  A theoretical scheme for the realization of the sphere-coherent motional
states in an optomechanical cavity in the presence of a two-level atom is
proposed. To this end, the analogy between an atom-assisted optomechanical
cavity and a laser-driven trapped-ion system is used. This analogy provides us
with a theoretical tool to show how sphere-coherent states can be generated for
the motional degree of freedom of the macroscopic mechanical oscillator from
atom-field-mirror interactions in a multi-mode optomechanical cavity. Some
nonclassical properties of the generated state of the mechanical oscillator,
including the degree of quadrature squeezing and the negativity of the Wigner
distribution are studied. We also examine the effects of the dissipation
mechanisms involved in the system under consideration, including the atomic
spontaneous emission and the damping of the motion of the mechanical
oscillator, on the generated motional sphere-coherent states.
