We propose a multilevel scheme to coherently transfer the population of a diatomic molecule, either polar or nonpolar, from a rovibrational level to a target rovibrational level of the same electronic state or another. It involves a linear chain of $N$ rovibrational levels alternating between the initial electronic state and a second electronic state, conveniently selected according to the dipole couplings between consecutive levels. A set of $N-1$ simultaneous weak ($\approx {10}^4\mathrm{W}/{\mathrm{cm}}^2$) laser pulses, with simple analytical shapes, each in resonance between two neighbors of the chain, transfers the population from the initial rovibronic state gradually and consecutively through the chain, until at the end of the process it resides in the target rovibronic state, as in a kind of ping-pong game between the two electronic states. Using the partial-wave expansion of the molecular wave function, vibrational bases within the $J$ manifolds of each electronic state, and the rotating-wave approximation (RWA), we map the radial Hamiltonian to the one of a spin $s=(N-1)/2$ under a static magnetic field, providing an analytical formula for the populations of the linked states. As an illustration, we apply this pseudospin representation to the stabilization into the absolute ground state of a KRb molecule initially in the high-lying $\upsilon =75, J=6$ level of the ground electronic state $X^1{\mathrm{\Sigma }}^{+}$. With a chain of seven rovibronic states, three of them belonging to the excited $A^1{\mathrm{\Sigma }}^{+}$ electronic state, and pulses of 0.4 ns of duration, the population is fully transferred into the target state in about 1 ns. In addition, we perform a numerical simulation of the ping-pong process, taking into account the entire rovibrational space of both electronic states and without invoking the RWA, finding a good agreement with the results of the pseudospin model.

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• Coherent control
• Cooling & trapping
• Molecules
• Rabi model
• Rotating wave approximation