  We show how sub-Planck phase-space structures in the Wigner function can be
used to achieve Heisenberg-limited sensitivity in weak force measurements.
Nonclassical states of harmonic oscillators, consisting of superpositions of
coherent states, are shown to be useful for the measurement of weak forces that
cause translations or rotations in phase space, which is done by entangling the
quantum oscillator with a two-level system. Implementations of this strategy in
cavity QED and ion traps are described.
