Coherent Population Trapping with a controlled dissipation: applications in optical metrology

We analyze the properties of a pulsed Coherent Population Trapping protocol that uses a controlled decay from the excited state in a $\Lambda$-level scheme. We study this problem analytically and numerically and find regimes where narrow transmission, absorption, or fluorescence spectral lines occur. We then look for optimal frequency measurements using these spectral features by computing the Allan deviation in the presence of ground state decoherence and show that the protocol is on a par with Ramsey-CPT. We discuss possible implementations with ensembles of alkali atoms and single ions and demonstrate that typical pulsed-CPT experiments that are realized on femto-second time-scales can be implemented on micro-seconds time-scales using this scheme.