Coherent Control of Rotational Wave-Packet Dynamics via Fractional Revivals

We show (i) how the evolution of a wave packet created from an initial thermal ensemble can be controlled by manipulating interferences during the wave packet’s fractional revivals and (ii) how the wave-packet evolution can be mapped onto the dynamics of a few-state system, where the number of states is determined by the amount of information one wants to track about the wave packet in the phase space. We illustrate our approach by (i) switching off and on field-free molecular axis alignment induced by a strong laser pulse and (ii) converting alignment into field-free orientation, starting with rotationally cold or hot systems.

Figure 1

(a) Evolution of an angular wave packet initially localized at $\theta =0$ and $\theta =\pi$. Absolute value of the wave function is shown by brightness with black being zero amplitude. (b) Angular distribution for initial wave packet $\Psi (t)$. (c) Time evolution of wave packet’s alignment. (d) Aligned (A) and antialigned (AA) regions on the rotor’s trajectory.

Figure 2

(a),(b) Evolution of the states $|0⟩$ and $|1⟩$ on the revival time scale. Wave function amplitude is shown by brightness and the phase is shown by shading (color—or hue in the HSL color system). (c),(d) Evolution of the wave function and of $⟨{cos}^2\theta ⟩$ for the alignment being switched off and on. Arrows indicate the moments when the laser pulses are applied.

Figure 3

(a),(b) Evolution of the states $|0^{\prime }⟩$ and $|1^{\prime }⟩$ in the control scenario discussed in the text. Brightness shows probability density. (c) Orientation of the state $|1^{\prime }⟩$ (dashed line), $|0^{\prime }⟩$ (thin line), and of their incoherent sum (thick line). Laser pulse is shown by the arrows.

Figure 4

(a) Alignment of ${\mathrm{O}}_{\mathrm{2}}$ molecules at 50 K with (thick line) and without (thin line) the control pulses. (b) Alignment (thin line) and orientation (thick line) of OCS molecules at 10 K with the control pulse.