Electron-rotation coupling in UV photodissociation of aligned diatomics

We investigate the effect of electron-rotation coupling ($\mathbf{R}-\mathrm{\Omega }$ coupling) on fs UV photodissociation dynamics of aligned diatomic molecules. We consider the showcase of ground-state $\mathrm{Mg}{\mathrm{H}}^{+}$ (${}^1{\mathrm{\Sigma }}^{+}$) pumped by an fs IR pulse, which initiates rotational dynamics leading to field-free molecular alignment. A time-delayed fs UV pulse probes the degree of alignment of the rotational wave packet in the framework of photodissociation spectroscopy. The molecular alignment correlates directly with the angular distribution of the photofragments in the dissociative ${}^1\mathrm{\Pi }$ state, as it is shown in our simulations comparing the cases when the $\mathbf{R}-\mathrm{\Omega }$ coupling is included and ignored. We show how the angular distribution of the photofragment is strongly affected by the $\mathbf{R}-\mathrm{\Omega }$ coupling at various delay times with specific molecular alignment. It was shown that increases of the fs UV pulse intensity and the degree of alignment enhance the effect of $\mathbf{R}-\mathrm{\Omega }$ coupling on the angular distribution of the photofragments. On the contrary, an increase of the initial temperature tends to reduce the effect of $\mathbf{R}-\mathrm{\Omega }$ coupling, which is explained by the fact that such an effect turns smaller as the increasing of magnetic state $|{\mathrm{M}}_0|$ for each initial rotational state ${\mathrm{J}}_0$; furthermore, higher excited rotational state ${\mathrm{J}}_0$ contains more magnetic states ${\mathrm{M}}_0$, and the results have been averaged over all degenerated ${\mathrm{M}}_0$ states.

Figure 1

(a) Illustration of the dissociative IR-pump–UV-probe scheme for diatomics; (b) PECs of $\mathrm{Mg}{\mathrm{H}}^{+}$ for ${}^1{\mathrm{\Sigma }}^{+}$ and ${}^1\mathrm{\Pi }$ electronic states; (c) the PDM, and TDMs for the states involved (data are reproduced from Ref. [41]). The parallel ${\alpha }_{\parallel }$ and perpendicular ${\alpha }_{\perp }$ components of the dipole polarizability of the ground state (data are reproduced from Ref. [42]). The IR-pump pulse (${\omega }_1=$ 1.24 eV) triggers ground-state ${}^1{\mathrm{\Sigma }}^{+}$ alignment dynamics which are resonantly probed by time-delayed UV pulses (${\omega }_2=$ 6.56 eV) in the framework of the photodissociation spectroscopy of ${}^1\mathrm{\Pi }$ state.

Figure 2

(a) Degree of molecular alignment ${\langle {cos}^2\beta \rangle }_{\mathrm{\Sigma }}\left(t\right)$ in the electronic ground-state ${}^1{\mathrm{\Sigma }}^{+}$ induced by the IR-pump pulse of intensity ${10}^{13}\mathrm{W}/{\mathrm{cm}}^2$, and pump pulse is centered at $t_1$ = 0 fs; ${\mathrm{t}}_{\mathrm{P}1}$, ${\mathrm{t}}_{\mathrm{P}2}$, and ${\mathrm{t}}_{\mathrm{P}3}$ are the moments with maximal degrees of alignment; ${\mathrm{t}}_{\mathrm{V}1}$, ${\mathrm{t}}_{\mathrm{V}2}$, and ${\mathrm{t}}_{\mathrm{V}3}$ are the moments of alignment reach minimum value; and ${\mathrm{t}}_{\mathrm{M}1}$, ${\mathrm{t}}_{\mathrm{M}2}$, ${\mathrm{t}}_{\mathrm{M}3}$, ${\mathrm{t}}_{\mathrm{M}4}$, ${\mathrm{t}}_{\mathrm{M}5}$, and ${\mathrm{t}}_{\mathrm{M}6}$ are the moments of alignment equals to 1/3 (“isotropic” cases of ${\langle {cos}^2\beta \rangle }_{\mathrm{\Sigma }}\left(t\right)=1/3$). (b)–(m) Density of rotational wave packet at corresponding time (black lines), and density of rotational wave packet before the pump pulse (blue lines).

Figure 3

ADP in the dissociative state ${}^1\mathrm{\Pi }$ for the probe pulse centered at the moments correspondent to the minimum values ${\mathrm{t}}_{\mathrm{V}1}$, ${\mathrm{t}}_{\mathrm{V}2}$, and ${\mathrm{t}}_{\mathrm{V}3}$ and maximum values ${\mathrm{t}}_{\mathrm{P}1}$, ${\mathrm{t}}_{\mathrm{P}2}$, and ${\mathrm{t}}_{\mathrm{P}3}$ of molecular alignment. The probe pulse intensities are ${10}^{11}\mathrm{W}/{\mathrm{cm}}^2$(black lines), ${10}^{12}\mathrm{W}/{\mathrm{cm}}^2$(blue lines), and ${10}^{13}\mathrm{W}/{\mathrm{cm}}^2$(red lines). Simulations compare theory with and without $\mathbf{R}-\mathrm{\Omega }$ coupling, shown by solid lines and dashed lines, respectively.

Figure 4

ADP profiles in the dissociative state ${}^1\mathrm{\Pi }$ for the moments ${\mathrm{t}}_{\mathrm{M}1}$ – ${\mathrm{t}}_{\mathrm{M}6}$ with “isotropic” molecular alignment. All notations and pulse parameters are the same as in Fig. 4; gray lines show the ADP without pump pulse.

Figure 5

Degree of molecular alignment (a) at initial rotational temperature T = 10 K (black lines) and T = 0 K (gray lines); ${\mathrm{t}}_{\mathrm{V}}$, ${\mathrm{t}}_{\mathrm{M}}$, and ${\mathrm{t}}_{\mathrm{P}}$ moments correspond to the moments when alignment is minimum, 1/3 (“isotropic”), and maximum, respectively. IR-pump-pulse intensity is ${10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ and the pulse is centered at t = 0 fs. The density of rotational wave packet without the pump pulse (b) and at moments ${\mathrm{t}}_{\mathrm{V}}$, ${\mathrm{t}}_{\mathrm{M}}$, and ${\mathrm{t}}_{\mathrm{P}}$ (c)–(e), respectively. The dashed red, blue, and green lines correspond to the contribution from ${\mathrm{J}}_0$ = 0, ${\mathrm{J}}_0$ = 1, and ${\mathrm{J}}_0$ = 2 at T = 10 K, respectively [plots (a–e)].

Figure 6

ADP for the pump-free system (a) and various degrees of alignment: Minimal (b), “isotropic” (c), and maximal (d). Initial rotational temperature is T = 10 K (black lines) and T = 0 K (blue lines). The probe pulse intensity is ${10}^{13}\mathrm{W}/{\mathrm{cm}}^2$. Simulations compare theory with and without $\mathbf{R}-\mathrm{\Omega }$ coupling taken into account and are shown by solid and dashed lines, respectively.

Figure 7

(a) Degree of molecular alignment for initial rotational state ${\mathrm{J}}_0$ = 0, 1, and 2 by IR-pump pulse with intensity ${10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ (centered at $t$ = 0 fs). (b) ADP profiles in the dissociative state ${}^1\mathrm{\Pi }$ originated from three initial states ${\mathrm{J}}_0=0,1,2$ averaged over contributions from all magnetic ${\mathrm{M}}_0$ states. (c, d) Partial ADPs for each ${\mathrm{M}}_0$ states are shown for the case of ${\mathrm{J}}_0=1$ (c) and ${\mathrm{J}}_0=2$ (d). Our simulations in (b) and (c) compare the cases with (solid lines) and without (dashed lines) $\mathbf{R}-\mathrm{\Omega }$ coupling taken into account. The rotational dynamics are probed at moment $\mathrm{P}$ [see (a)] with UV pulse intensity ${10}^{13}\mathrm{W}/{\mathrm{cm}}^2$.