Improving coherent population amplitudes in open $\Lambda$-systems

A novel scheme based on optical pumping for transforming open $\Lambda $-systems to closed $\Lambda $-systems is proposed and is experimentally implemented on a sample of $^{87}$Rb atoms confined in a vapor cell. A seven-fold improvement in the amplitude of a coherent population trapping (CPT) resonance is observed at sufficient light intensities. The density matrix formalism is used to derive an analytic expression that highlights the differences between a closed and an open $\Lambda $-system in CPT and its consequences on the performance of atomic clocks are discussed.