Is it possible to trap a single photon? If yes, at what cost?
Well, you can't reflect a photon of any known matter without destroying the original photon (and creating a new one in its stead). And since it has no electrical charge, you can't affect it with an EM field either. In theory, it should be possible to produce a gravitational field strong enough to get a photon to orbit around the source, but you'll probably get a black hole in the process... unless you're willing to compromise for a very large orbit radius...
As is often the case in many questions involving SR and/or QM, the question becomes ambiguous if one doesn't define it clearly. This is due to certain classical connotations associated with the properties being asked.
If by asking
"is it possible to trap a single photon?"
"can we store the info such as phase, energy, and coherence" of a number of photons for a period of time, and then retransmit those info without any significant loss?"
then the answer is YES. The report from a few years ago by the Lena Hau group at Harvard demonstrated this. Here, they managed to halt the "speed" of light to 0 m/s in an atomic cloud medium.
 C. Liu et al., Nature v.409, p.490 (2001).
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