Heuristic optimization of analytic laser pulses for vibrational stabilization of ultracold KRb

Abstract

We proposed a methodology that allows to maximize the population transfer from a high vibrational state of the a3Σ+ triplet state to the vibrational ground state of the X1Σ+ singlet state though the optimization of one pump and one dump laser pulses. The pump pulse is optimized using a fitness function, heuristically improved, that includes the effect of the spin-orbit coupling of the KRb [b-A]-scheme. The dump pulse is optimized to maximize the population transfer to the ground state. We performed a comparison with the case in which the pump and dump pulses are optimized to maximize the population transfer to the ground state employing a genetic algorithm with a single fitness function. The heuristic approach turned out to be 70% more efficient than a quantum optimal control optimization employing a single fitness function. The method proposed provides simple pulses that have an experimental realm.

Vibrational ladder-descending photostabilization of a weakly bound molecule: Quantum optimal control with a genetic algorithm

“…To find the optimal LCP parameters, we adapted the QOC+GA methodology of Arango and coworkers [21,26]. The i-th individual is a pulse whose chromosome consists of the 5-vector of genes γ i ≡ (ε 0 , ω 0 , τ 0 , τ, C).…”

“…Arango and coworkers [21] implemented a pump-dump scheme for the vibrational stabilization into the electronic ground state, X 1 Σ + , of a model 39 K 87 Rb Feschbach molecule formed in the lowest electronic triplet state, a 3 Σ + , using the [b − A] scheme that involves the spin-orbit-coupled intermediate electronic states b 3 Π and A 1 Σ + [23]. The pump pulse stimulates the b 3 Π ← a 3 Σ + absorption and the dump pulse stimulates the A 1 Σ + → X 1 Σ + emission.…”

“…However, the resulting optimal pulse has a complicated structure, making it difficult to achieve experimentally. Regardless of whether the molecules are left in the ground or an excited electronic state, it has been demonstrated that pumpdump [20,21] and STIRAP [19,22,23] methodologies can achieve stabilization. Nevertheless, the involvement of intermediate excited electronic states can introduce complications, like fast spontaneous decay, internal conversions and intersystem crossings.…”

“…Nevertheless, the involvement of intermediate excited electronic states can introduce complications, like fast spontaneous decay, internal conversions and intersystem crossings. Moreover, in these two schemes it may happen that the initial bound level has relatively small Franck-Condon factors for the transitions to the vibrational levels of the intermediate excited electronic states [21]. Therefore, in this situation it is convenient to introduce a prior step to drive the molecules to the lower-lying levels with the highest Franck-Condon factors.…”

“…II we explain our LD method in the context of the model of Ref. 21, where a weakly bound KRb Feshbach molecule in the lowest triplet electronic state is driven to a lowerlying vibrational level to optimize a subsequent pumpdump stabilization scheme. In Sec.…”