  We study the generation of angular momentum carrying states for a single cold
particle by breaking the symmetry of a spatial adiabatic passage process in a
two-dimensional system consisting of three harmonic potential wells. By
following a superposition of two eigenstates of the system, a single cold
particle is completely transferred to the degenerate first excited states of
the final trap, which are resonantly coupled via tunneling to the ground states
of the initial and middle traps. Depending on the total time of the process,
angular momentum is generated in the final trap, with values that oscillate
between $\pm\hbar$. This process is discussed in terms of the asymptotic
eigenstates of the individual wells and the results have been checked by
simulations of the full two-dimensional Schr\"odinger equation.
