses by high and low-pass filters, respectively, and (3) use these pulses to trigger the sawtooth ramp generators.

Times three amplification of the composite video signal is accomplished by the sync amp transistor which also inverts the signal so that the sync pulses become positive. Passage through the coupling capacitor and diode drops the video signal below ground while leaving the sync pulses stick about one volt above ground. This signal is applied to the base of the sync separator transistor.  It's base is biased so that it only conducts on the positive sync pulses which are amplified and inverted once again. The sync out signal is fed to the low and high-pass filters.

To minimize the effect of noise in the synchronizing pulses (which can cause momentary loss of vertical and/or horizontal synchronization), the input composite video signal is also fed to the emitter of the noise clipper transistor which is base-biased to 0.24 volts. The transistor cannot conduct except on negative noise peaks that exceed the amplitude of the negative sync pulses (the emitter of the noise clipper is at the same voltage as the base of the sync amp) so that the only signals appearing at the collector of the noise clipper are negative noise peaks exceeding the amplitude of the sync pulses. Note that there is no phase inversion. The negative noise peaks are capacitively coupled to the base of the noise gate transistor whose base is biased so that it is normally conducting. Since the sync separator and noise gate are connected in series, both transistors must conduct for either of them to. Thus noise pulses exceeding the synchronizing pulse amplitude will turn off the noise gate as well as the sync separator, thereby blocking any sync out. The vertical and horizontal ramps will not be triggered for the duration of the noise. 13

The separation of the vertical and horizontal sync pulses is based on frequency -- the vertical sync pulses last 27.3 µsec while the horizontal pulses are only 5 µsec long. The time constants of the low-pass and high-pass filters are chosen to take advantage of this difference. The voltages developed at the outputs of the respective filters are converted to TTL pulses by the op-amp comparators to provide for clean triggering of the 555 oscillators. Each of the oscillators is configured with a transistor constant current source to linearly charge a capacitor. The voltage on the capacitor assumes a sawtooth waveform whose period is determined by its capacitance and the charging current. The vertical and horizontal charging currents are separately adjusted by the potentiometers providing the transistor biases. The vertical ramp is further buffered, inverted and +DC offset by the op-amps so that the raster starts in the upper left-hand corner of the oscilloscope display.

1 Pasco Electroformed double-slit slide OS-9165B; the slit widths are 0.04 mm and are spaced either 0.250 or 0.500 mm apart
2 COHU model 4410/ISIT/IT3498 (ISIT = Intensified Silicon Intensified Target)
3 This is equivalent to 1.9×10-7 lux (lux (lx) = lumen/m2, thus 1 fc = 10.76 lx). Note that this is a factor of 10 million times more sensitive than a Camcorder.
4 We are not interested in a "usable picture" in this experiment but rather the overall efficiency -- what percentage of the photons entering the vidicon are actually detected. The efficiency was determined by measuring the photon rate while a known flux (ranging from 2×105 to 2×108 photons/sec/cm2) of 600 nm light was incident on the video camera. An Optronic Laboratory model 310 Low Light Level Calibration Standard was used as the light source.
5 designed and built by Paul Titcomb (1986)
6 Tektronix model 7313 analog storage scope with two 7A18 dual channel plug-ins.
7 These flashes are much brighter than legitimate photon events -- indeed they appear as 1.8 volt pulses and are much greater compared to the 1 volt p-p nominal video signal.
8 Ortec model 551 Timing SCA
9 Persistent phosphor screen
10 Porta-Pattern™ is convenient for this purpose.
11 Typically these settings are 0.2 volts/div, uncalibrated. The width-to-height aspect ratio is 4-to-3.
12 See, for example: S. Parker, Am J Phys 39, 420-424 (1971), "A Single-Photon Double-Slit Interference Experiment"; S. Parker, Am J Phys 40, 1003-1006 (1972), "Single-Photon Double-Slit Interference -- A Demonstration"; In these two experiments, a person directly views the interference pattern and a photomultiplier is invoked to prove that there is only one photon at a time in the apparatus.
Y. Tsuchiya, E. Inuzuka, T. Kurono, and M. Hosoda, Advances in Electronics and Electron Physics, Vol. 64A, (Academic Press, London, 1985) pp 21-31 "Photon-Counting Imaging and Its Application"; Tsuchiya et al have developed a sophisticated photon-counting image acquisition system which is far beyond the reach of a lecture demonstration organization. To test its application, they performed Young's interference experiment and have published marvelous photographs of their results in this book.
13 For further details, see M. Kivor and M. Kaufman, Television Electronics: Theory and Servicing, 8th ed (Van Nostrand Reinhold, NY, 1983)