Gate fidelity, dephasing, and ‘magic’ trapping of optically trapped neutral atom

Abstract

The fidelity of the gate operation and the coherence time of neutral atoms trapped in an optical dipole trap are figures of merit for the applications. The motion of the trapped atom is one of the key factors which influence the gate fidelity and coherence time. However, it has been considered as a classical oscillator in analysis of the coherence time. Here we treat the motion as a quantum oscillator, and the population on the vibrational states of the atom are taken into account in analyzing the gate fidelity and decoherence. We show that the fidelity of a coherent rotation gate between two hyperfine states is dramatically limited by the population distribution on the vibrational states. We also find that the description of the decoherence caused by the previously regarded inhomogeneous dephasing due to the thermal motion of the atom is actually homogeneous in a quantum view. The phase between the two hyperfine states is still preserved on different vibrational states, and the observed interference fringe will recover naturally if the differential frequency shift is stable and the vibrational states do not change. The decoherence due to the fluctuations of the trap laser intensity is also discussed. Both the gate fidelity and coherence time can be dramatically enhanced by cooling the atom into vibrational ground states and/or by using a blue-detuned trap. More importantly, we propose a ``magic'' trapping condition by preparing the atom into specific vibrational states.