Generation of a decoherence-free entangled state using a radio-frequency dressed state

We propose the generation of entangled states with trapped calcium ions using a combination of an rf dressed state and a spin-dependent force. By using this method, a decoherence-free entangled state of rf qubits can be directly generated, and ideally its fidelity is close to unity. We demonstrate an rf entangled state with a fidelity of 0.68±0.08, which has a coherence time of more than 200 ms by virtue of the fact that it is an eigenstate with energy gaps between adjacent levels. Using the same technique, we also produce a qutrit-qutrit entangled state with a fidelity of 0.77±0.09, which exceeds the threshold value for separability of 2/3.