Optimal control of photoassociation of cold atoms and photodissociation of long-range molecules: Characteristic times for wave-packet propagation

Abstract

This paper aims at studying the time-dependent effects involved in the photoassociation reaction for a sample of cold alkali-metal atoms, within a two-channel model where the vibrational motion in the excited state is coupled by laser light to the continuum state describing two colliding atoms in the lowest triplet electronic state $(a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}).$ Both photodissociation and photoassociation processes are considered at a time scale shorter than the radiative lifetime, so that spontaneous emission does not have to be considered. The characteristic times are then the vibrational period in the excited state, which for alkali-metal dimers can be estimated of the order of a few hundreds of picoseconds, and the Rabi period, depending upon the laser intensity. Numerical calculations using wave-packet propagation are performed for the coupling of the vibrational motion in the ${\mathrm{Cs}}_{2}{1}_{g}{(6s+6p}_{3/2})$ and ${a}^{3}{\ensuremath{\Sigma}}_{u}^{+}(6s+6s)$ channels by a cw laser slightly red detuned relative to the ${\mathrm{D}}_{2}$ resonance line. The results show Rabi oscillations in the populations of the two channels during time intervals when the vibrational motion is stopped at the outer turning point. At intensities of $\ensuremath{\approx}250\mathrm{kW}{\mathrm{cm}}^{\ensuremath{-}2},$ a new characteristic time appears, a factor of 2 larger than the classical vibrational period, which corresponds to vibrational motion in the upper adiabatic potential created by the coupling. Such an effect modifies the scattering length for collisions in the lower state, and it clearly opens a possibility of control by tuning the laser intensity.