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Ultra-fast stochastic cooling would be desirable in certain applications, forexample, in order to boost final luminosity in a muon collider or neutrinofactory, where short particle lifetimes severely limit the total time availableto reduce beam phase space. But fast cooling requires very high-bandwidthamplifiers so as to limit the incoherent heating effects from neighboringparticles. A method of transit-time optical stochastic cooling has beenproposed which would employ high-gain, high-bandwidth, solid-state lasers toamplify the spontaneous radiation from the charged particle bunch in astrong-field magnetic wiggler. This amplified light is then fed back onto thesame bunch inside a second wiggler, with appropriate phase delay to effectcooling. But before amplification, the usable signal from any one particle isquite small, on average much less than one photon per pass, suggesting that theradiation should be treated quantum mechanically, and raising doubts as towhether this weak signal even contains sufficient phase information necessaryfor cooling, and whether it can be reliably amplified to provide the expectedcooling on each pass. A careful examination of the dynamics, where theradiation and amplification processes are treated quantum mechanically,indicates that fast cooling is in principle possible, with cooling rates whichessentially agree with classical calculations, provided that the effects of theunavoidable amplifier noise are included. Thus, quantum mechanicaluncertainties do not present any insurmountable obstacles to optical cooling,but do establish a lower limit on cooling rates and achievable emittances.

Quantum Mechanical Treatment of Transit-Time Optical Stochastic Cooling of Muons