Interference of a Single Photon
This Page contains information about an experiment done with a single photon
counting CCD camera. A brief description of the experiment is given and then
the results are shown. The experiments (as well as a number of others) were
carried out under an NSF ILI grant 9251313 to Robert Austin and Lyman Page at
Princeton University.
Background
Our classical notions of what constitutes waves and particles are hopeless when
it comes to interpreting quantum phenomena. Perhaps the most lucid explanation
of the peculiar manner in which quanta act is given in the first chapter of the
third volume of the Feynman lecture series. Although Feynman talks about
electrons acting as both particles and waves, we may apply the same reasoning
to photons. Most students of physics learn about Young's double slit
diffraction in their first year. In the limit of very thin slits separated by a
distance d, the intensity pattern on a screen a distance D$>>$d behind the
slits is given by:
$$
I = I_0\cos^{2}\bigr({2\pi d\over 2\lambda}\sin(\theta )\bigl)
$$
where $\theta$ is the angle from the center of the slits to the point on the
screen where the intensity is measured. The essential point is that the waves
are spread over a range in angles and there are multiple maxima (many more
than the number of slits). Light may also be considered from the quantum point
of view. Photomultiplier tubes count single photons; many texts show
the positron/electron pairs from the decay of a gamma ray. If
we think of the photons as rocks then if they are thrown at a wall containing
two holes they should land in two piles on the other side of the wall. In the
demonstration, we illuminate a triple slit with a laser beam that has been
attenuated to such a degree that the {\it mean} path between photons is
$\approx 2\times 10^{3}$ meters. We show that despite this large distance, a
diffraction patterns obtains -- the photon has ``interfered'' with itself.
The ability to demonstrate this phenomena has been around for a long
time, G. Reynolds did it in 1938 and a Soviet group did it (incorrectly) before
him. With the advent of photon counting CCD cameras the demonstration is easy
and visually startling.
The Demonstration
A 40 by 80 cm aluminum box of depth 25 cm holds the slits and a
mirror. The inside of the box is painted flat black and black felt is used near
all the seams. A 1 mW He-Ne laser ($\lambda = 632.8 {\rm nm}$, $3\times
10^{15}~$photons/sec) illuminates a 1/8 diameter hole drilled into one end of
the box. Neutral density filters mounted in a black felt-lined holder attenuate
the laser light by a factor of $\alpha = 5\times10^{-11}$. Thus, the mean
distance between photons is 2 km. Then, the attenuated light passes through the
slits, bounces off the mirror at the far end of the box and returns to enter
the aperture of a Hamamatsu model C2400-30 photon counting camera. The top of
the aluminum box is hinged for easy access and all the alignment is done with
the neutral density filters removed.
The Hamamatsu camera is a remarkable device. In essence, it has two
successive micro-channel plates followed by a CCD chip. The camera has a 768
by 420 pixel array that is read at video rates. At maximum sensitivity, near
$\lambda = 400~$nm, the camera's quantum efficiency is near .3; near $\lambda
= 680~$nm, it is 0.001. The images are acquired with an Argus-10 video receiver
also made by Hamamatsu. The Argus can average many video frames and displays
the data on a video screen. The output of the Argus is fed to CCD frame-grabber
card (we use a Dipex card but most any will do) controlled by a 486DX based
computer. The computer periodically samples the video output of the Argus and
stores the data for future use.
The following pictures were taken with the above setup.
The width of each slit is 0.04 mm and the separation is 0.125 mm.
The coherence length of the laser has not yet been measured.
This shows the result after counting for 1/30 second. The few white
dots in the image are photons. One expects to get
$3.2\times10^{15}$ X $\alpha$ X (quantum efficiency) X (time) = 5 photons.
Note that the photons are distinct.
This is the image after averaging for 1 second. The interference
pattern is beginning to immerge but it is clear that it is
made up of photons. Though one might believe that there are three
``piles of rocks,'' one would be hard pressed to be sure that there were
more.
Same image as the above after averaging for 100 seconds. Even
though there were only three slits, 5 maxima are clearly visible.
Here we have an interference pattern made up of discrete particle
detections.
References
-
The Feynman Lectures on Physics. Vol. 3, R. P. Feynman,
R. B. Leighton, & M. Sands, Addison-Wesley, 1965