Coherent control of cold-molecule formation through photoassociation using a chirped-pulsed-laser field

Enhancement of the production of cold molecules via photoassociation is considered for the ${\mathrm{Cs}}_2$ system. The employment of chirped picosecond pulses is proposed and studied theoretically. The analysis is based on the ability to achieve impulsive excitation which is given by the ultracold initial conditions where the nuclei are effectively stationary during the interaction with a field. The appropriate theoretical framework is the coordinate-dependent two-level system. Matching the pulse parameters to the potentials and initial conditions results in full Rabi cycling between the electronic potentials. By chirping the laser pulse, adiabatic transfer leading to the population inversion from the ground to the excited state is possible in a broad and tunable range of internuclear distance. Numerical simulations based on solving the time-dependent Schrödinger equation (TDSE) were performed. The simulation of the photoassociation of ${\mathrm{Cs}}_2$ from the ground ${}^3{\Sigma }_u^{+}$ to the excited $0_g^{-}$ state under ultracold conditions verifies the qualitative picture. The ability to control the population transfer is employed to optimize molecular formation. Transfer of population to the excited $0_g^{-}$ surface leaves a void in the nuclear density of the ground ${}^3{\Sigma }_u^{+}$ surface. This void is either filled by thermal motion or by quantum “pressure” and it is the rate-determining step in the photoassociation. The spontaneous-emission process leading to cold-molecules is simulated by including an optical potential in the TDSE. Consequently, the rate of cold molecule formation in a pulsed mode is found to be larger than that obtained in a continuous-wave mode.