Molecular alignment echoes probing collision-induced rotational-speed changes

We show that the decays with pressure of the rotational alignment echoes induced in ${\mathrm{N}}_2\mathrm{O}$-He gas mixtures by two ultrashort laser pulses with various delays show detailed information about collision-induced changes of the rotational speed of the molecules. Measurements and classical calculations consistently demonstrate that collisions reduce the echo amplitude all the more efficiently when the echo appears late. We quantitatively explain this behavior by the filamentation of the classical rotational phase space induced by the first pulse and the narrowing of the filaments with time. The above-mentioned variation of the echo decay then reflects the ability of collisions to change the molecular rotation speed by various amounts, enabling refined tests of models for the dissipation induced by intermolecular forces. We also demonstrate that the collision-induced changes of the rotational speed within the filaments are the classical equivalents of the nonsecular transfers among quantum coherences, thus evidencing the correspondence between the classical and quantum worlds.

Figure 1

Alignment factors for ${\mathrm{N}}_2\mathrm{O}$ diluted in He at various densities. (a) Computed values for ${\tau }_{12}=3.0\mathrm{ps}$. (b) Measured values for ${\tau }_{12}=3.1\mathrm{ps}$.

Figure 2

Density-normalized decay time constants ${\tau }_{\mathrm{E}}\left({\tau }_{12}\right)$ of the echoes for ${\mathrm{N}}_2\mathrm{O}$ diluted in He at 295 K obtained from measured (red open circles, from [22]), CMDS- (black open triangles) and rCMDS-computed (blue full circles) alignment factors for various densities and fixed delays. The insert shows the predicted values over a broader time interval.

Figure 3

Time-dependent CMDS predictions for collision-free ${\mathrm{N}}_2\mathrm{O}$ gas excited by laser pulses at $t=0$ and $t=3$ ps. Left: Probability density (from blue to red with increasing value) for the ${\mathrm{N}}_2\mathrm{O}$ molecules whose axis makes an angle $\theta =0^{{}^{\circ }}$ with the laser polarization to have an angular velocity ω. Right: Alignment factor.

Figure 4

CMDS results for collision-free ${\mathrm{N}}_2\mathrm{O}$ excited by a laser pulse centered at $t=0$. (a) Probability distribution (i.e., normalized number of molecules so that the integration over $\omega$ leads to a unit area) of angular velocities at different times for the molecules whose axis makes an angle of 0° with the laser polarization (the black line being the CMDS predicted Boltzmann distribution before the pulse). (b) Number of filaments ($n$, blue full circles, left $y$ axis) and mean distance between successive filaments ($\mathrm{\Delta }{\omega }_{\mathrm{p}}$, red triangles, right $y$ axis). (c) Mean full width at half maximum $\mathrm{\Delta }{\omega }_{\mathrm{FWHM}}$ of the filaments.

Figure 5

Decay time constants of molecules’ loss ${\tau }_{\mathrm{Loss}}$ (black line) obtained from CMDS (see text) and of the measured (red open circles with error bars) echo decays from Fig. 2 vs the average filament width (see text).