Control of(1+1+1′)-photon dissociation dynamics in the NaH molecule using three delayed ultrashort pulses

Abstract

We have calculated $(1+1+{1}^{\ensuremath{'}})$-photon dissociation cross section of the NaH molecule from ${v}^{\ensuremath{''}}=0$ level of the ground $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ state to the repulsive ${B}^{1}\ensuremath{\Pi}$ state via the bound $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ state by using three delayed ultrashort pulses. Two delayed $4\phantom{\rule{0.3em}{0ex}}\text{femtosecond}$ pulses have been used for the first step transition to design interfering wave packets on the intermediate $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ state and the third delayed ultrashort pulse (either $\ensuremath{\delta}$-function or $4\phantom{\rule{0.3em}{0ex}}\text{femtosecond}$) excites these wave packets to the dissociating state. We have shown that control over dissociation dynamics can be achieved by controlling delay between three pulses, the pulse durations, and the carrier frequencies. We have considered two values of delay between the first two $4\phantom{\rule{0.3em}{0ex}}\text{femtosecond}$ pulses for which it is possible to inhibit and enhance the deexcitation channel to the ground state and hence for these two delays the maximum of the cross section in the dissociation spectrum can be enhanced or diminished respectively for the $\ensuremath{\delta}$-function transition to the dissociating state by the third ultrashort pulse. The dissociation spectrum also depends on the delay of the third pulse. The dependence of the dissociation cross section on the delays of pulses and on the carrier frequency of the third pulse has been demonstrated for two step dissociating transition by three delayed $4\phantom{\rule{0.3em}{0ex}}\text{femtosecond}$ pulses of Gaussian shape. It has been suggested that the oscillation of dissociation cross section with time delay of the third pulse can be realized as time dependent quantum gates and the nature of quantum gates can be controlled by choosing pulses of different shape, duration, and photon energy (or carrier frequency) as well as delay between the pulses. This aspect of realization and precise control of time dependent quantum gate in light molecules by using three ultrashort pulses $(4\phantom{\rule{0.3em}{0ex}}\text{femtosecond})$ has not been explored before.