  Quantum sensitivity is an important issue in the field of quantum metrology
where sub-Planck scale structures play crucial role in the Heisenberg limited
measurement. We investigate the mesoscopic superposition structures,
particularly for well-known cat-like and compass-like states, in the rotating
Morse system where sub-Planck scale structures originate in the dynamics of a
suitably constructed SU(2) coherent state. A detail study of the sensitivity
analysis reveals that rotational coupling in the vibrational wave packet can be
used as a probe to enhance the sensitivity limit in a diatomic molecule. The
maximum sensitivity limit is identified with the rotational amendment, and a
quantitative measure of the angle of rotation for different rotational levels
is also given. The correspondence of the numerical result with the angle of
rotation is also delineated in phase-space Wigner representation.
