  Ultra-fast stochastic cooling would be desirable in certain applications, for
example, in order to boost final luminosity in a muon collider or neutrino
factory, where short particle lifetimes severely limit the total time available
to reduce beam phase space. But fast cooling requires very high-bandwidth
amplifiers so as to limit the incoherent heating effects from neighboring
particles. A method of transit-time optical stochastic cooling has been
proposed which would employ high-gain, high-bandwidth, solid-state lasers to
amplify the spontaneous radiation from the charged particle bunch in a
strong-field magnetic wiggler. This amplified light is then fed back onto the
same bunch inside a second wiggler, with appropriate phase delay to effect
cooling. But before amplification, the usable signal from any one particle is
quite small, on average much less than one photon per pass, suggesting that the
radiation should be treated quantum mechanically, and raising doubts as to
whether this weak signal even contains sufficient phase information necessary
for cooling, and whether it can be reliably amplified to provide the expected
cooling on each pass. A careful examination of the dynamics, where the
radiation and amplification processes are treated quantum mechanically,
indicates that fast cooling is in principle possible, with cooling rates which
essentially agree with classical calculations, provided that the effects of the
unavoidable amplifier noise are included. Thus, quantum mechanical
uncertainties do not present any insurmountable obstacles to optical cooling,
but do establish a lower limit on cooling rates and achievable emittances.
