Clock frequency estimation under spontaneous emission

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.