  We present an efficient scheme for the controlled generation of pure
two-qubit states possessing {\em any} desired degree of entanglement and a {\em
prescribed} symmetry in two cavity QED based systems, namely, cold trapped ions
and flying atoms. This is achieved via on-resonance ion/atom-cavity couplings
which are time-dependent and asymmetric, leading to a trapping vacuum state
condition which does not arise for identical couplings. A duality in the role
of the coupling ratio yields states with a given concurrence but opposing
symmetries. The experimental feasibility of the proposed scheme is also
discussed.
