Phase-dependent field-free molecular alignment and orientation

We investigated the temporal behavior of alignment and orientation of LiH following a femtosecond laser pulse excitation comprising two fields at center frequencies $\omega$ and $2\omega$ (e.g., $E\left(t\right)=E\left[cos\left(\omega t\right)+cos(2\omega t+\Phi )\right]$) shifted by a phase $\Phi$. The effects of repopulations and rephasing of rotational states on the resulting alignment and orientation were evaluated. The population distribution of rotational states is only changed during the exciting pulse. Afterwards the established rotational state distribution is maintained in the absence of collisions. The phases of rotational states play the most crucial role in determining the time evolution of molecular alignment and orientation. Equal alignment and rotational populations are obtained when the phases are chosen $\Phi =0$ and $\Phi =\pi$. However, orientation is different due to the fact that in the case $\Phi =\pi$ the mutual phases of even rotation states are not changed but the phases of odd rotational states are shifted by $\pi$, comparing with that of $\Phi =0$. The effect of temperature on molecular orientation was also addressed. It was shown that an efficient field-free molecular orientation can be observed even at room temperature.

Figure 1

The adiabatic and diabatic potentials for the ground molecular state $1{}^1{\Sigma }^{+}$ and first excited state $2{}^1{\Sigma }^{+}$ of $\mathrm{LiH}$.

Figure 2

(a) Time evolution of molecular alignment $\langle {cos}^2\theta \rangle$, (b) Time evolution of molecular orientation $\langle cos\theta \rangle$ and (c) polar plot representation of the angular distribution at different times indicated in (a) and (b) for an ensemble of $\mathrm{LiH}$ molecules at the rotational temperature of 0 K by a femtosecond two-color laser pulse with the laser intensity of $5.0\times {10}^{13}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$, the pulse duration of $100\mathrm{fs}$, and $\Phi =0$. The linear polarizations of the femtosecond two-color laser pulse are aligned vertically in the plane of the figure.

Figure 3

(a) Degree of molecular orientation $〈cos\theta 〉$, (b) maximum degrees of molecular orientation as a function of the phase $\Phi$.

Figure 4

(a) Time evolution of molecular alignment $\langle {cos}^2\theta \rangle$, (b) time evolution of molecular orientation $\langle cos\theta \rangle$, and (c) polar plot representation of the angular distribution at different times indicated in (a) and (b) for an ensemble of $\mathrm{LiH}$ molecules at the rotational temperature of $0\mathrm{K}$ by a femtosecond two-color laser pulse, the parameter of which is the same as those used in Fig. 1 except that $\Phi =0.5\pi$. The linear polarizations of the femtosecond two-color laser pulse are aligned vertically in the plane of the figure.

Figure 5

(a) Time evolution of molecular alignment $\langle {cos}^2\theta \rangle$, (b) time evolution of molecular orientation $\langle cos\theta \rangle$, and (c) polar plot representation of the angular distribution at different times indicated in (a) and (b) for an ensemble of $\mathrm{LiH}$ molecules at the rotational temperature of $0\mathrm{K}$ by a femtosecond two-color laser pulse, the parameter of which is the same as those used in Fig. 1 except that $\Phi =\pi$. The linear polarizations of the femtosecond two-color laser pulse are aligned vertically in the plane of the figure.

Figure 6

The populations of rotational states after the interaction with the femtosecond two-color laser pulse. (a) $\Phi =0$, (b) $0.5\pi$, and (c) $\Phi =\pi$.

Figure 7

The phases $\phi$ of rotational states at time E in Fig. 1. (a) $\Phi =0$, (b) $\pi$, and (c) the phase difference $\Delta \phi$ of rotational states between $\Phi =0$ and $\pi$.

Figure 8

(a) Maximum degrees of molecular orientation and (b) time evolutions of thermally averaged orientation degree ${\langle cos\theta \rangle }_T\left(t\right)$ at different initially rotational temperatures $T$.