  We investigate the quantum dynamics of a driven two-level system under
spontaneous emission and its application in clock frequency estimation. By
using a Lindblad equation to describe the system, we analytically obtain its
exact solutions, which show three different regimes: Rabi oscillation, damped
oscillation and overdamped decay. From the analytical solutions, we explore how
the spontaneous emission affects the clock frequency estimation. We find that,
under a modest spontaneous emission rate, the transition frequency can still be
inferred from the Rabi oscillation. Our results provide potential practical
applications in frequency measurement and quantum control under decoherence.
