  A simple formula is derived for the maximum squeezing rate which occurs at
the initial stages of the squeezing process: the rate only depends on the
second partial derivatives of a classical Hamiltonian. Rules for optimum
rotation of the phase space are found to keep the state optimally located and
oriented for fastest squeezing. These operations transform the phase-space
point of interest into a saddle point with opposite principal curvatures.
Similar results are found for the Bloch-sphere phase space and spin squeezing.
Application of the general formulas is illustrated by several model examples
including parametric downconversion, Kerr nonlinearity, Jaynes-Cummings
interaction, and spin squeezing by one-axis twisting and two-axis
countertwisting.
