Influence of ground-Rydberg coherence in two-qubit gate based on Rydberg blockade

For neutral atom qubits, the two-qubit gate is typically realized via the Rydberg blockade effect, which hints about the special status of the Rydberg level besides the regular qubit register states. Here, we carry out experimental and theoretical studies to reveal how the ground-Rydberg coherence of the control qubit atom affects the process of two-qubit Controlled-Z ($C_Z$) gate, such as the commonly used ground-Rydberg $pi$-gap-$pi$ pulse sequence originally proposed in Phys. Rev. Lett. textbf{85}, 2208 (2000). We measure the decoherence of the control qubit atom after the $pi$-gap-$pi$ pulses and make a direct comparison with the typical decoherence time $tau_{gr}$ extracted from Ramsey fringes of the ground-Rydberg transition. In particular, we observe that the control qubit atom subject to such pulse sequences experiences a process which is essentially similar to the ground-Rydberg Ramsey interference. Furthermore, we build a straightforward theoretical model to link the decoherence process of control qubit subject to $C_Z$ gate $pi$-gap-$pi$ pulse sequence and the $tau_{gr}$, and also analyze the typical origins of decoherence effects. Finally, we discuss the $C_Z$ gate fidelity loss due to the limits imposed by the ground-Rydberg coherence properties and prospective for improving fidelity with new gate protocols.