  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.
