Time-dependent analysis of tunneling effect in the formation of ultracold molecules via photoassociation of laser-cooled atoms

Abstract

The paper contains a time-dependent investigation of the tunneling effect observed in the photoassociation spectrum of Cs2 and attributed to the 0g -(6s, 6p 3/2) double well. When by photoassociation of two cold cesium atoms a vibrational level of the outer well is populated, tunneling is an efficient mechanism for transferring the population to the inner well (R < 15a 0), where spontaneous emission may lead to formation of cold molecules in low vibrational levels of the a 3Σ+ u(6s, 6s) electronic state. This tunneling effect is analyzed by wavepackets propagation, first considering the double well potential alone, and following a packet made by a superposition of states initially located at large distances. Characteristic times for the vibration dynamics, corresponding to a beating phenomenon between the two wells, to partial “revival” at large distances, and to maxima in the population localized in the inner well are reported and discussed. Second, we simulate the two-channels a 3Σ+ u(6s, 6s)↦0g -(6s, 6p 3/2) photoassociation at detunings around 2.9 cm-1: the inner well can be populated either by the excitation of a vibrational level of the external well (resonant excitation), or by tuning the photoassociation laser at the energy of the inner well level which displays tunneling (“off-resonance excitation”). In the first case the photoassociation is efficient, while the tunneling probability is small; in the second, the tunneling probability is large, so that despite the poor efficiency of the photoassociation process, more population can be transferred to the inner well. This second choice is shown to be very sensitive to the laser intensity, which could be used to control the population of the inner well and hence the formation of ultracold molecules in low vibrational levels.