  We propose a scheme for preparation of entangled coherent states for the
motion of an ion in a two-dimensional anisotropic trap. In the scheme, the ion
is driven by four laser beams along different directions in the ion trap plane,
resulting in carrier excitation and couplings between the internal and external
degrees of freedom. When the total quantum number of the vibrational modes
initially has a definite parity, the competition between the unitary dynamics
and spontaneous emission will force the system to evolve to a steady state,
where the vibrational modes are in a two-mode cat state. We show that the
method can be extended to realization of entangled coherent states for three
vibrational modes of an ion in a three-dimensional anisotropic trap.
