Taylor exposed photographic plates for up to 3 months to obtain interference patterns using his very weak light source. Today, we can conduct the same experiment within a few minutes, using the setup shown in the block diagram of Figure 90. The basic idea remains the same—to illuminate the double slit with a very weak beam. So weak in fact, that there is a reasonably high assurance that only a single photon of the laser beam is present in the device at a time.
Figure 90 This is the experimental setup that we constructed to demonstrate single-photon interference. Just as in the experiment of Figure 33, a laser beam is attenuated with neutral-density filters of at least D = 6.73, to the point where only one photon is present within the apparatus. Each photon then passes through a double slit. We used an extremely sensitive TV camera to detect the individual photons. Two HeNe-line band-pass filters (Edmund Industrial Optics model NT43-133) and two apertures (1-in. flat washers from the hardware store) keep stray, nonlaser photons from adding to the noise.
As shown in Figure 90, the distance between our two-slit slide and the detector is 10 cm, which means that a photon takes:
to traverse this distance. As such, at most one photon hits the photocathode as long as photons arrive at a frequency of less than 1/0.33 [ns] = 3.03 × 109[photons/s].
Our HeNe laser produces photons at a wavelength of λ = 632 nm, each with an energy:
We measured the optical power output of our laser to be 5 mW, so we can calculate the number of photons produced by our laser each second, just as (Figure 33):
By placing the attenuators before the two-slit slide, we can be assured there will be at most one photon within the 10-cm path between the slits and the detector if the density of the attenuators is at least:
Therefore, any density for the system over D = 6.72 results in an average population of less than one photon at a time within the optical assembly.
As we saw before, the optical densities of neutral-density filters used in combination are additive. We use a combination of three D = 1 (Thorlabs NE10A), one D = 2 (Thorlabs NE20A), and a D = 5 (Thorlabs NE50A) filter for a total of D = 10, allowing a maximum of 1.6 × 106 photons/s to reach the double slit.
The attenuated beam illuminates a 45 μm-separation double slit (cut out from an IF-508 diffraction mosaic slide from Industrial Fiber-optics). Since our HeNe laser produces a 0.8-mm-diameter spot with a Gaussian distribution, only about 7% of the photons can actually pass through the narrow slits toward the detectors. Each of the laser-line filters allows only 45% of desirable 632-nm photons through, so only 22,680 photons/s reach the detector.
The average time between photon arrivals at the camera is thus 44 μs. Since any individual photon goes across the 10-cm length of the apparatus with a flight time of 0.33 ns, there is on average a photon in flight between the neutral-density filter and the camera for only about 0.33 ns out of every 44 μs. Thinking in particle terms, this means that for 99.99925% of the time there are “no” photons in flight, while for only 0.00075% of the time there is “one” photon in flight in the apparatus. Since photon bunching is insignificant, the probability of there being two photons in flight simultaneously is thus negligible. All the interference effects observed in this apparatus can thus be attributed to the “weird” behavior of individual photons, traversing through the double slit one at a time!
In this case, the interference pattern doesn’t appear instantaneously, as it does when the double slit is illuminated by the laser beam without attenuation. Since only a single photon strikes the camera’s sensor at a time, only localized impacts of individual photons are observed. The interference pattern appears only after adding up (integrating) many of these individual, localized impacts.
We integrated successive video frames using the short MATLAB program shown in Listing 1. The freeware utility VFM† (Vision for MATLAB by Farzad Pezeshkpour) allows MATLAB to access video source devices, such as frame-grabber boards and USB cameras. Our program first captures the static dark background image that almost every camera produces with no light impinging on it. Frames are acquired and added to each other, one at a time. The dark static image is subtracted from each frame during the integration process to make it easier to distinguish the strikes produced by the photons. As a result, the interference pattern emerges slowly from the background noise as shown in Figure 91.
Figure 91 Integration of image frames from a low-light-level camera exposed to single photons flying through a double-slit apparatus. The interference pattern emerges slowly from the background noise. The camera that we used has an onboard integrator, so each frame integrated by the computer is the result of 64 frames integrated by the camera itself. In turn, each frame is exposed for up to 33 ms.
Listing 1 MATLAB program to integrate image frames.
%————————————————————————————————————————————————————————————
% Matlab program to integrate video image frames from single-photon
% interference setup.
%
% © David Prutchi, Ph.D. 2008
%
% This program uses VFM (Vision for Matlab) to acquire
% image frames through a Windows video capture card.
%
%————————————————————————————————————————————————————————————
% From the VFM preview window, configure VFM to 640×480 video resolution
%
noise(480,640) = 0; % initialize array that will hold static dark image
a = vfm(‘grab’,10); % acquire 10 frames
dark = double(a); % convert from image format to double-precision numbers
% Integrate 10 frames
for n = 1:10
noise =
noise+dark(:,:,1,n)+dark(:,:,2,n)+dark(:,:,3,n);
end
noise = noise/10; % Calculate average dark static image
clf % Clear figure
imagesc (noise) % Display average dark static image
colorbar
title(‘Dark Static Image’)
drawnow
clear a % Clear the image buffer
clear dark % Clear the double-precision image buffer
% Ask user to turn LASER on
beep
disp(‘PLEASE TURN LASER ON’)
pause(2)
beep
pause(2)
beep
pause(2)
c(480,640) = 0; % initialize array that will hold
interference pattern
for n = 1:200 % number of frames to be integrated
a = vfm(‘grab’,1);
b = double(a);
n
c = c+b(:,:,1)+b(:,:,2)+b(:,:,3) -noise;
if n = = 1
figure(2)
subplot(2,3,1)
imagesc(c,[0,max(max(c))])
title(‘Frames Integrated = 1’)
drawnow
end
if n = = 10
figure(2)
subplot(2,3,2)
imagesc(c,[0,max(max(c))])
title(‘Frames Integrated = 10’)
drawnow
end
if n = = 25
figure(2)
subplot(2,3,3)
imagesc(c,[0,max(max(c))])
title(‘Frames Integrated = 25’)
drawnow
end
if n = = 50
figure(2)
subplot(2,3,4)
imagesc(c,[0,max(max(c))])
title(‘Frames Integrated = 50’)
drawnow
end
if n = = 100
figure(2)
subplot(2,3,5)
imagesc(c,[0,max(max(c))])
title(‘Frames Integrated = 100’)
drawnow
end
if n = = 200
figure(2)
subplot(2,3,6)
imagesc(c,[0,max(max(c))])
title(‘Frames Integrated = 200’)
drawnow
end
figure(3)
clf
imagesc(c,[0,max(max(c))])
colorbar
drawnow
end
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