Suppressing Motional Dephasing of Ground-Rydberg Transition for High-Fidelity Quantum Control with Neutral Atoms

The performance of many control tasks with Rydberg atoms can be improved via suppression of the motion-induced dephasing between the ground state and Rydberg states of neutral atoms. This dephasing often occurs during the gap time when the atom is shelved in a Rydberg state before its deexcitation. This paper presents two theories about how to suppress this dephasing. First, by using laser fields to induce a specific extra phase change in the Rydberg state during the gap time, it is possible to faithfully transfer the Rydberg state back to the ground state after the gap. Although the Rydberg state transitions back and forth between different eigenstates during the gap time, it preserves the blockade interaction between the atom of interest and a nearby Rydberg excitation. This simple method of suppressing the motional dephasing of a flying Rydberg atom can be used in a broad range of methods of quantum control of neutral atoms. Second, we find that the motional dephasing can also be suppressed by using a transition in a "V"-type dual-rail configuration. The left (right) arm of this "V" represents a transition to a Rydberg state vertical bar r(1(2))> with a Rabi frequency Omega e(ik)(z) (Omega e(-ikz)), where z is frozen without atomic drift, but changes linearly in each experimental cycle. Such a configuration is equivalent to a transition between the ground state and a hybrid time-dependent Rydberg state with a Rabi frequency root 2 Omega, such that there is no phase error whenever the state returns to the ground state. We study two applications of the second theory: (i) it is possible to faithfully transfer the atomic state between a hyperfine ground state and Rydberg states vertical bar r(1(2))> with no gap time between the excitation and deexcitation; and (ii) if infrared laser fields are added to induce a transition between vertical bar r(1(2))> and a nearby Rydberg state vertical bar r(3)> via a greatly detuned low-lying intermediate state during the gap time, the atom can keep its internal state in the Rydberg level as well as adjust the population branching in vertical bar r(1(2))> during the gap time. This allows an almost perfect Rydberg deexcitation after the gap time, making it possible to recover a high fidelity in a Rydberg blockade gate. These theories pave the way for high-fidelity quantum control over neutral Rydberg atoms without cooling qubits to motional ground states in optical traps.