Molecular rotational dynamics in nonadiabatically switching homogeneous electric fields

We investigate the rotational dynamics of heteronuclear diatomic molecules possessing a ${{}^1\Sigma }^{+}$ electronic ground state exposed to a strong external time-dependent homogeneous electric field. An exponential switching on and off is employed for the electric field. We analyze the orientation and hybridization of the angular motion, together with the population of pendular and rotational states in the constant-field and field-free regimes, as the switching times are modified. Exact results are compared with those of an $N$-mode approach to the rotational dynamics derived within the effective rotor approximation. It is demonstrated that robust predictions are possible with respect to the number of pendular states and partial waves involved in the constant and postpulse regimes, respectively. The final wave packet shows a wide variety of localization and orientation phenomena arranged in characteristic patterns, which alternate between two angular hemispheres and are periodic in time.

Figure 1

Electric field profile $\mathcal{F}\left(t\right)$ as a function of time for $\Delta t_{\text{on},i}=\Delta t_{\text{off},\text{on}}=\Delta t_{f,\text{off}}=T_r$, and maximal field strength $F={10}^{-4}\text{a}\text{.u}\text{.}$

Figure 2

(Color online) Angular probability density $\text{sin}\theta \rho \left(\theta ,t\right)$ for $t\ge t_f$ for systems with rotational dynamics dominated by (a) only the ground state, corresponding to adiabatic switching, (b) the two lowest levels, (c) the first three states, and (d) the first, second, and fourth rotational levels; see text.

Figure 3

Electronic potential energy curve (PEC) and electric dipole moment function (EDMF) of the electronic ground state of the LiCs molecule. Both quantities are given in atomic units.

Figure 4

The coefficients ${\left|c_0\right|}^2$ (dotted line), ${\left|c_1\right|}^2$ (dashed line), and ${\left|c_2\right|}^2$ (solid line) in the final field-free regime, as a function of the duration of the switching times $\Delta t_{\text{on},i}=\Delta t_{f,\text{off}}$ and for maximal field strength $F={10}^{-4}\text{a}\text{.u}\text{.}$

Figure 5

Number of partial waves contributing to the postpulse rotational dynamics as a function of the switching times $\Delta t_{\text{on},i}∕T_r=\Delta t_{f,\text{off}}∕T_r$, for several maximal field strengths $F={10}^{-4}$ (a), $5\times {10}^{-5}$ (b), and ${10}^{-5}$ (c) a.u. The full lines correspond to logarithmic fits to the numerical results; see text for details.

Figure 6

(Color online) Angular probability density $\text{sin}\theta \rho \left(\theta ,t\right)$ in the final field-free regime, after an evolution determined by switching times $\Delta t_{\text{on},i}=\Delta t_{f,\text{off}}=186.75\text{ps}$ and a maximal field strength $F={10}^{-4}\text{a}\text{.u}\text{.}$

Figure 7

Expectation value $⟨\text{cos}\theta ⟩$ during the field-free regime for switching times $\Delta t_{\text{on},i}=\Delta t_{f,\text{off}}=186.75$ (solid line), 167 (dashed line), and 44.5 ps (dash-dotted line), for a maximal field strength $F={10}^{-4}\text{a}\text{.u}\text{.}$

Figure 8

(Color online) Same as Fig. 6 but for the switching times $\Delta t_{\text{on},i}=\Delta t_{f,\text{off}}=167\text{ps}$.

Figure 9

(Color online) Same as Fig. 6 but for the switching times $\Delta t_{\text{on},i}=\Delta t_{f,\text{off}}=44.5\text{ps}$.

Figure 10

Coefficients ${\left|d_0\right|}^2$ (solid line), ${\left|d_1\right|}^2$ (dashed line), ${\left|d_2\right|}^2$ (dash-dotted line), and ${\left|d_3\right|}^2$ (dotted line) in the constant-field regime, as a function of the duration of the switching on time $\Delta t_{\text{on},i}$ and for $F={10}^{-4}\text{a}\text{.u}\text{.}$

Figure 11

Number of pendular states contributing to the rotational dynamics during the constant-field regime as a function of the switching-on time $\Delta t_{\text{on},i}∕T_r$, for several maximal field strengths $F={10}^{-4}$ (a), $5\times {10}^{-5}$ (b), and ${10}^{-5}$ (c) a.u. The full lines correspond to exponential fits to the numerical results; see text for details.

Figure 12

Expectation value $⟨{\mathbf{J}}^2⟩$ during the constant-field regime for a switching on time $\Delta t_{\text{on},i}=T_r$ and maximal field strength $F={10}^{-4}\text{a}\text{.u}\text{.}$