Human rhodopsin has a quantum efficiency (QE) of about 25% (there's a 25% chance a single photon will be absorbed and produce the rod-cell signal). By comparison, cat rhodopsin is more than 90% quantum efficient. 25% QE is sufficiently high to be observable -- a source of single photons can be seen by a dark-adpated person with normal vision.
Step 1: Not Ready for Prime Time
If someone else decides to tackle it, please feel free to contact me and I'll make this a collaboration.
Step 2: Producing Single Photons
NOTE: I have modified the ND notation below to refer explicitly to the optical density, rather than fractional lens area. I was unware of the confusion until Instructables user jefc_uk pointed it out. Thanks!
You'll need a steady source of well-collimated photons. A green laser pointer (~532 nm) will do nicely. But how many photons does it generate? A wavelength of 532 nm corresponds to 3.53×10-19 joules. So a small 1mW laser pointer puts out 2.8×1015 photons per second (watt = joule/s). You can use a red laser pointer, but your eye will be less efficient (see intro). Estimate the number of photons your pointer produces given its wavelength and power rating.
How do you reduce that to one photon at a time? With filters. An ND3.0 neutral density filter (optical density of 3.0) reduces the output light by 10-3 compared to the input, so a stack of just five ND3.0's in front of this laster pointer would result in (on average) just 2.8 photons per second! A stack of four ND4.0's (each reducing the output by 10-4)would give you 0.28 photons/s on average.
If you don't have neutral density filters, you can make a decent approximation, by stacking sheets of black trash-bag plastic. To make this work you have to measure the attenuation yourself, so you'll need a photodetector, something which gives an output (voltage, resistance, current, whatever) proportional to the intensity of light.
Shine the laser on your detector with no filters in place, and record the output. Do the same with one, two, etc. filter layers, and make a plot of output (on a log scale) vs. number of filters. Hopefully, you get down to 0.001 or 0.0001 with just a few layers. with the log plot, you can draw a straight line to extrapolate how many layers you need to get down to a few photons/s.
Ideally, you'd also like a single-photon counter, something like an avalanche photodiode, connected to a piezo-speaker, so that you can hear "clicks" each time a photon comes through the final stack of filters, and confirm that the rate is as low as you expect. Building such a thing is a whole separate project in itself, so I'm just going to assume that you have one.
Step 3: Make a Dark Room -- or a Dark Box
Otherwise, use thick (3-5 mm) black felt and gaffer's tape to seal any windows and doorframes. When you turn off the lights, you should not see any light coming in through cracks or edges. If you do, fix them and check again.
I'm coming to the conclusion that this is too complicated for the problem at hand. It may turn out to be better to build a light-box with a gasketed hole at one end for the laser pointer, and a viewing window with draped headcover at the other.
Step 4: Set Up Your Photon Gun
Attach the ND filters (or plastic sheets) to the front of your laser, sealing around the edges with gaffer's tape. You don't want any light scattering out the sides.
Put the laser on a table or stand pointed at where you'll be sitting.
Even a 1 mW laser pointer can damage retinal cells from direct impact. Not enough to blind you, but enough to potentially contribute to vision issues later in life. Don't point the laser at your face until you have the ND filters installed.
If you're doing this by yourself, you may want to have a piece of tape set up to hold the pointer's button down. Otherwise, your lab partner will take care of it.
Step 5: Sit in the Dark
Step 6: Fire Away!
If you have a lab partner, you can make a real experiment out of it. Sit quietly, and have them turn the laser on and off without telling you. If things are working correctly, then you should be able to identify when the laser has been turned on, and when it's off. Keep track of hits and misses for many (at least 20) trials, and measure whether or not what I've described actually works.
Step 7: Other Single-photon Experiments
How about "self-interference" and wave-particle duality with a double-slit experiment?
If you are really ambitious, and have access to a proper optical table and research equipment, you could even try measuring entanglement, or trying a delayed-choice experiment.
Of course, if you have access to that kind of equipment, you're probably already a postdoc or facult in quantum optics, and are about to write a long comment about all the stuff I've gotten wrong :-)