Formation of ultracold deeply-bound molecules via multi-state chainwise coincident pulses technique

In this paper, a theoretical method for the efficient creation and detection of deeply bound molecules in three-state $\Lambda$-type and five-state M-type molecular systems is proposed. The method is based on the three-state coincident pulses technique and the generalized five-state coincident pulses technique. For the three-state system, the technique can efficiently transfer the populations from the Feshbach state to the deeply-bound state via a train of $N$ pairs of resonant and coincident pump and Stokes pulses, with negligible transient populations of excited states. For the five-state system, it is found that this M-type system can be generalized into a $\Lambda$-type structure with the simplest resonant coupling under the assumption of large one-photon detuning together with a requirement of the relation among the four incident pulses. Thereafter, this generalized model permits us to employ the reduced three-state propagator to design four coincident pulses to achieve the desired population transfer. For the numerical study, $^{87}$Rb$_2$ is considered and, it is shown that the weakly-bound Feshbach molecules can be efficiently transferred to their deeply-bound states without strong laser pulses, and the populations of all intermediate states can be well suppressed.