Quantum logic gate operation between different ions in a trap

We suggest a scheme for realizing a universal two-quantum-bit (qubit) operation. The scheme uses two laser beams with different intensities to illuminate two different ions in a harmonic trap. Both beams are tuned to the red motional sideband. We find that, under certain conditions, the interaction will realize a universal two-qubit operation, the controlled-rotation operation, which is to rotate the phase of the state by pi only when the two states are both in the [1] state. The scheme requires careful control of laser intensity and Lamb-Dicke parameters. But after we reach the required parameters, the logic operation is very simple.