Theoretical description of the mixed-field orientation of asymmetric-top molecules: A time-dependent study

We present a theoretical study of the mixed-field-orientation of asymmetric-top molecules in tilted static electric field and nonresonant linearly polarized laser pulse by solving the time-dependent Schrödinger equation. Within this framework, we compute the mixed-field orientation of a state-selected molecular beam of benzonitrile $\left({\mathrm{C}}_7{\mathrm{H}}_5\mathrm{N}\right)$ and compare with the experimental observations [J. L. Hansen et al., Phys. Rev. A 83, 023406 (2011)] and with our previous time-independent descriptions [J. J. Omiste et al., Phys. Chem. Chem. Phys. 13, 18815 (2011)]. For an excited rotational state, we investigate the field-dressed dynamics for several field configurations as those used in the mixed-field experiments. The nonadiabatic phenomena and their consequences on the rotational dynamics are analyzed in detail.

Figure 1

The theoretical orientation ratio $N_{\mathrm{up}}/N_{\mathrm{tot}}$ as a function of the population of the molecular beam of benzonitrile using a probe laser circularly polarized perpendicular to the screen computed by the diabatic model (red solid line), by time-dependent (TD) description for parallel-fields (blue dashed line), and by time-dependent description for tilted fields (green dot-dashed line). The field configuration is $I_0=7\times {10}^{11}\mathrm{W}/{\mathrm{cm}}^2,E_s=286\mathrm{V}/\mathrm{cm}$, and $\beta ={135}^{\circ }$.

Figure 2

The 2D projection of the probability density of the state ${\left|3_{0,3}1\right.〉}_{\text{t}}$ at the peak intensity computed using (a) the adiabatic approximation, (b) the diabatic model, and (c) the time-dependent description for tilted fields. The field configuration is $I_0=7\times {10}^{11}\mathrm{W}/{\mathrm{cm}}^2,E_s=286\mathrm{V}/\mathrm{cm}$, and $\beta ={135}^{\circ }$.

Figure 3

For the ${\left|3_{0,3}1\right.〉}_{\text{t}}$ state, expectation value $〈cos\theta 〉$ as a function of $I\left(t\right)$ for laser pulses with peak intensity $I_0=7\times {10}^{11}\mathrm{W}/{\mathrm{cm}}^2$ and temporal widths $\tau =0.5$ (red solid), 1 (blue dashed), 5 (orange dotted), and $10\mathrm{ns}$ (green dot-dashed). The electric field has strength $E_s=300\mathrm{V}/\mathrm{cm}$, and is tilted an angle (a) $\beta =0^{\circ }$, (b) $\beta ={30}^{\circ }$, and (c) $\beta ={60}^{\circ }$.

Figure 4

For the ${\left|3_{0,3}1\right.〉}_{\text{t}}$ state, expectation value $〈cos\theta 〉$ as a function of $I\left(t\right)$ for a $10\text{−}\mathrm{ns}$ laser pulse with peak intensity $I_0=7\times {10}^{11}\mathrm{W}/{\mathrm{cm}}^2$. The electric field has strengths (a) $E_s=5\mathrm{kV}/\mathrm{cm}$, (b) $E_s=10\mathrm{kV}/\mathrm{cm}$, and (c) $E_s=20\mathrm{kV}/\mathrm{cm}$ and is tilted by $\beta =0^{\circ }$ (red solid line), $\beta ={30}^{\circ }$ (blue dashed line), and $\beta ={60}^{\circ }$ (orange dotted line).

Figure 5

For the ${\left|3_{0,3}1\right.〉}_{\text{t}}$ state, expectation value $〈cos\theta 〉$ as a function of $I\left(t\right)$ for a $10\text{−}\mathrm{ns}$ laser pulse with peak intensity $I_0=7\times {10}^{11}\mathrm{W}/{\mathrm{cm}}^2$ for (a) tilted fields with $\beta ={30}^{\circ }$ and for (b) parallel fields with the electric field parallel to the LFF $Z$ axis of strength $E_{s}cos{30}^{\circ }$. The electric-field strengths are $E_s=300\mathrm{V}/\mathrm{cm}$ (red solid line), $E_s=1\mathrm{kV}/\mathrm{cm}$ (blue dashed line), $E_s=10\mathrm{kV}/\mathrm{cm}$ (orange dotted line), and $E_s=20\mathrm{kV}/\mathrm{cm}$ (green dot-dashed line).

Figure 6

For the adiabatic pendular states ${\left|3_{0,3}3\right.〉}_{\mathrm{p}}$ (red solid line), ${\left|3_{0,3}2\right.〉}_{\mathrm{p}}$ (blue dashed line), ${\left|3_{0,3}1\right.〉}_{\mathrm{p}}$ (orange dotted line), and ${\left|3_{0,3}0\right.〉}_{\mathrm{p}}$ (green dot-dashed line), energy and expectation value $〈M^2〉$ for a dc field tilted $\beta ={30}^{\circ }$ and with strength $E_s=300\mathrm{V}/\mathrm{cm}$ (a) and (d), $E_s=600\mathrm{V}/\mathrm{cm}$ (b) and (e), and $E_s=1000\mathrm{V}/\mathrm{cm}$ (c) and (f). The laser pulse has $\tau =10\mathrm{ns}$ and peak intensity $I_0=7\times {10}^{11}\mathrm{W}/{\mathrm{cm}}^2$. In the insets, the energy is given in units of ${\mathrm{cm}}^{-1}$ and the intensity in units of ${10}^8$ W/${\mathrm{cm}}^2$.

Figure 7

The squares of the projection of the time-dependent wave function ${\left|3_{0,3}1\right.〉}_{\text{t}}$ onto the adiabatic states of the $\left|3_{0,3}M\right.〉$ multiplet, i.e., ${\left|3_{0,3}3\right.〉}_{\mathrm{p}},{\left|3_{0,3}2\right.〉}_{\mathrm{p}},{\left|3_{0,3}1\right.〉}_{\mathrm{p}}$, and ${\left|3_{0,3}0\right.〉}_{\mathrm{p}}$ as a function of $I\left(t\right)$. The field configurations are $I_0=7\times {10}^{11}\mathrm{W}/{\mathrm{cm}}^2,\tau =10\mathrm{ns},\beta ={30}^{\circ }$, and (a) $E_s=300\mathrm{V}/\mathrm{cm}$, (b) $E_s=600\mathrm{V}/\mathrm{cm}$, and (c) $E_s=1000\mathrm{V}/\mathrm{cm}$. The labels of the states are the same as in Fig. 6.

Figure 8

For the time-dependent state ${\left|3_{0,3}1\right.〉}_{\text{t}}$, expectation $〈M^2〉$ as a function of $I\left(t\right)$ for the rotational state for (a) $E_s=300\mathrm{V}/\mathrm{cm}$ and $\beta ={30}^{\circ }$, (b) $E_s=300\mathrm{V}/\mathrm{cm}$ and $\beta ={60}^{\circ }$, and (c) $E_s=1000\mathrm{V}/\mathrm{cm}$ and $\beta ={30}^{\circ }$. The laser pulse has $I_0=7\times {10}^{11}\mathrm{W}/{\mathrm{cm}}^2$, and temporal widths $\tau =10\mathrm{ns}$ (red solid line), $5\mathrm{ns}$ (blue dashed line), $1\mathrm{ns}$ (orange dotted line), and $0.5\mathrm{ns}$ (green dot-dashed line).