Control of photodissociation with the dynamic Stark effect induced by THz pulses

We demonstrate how dynamic Stark control can be achieved on molecular photodissociation in the dipole limit, using single-cycle (full width at half maximum) laser pulses in the terahertz (THz) regime. As the laser-molecule interaction follows the instantaneous electric field through the permanent dipoles, the molecular potentials dynamically oscillate and so do the crossings between them. In this paper, we consider rotating-vibrating diatomic molecules (two-dimensional description) and reveal the interplay between the dissociating wave packet and the dynamically fluctuating crossing seam located in the configuration space of the molecules spanned by the $R$ vibrational and $\theta$ rotational coordinates. Our showcase example is the widely studied lithium fluoride molecule for which the two lowest $\mathrm{\Sigma }$ states are nonadiabatically coupled at an avoided crossing (AC); furthermore a low-lying pure repulsive $\mathrm{\Pi }$ state is energetically close. Optical pumping of the system in the ground state thus results in two dissociation channels: one indirect route via the AC in the ground $\mathrm{\Sigma }$ state and one direct path in the $\mathrm{\Pi }$ state. We show that applying THz control pulses with specific time delays relative to the pumping can significantly alter the population dynamics, as well as the kinetic energy and angular distribution of the photofragments.

Figure 1

(a) The lowest three adiabatic potential energy curves of the LiF molecule and the nonadiabatic coupling term $\tau$($R$) between the two $\mathrm{\Sigma }$ states (scale is on the right side). (b) Permanent dipole moment functions of the three adiabatic electronic states. (c) The transition dipole moment functions between the different electronic states.

Figure 2

(a) General form of the THz electric fields applied in the present work $\left(\hslash {\omega }_c=0.037\mathrm{eV},I_c=3.16\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2\right)$. Two particular CEP cases of interest are presented $({\phi }_c=0$ with solid red line and ${\phi }_c=\pi /2$ with dashed red line). The corresponding light-induced potential energy surfaces (LIPs) are shown in panel (b) for ${\phi }_c=0$ and in panel (c) for ${\phi }_c=\pi /2$.

Figure 3

Time evolution (horizontal axis) of the populations in each electronic state $({\mathrm{\Sigma }}_1$, bottom; ${\mathrm{\Pi }}_1$, middle; ${\mathrm{\Sigma }}_2$, upper panels in each column) calculated according to Eq. (7) for different $\mathrm{\Delta }t$ delay times (vertical axis) for two different carrier-envelope phases: panels (a), (c), and (e) for ${\phi }_c=0$ while panels (b), (d), and (f) for ${\phi }_c=\pi /2$. Transverse red lines mark the time moments when the electric field of the control pulse has minima/maxima.

Figure 4

Excited population in the ${\mathrm{\Pi }}_1$ and ${\mathrm{\Sigma }}_2$ states marked with blue and green dashed lines, and dissociation probability in the ${\mathrm{\Pi }}_1$ and ${\mathrm{\Sigma }}_1$ states marked with blue and green continuous lines. Red lines represent the sum of the excited and dissociated population of the above two channels. The control pulse carrier-envelope phase is (a) ${\phi }_c=0$, (b) ${\phi }_c=\pi /2$.

Figure 5

Angular distribution (vertical axis) of the photofragments in the ${\mathrm{\Sigma }}_1$ (bottom) and ${\mathrm{\Pi }}_1$ (middle) electronic states, and the sum of the two channels (top) as a function of time delay (horizontal axis) between the pump and the control pulses for the two investigated carrier-envelope phases: panels (a), (c), and (e) for ${\phi }_c=0$ while panels (b), (d), and (f) for ${\phi }_c=\pi /2$. The distributions associated with each delay time were calculated conforming to Eq. (9).

Figure 6

Kinetic energy release distribution (vertical axis) of the photofragments in the ${\mathrm{\Sigma }}_1$ (bottom) and ${\mathrm{\Pi }}_1$ (middle) electronic states, and the sum of the two channels (top) as a function of time delay (horizontal axis) between the pump and the control pulses for the two investigated carrier-envelope phases: panels (a), (c), and (e) for ${\phi }_c=0$ while panels (b), (d), and (f) for ${\phi }_c=\pi /2$. The distributions associated with each delay time were calculated conforming to Eq. (8).