  We show that the two-axis counter twisting interaction squeezes a coherent
spin state into three states of interest in quantum information, namely, the
twin-Fock state, the equally-weighted superposition state, and the state that
achieves the Heisenberg limit of optimal sensitivity defined by the Cramer-Rao
inequality in addition to the well-known Heisenberg-limited state of spin
fluctuations.
