  We discuss the theory and experimental considerations of a quantum feedback
scheme for producing deterministically reproducible spin squeezing. Continuous
nondemolition atom number measurement from monitoring a probe field
conditionally squeezes the sample. Simultaneous feedback of the measurement
results controls the quantum state such that the squeezing becomes
unconditional. We find that for very strong cavity coupling and a limited
number of atoms, the theoretical squeezing approaches the Heisenberg limit.
Strong squeezing will still be produced at weaker coupling and even in free
space (thus presenting a simple experimental test for quantum feedback). The
measurement and feedback can be stopped at any time, thereby freezing the
sample with a desired amount of squeezing.
