### Question

Is it possible for a single photon to produce diffraction pattern?

Asked by:
Aladdin Abdul-Latif

### Answer

Yes and no. If you're really talking about just one photon, and say you're going
to shoot it a two-slit apparatus and measure where it winds up somewhere beyond the
slits, you will only measure one impact position - you won't really see a
'diffraction pattern' because there's only one photon.

In some sense, however, there is a diffraction pattern. The bizarre
quantum-mechanical 'photon' is described by a wave function that basically can give
us probabilities that the photon will hit any point on your detector. This wave
function will go partially through both slits, and the resulting wave function on
the other side WILL exhibit an interference pattern (!). This diffraction pattern
will show itself if you fire photons singly through the slits, i.e. fire one, wait
a bit, and fire another. Even though the photons are spaced so that they aren't
directly interfering with each other, they will build up a diffraction pattern on
the other side because of the diffraction pattern in each photon's individual wave
function.

Answered by:
Gregory Ogin, Physics Undergraduate Student, UST, St. Paul, MN

It is not possible for a single photon to produce a diffraction pattern. However,
this is only because it would be impossible to extrapolate a pattern with only one
data point. The probability function that describes where this photon is likely to
be detected will be obeyed by the photon. For instance you will never find this
photon where there should be a minima.

As an example suppose we set up a double slit diffraction experiment such that we
decrease the intensity of the incident light so that on average only one photon at
a time is striking the screen. This will produce the effect of single photon
diffraction because at the time each photon passes through the slits there are no
other photons around with which to interfere. But when this experiment is carried
out we still arrive at the results we would expect if we used a high intensity beam
and many photons were striking the screen at once. So as the single photonï¿½s wave
function passes through the slits it is diffracted and interferes with itself. In
this experiment it is shown that a single photon does produce a diffraction
pattern, which is the same as what one would expect from numerous photons, but it
takes many photons striking the screen before the pattern can be observed.

Answered by:
Justin Carstens, Physics Under Grad, UAF, Fairbanks