Fast entangling quantum gates can significantly enhance the performance of a trapped-ion quantum computer. In pursuit of implementing a fast two-qubit gate, we investigate the coherent excitation of a 40 Ca + ion with a train of picosecond pulses resonant to the 4S 1/2 « 4P 3/2 transition. The optical pulse train is derived from a mode-locked, stabilized optical frequency comb. We implement two techniques to characterize the pulse-ion interaction and show how all requirements can be met for an implementation of a fast phase gate operation.

We propose a method of entangling two spinor Bose-Einstein condensates using a geometric phase gate. The scheme relies upon only the ac Stark shift and a common controllable optical mode coupled to the spins. Our scheme allows for the creation of an S z S z type interaction where S z is the total spin. The geometric phase gate can be executed in times of the order of 2π /G, where G is the magnitude of the Stark shift. In contrast to related schemes which relied on a fourth order interaction to produce entanglement, this is a second order interaction in the number of atomic transitions. Closed expressions for the entangling phase are derived and the effects of decoherence due to cavity decay, spontaneous emission, and incomplete de-entangling of the light to the BEC are analyzed.