A conditional quantum phase gate between two 3-state atoms

We propose a scheme for conditional quantum logic between two 3-state atoms that share a quantum data-bus such as a single mode optical field in cavity QED systems, or a collective vibrational state of trapped ions. Making use of quantum interference, our scheme achieves successful conditional phase evolution without any real transitions of atomic internal states or populating the quantum data-bus. In addition, it only requires common addressing of the two atoms by external laser fields.