In the double slit experiment, using only one photon, will it create a diffraction pattern on an ultra sensitive screen? Given the double slit experiment, send one photon through the open slits, then stop.  With just that one photon traveling through both slits it will appear as a point on the screen.  If the screen was ultra sensitive would we see the typical diffraction pattern in addition to the single point?
 A: No.
As a rough guide particles behave like a wave when they they are travelling and they behave like a particle when they exchange energy with something else. During its path from the light source through the slits to the screen the light is delocalised, that is the photon doesn't have a position in the sense that macroscopic objects have a position. That's why it is able to pass through both slits at the same time.
However when the light interacts with the screen to create a spot this is a specific interaction that happens at a well defined position. For example if the screen is a photographic plate the photon will exchange energy with a specific silver atom in the photographic emulsion. The energy exchange happens only at this one spot so there is no faint diffraction pattern to be seen aywhere else on the screen.
This experiment can be done, and indeed has been done with diffracting electrons though I'm not sure about photons. Each particle creates a single spot, but the probability distribution of the spots corresponds to the diffraction pattern. So as more and more spots are recorded the diffraction pattern appears. This has been discussed here before. For example see Anna's answer to this question.
A: Here is a sequential picture of single photons accumulating into an interference pattern:


Single-photon camera recording of photons from a double slit illuminated by very weak laser light. Left to right: single frame, superposition of 200, 1’000, and 500’000 frames.

The experiment:

In 2003, A. Weis and R. Wynands at the University of Bonn (Germany) designed a lecture demonstration experiment of single photon interference from a double slit . Light from a laser pointer was so strongly attenuated that at each instant there was only a single photon between the double slit and the detector. The diffracted light was recorded by a single photon imaging camera consisting of an image intensifier (multichannel plate, MCP) followed by phosphor screen and a CCD camera. When adding consecutive camera frames one sees the gradual appearance of the smooth classical interference pattern (Fig. 1).

Study the left photo where single points are seen. Do you see any diffraction pattern? The single photon should be spread as in the last frame on the right after all, if it would be spread all over the x axis.
