Bose Condensation, Superfluidity, and the Quantum Hall Effect

Composite particles (e.g. 4He atoms) consisting of an even number of fermions can pretend to be bosons.  Bosons need not heed the Pauli exclusion principle and can instead Bose condense and do remarkable things.  Superconductivity, which is certainly remarkable, results (sort of) from the Bose condensation of electron pairs.  With this in mind, theorists have speculated since the early 1960s that excitons (electron-hole pairs in a semiconductor) might be able to do the same thing. 
 
	Bose condensation of excitons has traditionally been sought by first optically exciting electron-hole pairs and then hoping that they bind, cool down, and do something wonderful before they recombine back into photons.  In this talk I will describe a completely different approach, one that employs two parallel layers of electrons in a large magnetic field.  Remarkably, excitons exist and are stable in this system, Bose condense at low temperatures, and exhibit many truly surprising properties.  After a brief qualitative description of the system at hand, I will focus on our most recent results, some of which may seem paradoxical at first sight.