Deterministic entanglement of ions in thermal states of motion

We give a detailed description of the implementation of a Mølmer–Sørensen gate entangling two 40Ca ions using a bichromatic laser beam near-resonant with a quadrupole transition. By amplitude pulse shaping and compensation of ac-Stark shifts we achieve a fast gate operation without compromising the error rate. Subjecting different input states to concatenations of up to 21 individual gate operations reveals Bell state fidelities above 0.80. In principle, the entangling gate does not require ground state cooling of the ions as long as the Lamb–Dicke criterion is fulfilled. We present the first experimental evidence for this claim and create Bell states with a fidelity of 0.974(1) for ions in a thermal state of motion with a mean phonon number of n̄ = 20(2) in the mode coupling to the ions’ internal states. 3 Author to whom any correspondence should be addressed. New Journal of Physics 11 (2009) 023002 1367-2630/09/023002+19$30.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft