Quantum control of rovibrational dynamics and application to light-induced molecular chirality

Achiral molecules can be made temporarily chiral by excitation with electric fields, in the sense that an average over molecular orientations displays a net chiral signal [D. S. Tikhonov et al., Sci. Adv. 8, eade0311 (2022)]. Here, we go beyond the assumption of molecular orientations to remain fixed during the excitation process. Treating both rotations and vibrations quantum mechanically, we identify conditions for the creation of chiral vibrational wave packets, with net chiral signals, in ensembles of achiral molecules which are initially randomly oriented. Based on the analysis of symmetry and controllability, we derive excitation schemes for the creation of chiral wave packets using a combination of (a) microwave and IR pulses and (b) a static field and a sequence of IR pulses. These protocols leverage quantum rotational dynamics for pump-probe spectroscopy of chiral vibrational dynamics, extending the latter to regions of the electromagnetic spectrum other than the UV.

Figure 1

Creation of a vibrational wave packet in a planar molecule for the example of COFCl. (a) Vibrational eigenstates $|0\rangle$ and $|1\rangle$ of a normal mode $\chi$. (b) Vibrational wave packet as superposition of eigenstates $|0\rangle$ and $|1\rangle$. (c) Sketch of an in-plane normal mode $\chi =\zeta$ of COFCl. (d) Permanent dipole moment of COFCl with components ${\mu }_a^{\left(00\right)}$ and ${\mu }_b^{\left(00\right)}$ lying in the molecular plane. For the in-plane vibration, the transition dipole moment with components ${\mu }_a^{\left(01\right)}$ and ${\mu }_b^{\left(01\right)}$ lies also in the molecular plane. (e) Sketch of the out-of plane normal mode $\chi =\xi$ of COFCl. (f) Permanent dipole moment with components ${\mu }_a^{\left(00\right)}$ and ${\mu }_b^{\left(00\right)}$ lying in the molecular plane. The transition dipole moment for the out-of plane vibration with component ${\mu }_c^{\left(01\right)}$ perpendicular to the molecular plane.

Figure 2

Graph with asymmetric top eigenstates as nodes (horizontal lines) and transition matrix elements as edges (green, red, and blue arrows). (a) Interaction with a $z$-polarized IR pulse (green arrows). (b) Interaction with $x$-, $y$-, and $z$-polarized microwave pulses. Red arrows indicate transition matrix elements $\langle {\varphi }_j^{\prime }|{\mu }_a^{\left(00\right)}|{\varphi }_j\rangle$ and blue arrows correspond to transition matrix elements $\langle {\varphi }_j^{\prime }|{\mu }_b^{\left(00\right)}|{\varphi }_j\rangle$. (c) Graphical commutator between the transitions indicated by the green and red arrows, allowing the two coupled transitions indicated by the red arrows to decouple.

Figure 3

Excitation of a rotational wave packet in $\nu =0$ with two microwave pulses. The population dynamics is shown for the rotational states $|0_{00},0\rangle$ (blue solid line), $|1_{11},\pm 1\rangle$ (magenta solid line), and $|1_{10},0\rangle$ (red dashed line). The envelope of the two microwave pulses is indicated by the gray shapes; they are $x$ and $y$ polarized as indicated in the figure. Time is given in units of $t_0=\hslash /B\approx 30$ ps. The amplitude of the microwave fields is ${\mathcal{E}}_i=2\times {10}^4$ V/m for the three fields $i=1,2,3$.

Figure 4

Population dynamics after excitation with a long $z$-polarized IR pulse. Population is shown in the (a) ground and (b) excited vibrational states. The blue solid and red dashed lines correspond to the rotational states $|0_{00},0\rangle$ and $|1_{10},0\rangle$, respectively. (c) Envelope of elongation $\langle \widehat{\xi }\rangle \left(t\right)/{\xi }_0$ during the excitation with the IR pulse. [The oscillation of $\langle \widehat{\xi }\rangle \left(t\right)$ with $T=0.01t_0$ is too fast compared to the timescale of the plot to be resolved.] The maximal elongation $\pm {\langle \widehat{\xi }\rangle }_{\text{max}}/{\xi }_0$ is indicated by the horizontal dashed lines. In all panels, the envelope of the IR pulse is indicated by the gray shapes; the maximal amplitude is ${\mathcal{E}}_{\text{IR}}=5\times {10}^5$ V/m.

Figure 5

Population dynamics after excitation with a short $z$-polarized IR pulse for the (a) ground and (b) excited vibrational states. The blue solid and red dashed lines correspond to the rotational states $|0_{00},0\rangle$ and $|1_{10},0\rangle$, respectively, and the yellow dash-dotted and green dotted lines correspond to $|2_{11},0\rangle$ and $|2_{02},0\rangle$, respectively. (c) Elongation $\langle \widehat{\xi }\rangle \left(t\right)/{\xi }_0$ due to the excitation with the IR pulse. The solid, dashed, and dash-dotted lines correspond to $\varphi =\pi /2$, $-\pi /2$, and 0, respectively. The envelope of the IR pulse is indicated by the gray shapes; the maximal amplitude is ${\mathcal{E}}_{\text{IR}}=7.5\times {10}^7$ V/m.

Figure 6

Graph with rovibrational states $|J_{k_a,K_c},M\rangle |\nu \rangle$, $\nu =0,1$, as nodes and zeroth-order (solid lines) and first-order (dashed lines) transition matrix elements as edges. The red, green, and blue arrows correspond to transitions induced by control fields with $i=z$, ${\sigma }_{+}$, and ${\sigma }_{-}$, respectively. For convenience, the nodes are numbered from 1 to 20. (a) All nonvanishing transitions connecting node 1. (b) An additional set of nonvanishing transitions that is necessary to connect node 1 to all nodes greater than or equal to 11.

Figure 7

Population dynamics for excitation with a sequence of three IR pulses in the presence of a static electric field. Population is shown in the (a) ground and (b) excited vibrational states. The blue, red, and green lines correspond to the rotational states $|0_{00},0\rangle$, $|1_{10},\pm 1\rangle$, and $|1_{01},\pm 1\rangle$, respectively. (c) Envelope of the elongation $\langle \xi \rangle \left(t\right)/{\xi }_0$. The dashed lines indicate the maximal elongation $\langle \xi \rangle /{\xi }_0=\pm 1/2$. In all panels, the envelopes of the pulses are indicated by the gray shapes; the maximal amplitude is ${\mathcal{E}}_i=1.5\times {10}^5$, $6.5\times {10}^5$, and $5\times {10}^5$ V/m for $i=1$, 2, and 3, respectively. The polarization of the pulses is denoted by $x$, $y$, and $z$. Note that the population dynamics is shown in the field-free basis.

Figure 8

Transition matrix elements and populated states for the excitation process shown in Fig. 7. The transition matrix elements are shown for the excitation with the IR pulses (a) 1, (b) 2, and (c) 3 of Fig. 7. The solid arrows indicate transition matrix elements between field-free rotational states and dashed arrows correspond to transitions allowed only in the presence of a static electric field. The colors (green, blue, and red) indicate the type of transitions ($a$, $b$, and $c$ type). The gray circles show which states are populated at the end of the (a) first, (b) second, and (c) third pulses.