Results and Discussion

The in-plane principal axes of inertia and polarizability are shown in the ball-and-stick representation of indole in Figure 6.1 a. For both, two axes lie in the plane of the molecule with an angle of 2.75^◦ between them. Upon Coulomb explosion, several fragmentation channels were detected using a velocity map imaging spectrometer (VMI).

The resulting time-of-flight mass spectrum is depicted in Figure 6.1 b. Despite the low symmetry, several fragments showed anisotropic momentum distributions. To retrieve the degree of alignment we analysed the H⁺, C⁺⁺, and HNCH⁺ VMIs. The ion-momentum distributions for a delay time of t= 3.3 ps, corresponding to the highest observed degree of 3D alignment, are shown for two configurations of the alignment laser polarization , ie, with the major polarization axis parallel, 0^◦, and perpendicular, 90^◦, to the detector plane, shown in the upper and lower row ofFigure 6.1 c, respectively. A full tomographic 3D distribution was obtained from VMIs that were recorded by rotating the alignment laser polarization ellipse around the laboratory-fixed Y-axis from 0^◦ to 180^◦ in steps of 2^◦. Furthermore, ion-momentum distributions of H⁺ as a function of the delay time between the alignment laser and the probe laser, with some typical snapshots, are shown in Figure 6.1 d. t = 0 corresponds to the peak intensity of the alignment laser field, t= 3.3 ps to the strongest observed field-free alignment, andt= 7.33,13.34 ps correspond to later times where the alignment has already decreased due to dephasing of the field-free rotational wavepacket. Due to the larger count rates the H⁺ data was of a higher quality than for the other fragments. VMIs of other fragments displaying alignment are shown in the Supplementary Information.

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The delay-dependent measured 2D degree of alignment is shown for a variety of ion fragments in Figure 6.2. Assuming axial recoil, H⁺ fragments would have measurable momentum components only within theabplane of indole [252]. Hence, the H⁺ fragments are a measure of the planar alignment of indole in the laboratory frame. The slow rise of the alignment pulse aligned the plane of the indole molecules in a quasi-adiabatic fashion [110, 227] to a maximum 2D degree of alignment of hcos²θ2Di^exp_H+ = 0.74.

–10 –5 0 5 10 15 20

Delay (ps)

0.0 0.2 0.4 0.6 0.8 1.0

Intensity(1012 W/cm2 ) 0.6

0.7 0.8 0.9

cos2 θ2Dexp X+

C⁺ C⁺⁺

H⁺ NHCH⁺

0 100 200 300 400 500 600

Delay (ps) 0.60

0.65 0.70

cos2 θ2DH+ H⁺exp. H⁺sim.

0 100 200 300 400 500 600

Delay (ps) 0.5

0.7 0.9

cos2 δ

cos²θXxI= 0.83 cos²θY yI= 0.85 cos²θZzI= 0.88

a

b

c

Figure 6.2.: aTemporal evolution of the alignment of indole. The solid lines show the measured 2D degree of alignment

cos²θ2D

exp

X⁺ for different fragments X⁺ and the dashed lines indicate values of the 2D degree of alignment obtained without alignment laser. Statistical error bars, representing the standard error, are shown for selected delays. The grey area shows the intensity profile of the alignment laser pulse. b The alignment revival structure of H⁺ fragments for longer times is shown in red. The dotted green line shows the fitted simulation for the H⁺ fragment. c Simulated 3D degree of alignment, characterized through the single-scalar metric cos²δ

, see text/SI for details. Note the peak after truncation reaching cos²δ

= 0.89 at t= 3.3 ps.

6. Creating and Characterizing Strong Three-Dimensional Field-Free Alignment of Complex Molecules

Following the kick at the end of the alignment pulse, the degree of alignment increased slightly to hcos²θ_2Di^exp_H+ = 0.75 before monotonically decreasing over ∼10 ps towards hcos²θ_2Di^exp_H+ = 0.62, slightly higher than the value hcos²θ_2Di^exp_H+ = 0.6 observed without alignment laser, i. e., due to the geometric alignment from an isotropic distribution. At a delay of 3.3 ps the intensity of the alignment pulse decreased to the noise level, below 1 % of its maximum, and the “field-free” region begins. At this delay the degree of alignment was hcos²θ_2Di^exp_H+ = 0.75, which is even larger than the alignment measured just before the kick, confirming that the planar alignment in the field-free region is even better than for an adiabatic alignment pulse [103].

All other fragments showed similar dynamics to the H⁺ fragment, with the measured degrees of alignment larger for the C⁺⁺fragment and lower for the HNCH⁺ fragment. The difference in the measured alignment between the fragments was attributed to non-axial recoil or to the geometry of Coulomb explosion fragmentation, i. e., the velocity vectors of the fragments in the molecular frame.

The angular distribution of the ionic fragments within the indole plane enabled full determination of the 3D alignment. By rotating the polarization ellipse of the alignment laser around the laser propagation axis, at a fixed delay, the laboratory axes to which the a andb axes of indole align, are commensurately rotated. In the laboratory frame, the transverse momenta of ionic fragments recoiling within the plane of indole will depend on the rotation angle. By counting only those fragments impinging at the centre of the detector, within a small radius r, the distribution of fragments within the plane can be determined [151]. In the 3D reconstruction of the tomography of H⁺ fragments at t = 3.3 ps, shown in Figure 6.5 in the Supplementary Information, no fragments are observed at low momenta. Thus, the measured ion signal at the centre of the VMI can be related to the in-plane fragments recoiling along the detector normal. Angular scans of this “masked VMI” measurements are shown in Figure 6.3 for H⁺ and C⁺⁺

fragments, integrated over r = 20 pixel, as a function of the angle α between the Z laboratory axis and the laser’s major polarization axis. For both fragments, there is a clear angle-dependent structure on top of a significant isotropic background. C⁺⁺ ions show two smaller peaks at α ≈ ±30^◦ and a much stronger peak at α ≈ 88^◦. The H⁺ signal shows a peak atα ≈88^◦, similar to C⁺⁺, and a smaller peak at α≈0^◦. At 90^◦ the alignment laser’s major polarization axis pointed towards the detector. Since the radius of r = 20 pixel on the detector was chosen to be significantly smaller than any measured feature in the angular distribution, the width of the peaks at 88^◦ are related to the non-axial in-plane recoil of the fragments. Considering only the major peaks, centered around 88^◦ in Figure 6.3, we observed in-plane degrees of alignment of hcos²αi^exp_H+ = 0.82 and hcos²αi^exp_C++ = 0.88.

Experimentally, all ions with a given mass to charge ratio potentially contributed to the measured 2D momentum distributions, regardless of their origin and velocity vectors within the neutral indole molecule as it is multiply ionized and undergoes Coulomb explosion. There are seven sites from which the H⁺ fragments originate and eight sites from which the C⁺⁺ fragments originate. The positions and the labelling of the hydrogen atoms in indole is shown in Figure 6.1 a. Each site will result in a different momentum

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–30 0 30 60 90 120 α (degree)

0.75 0.80 0.85 0.90 0.95 1.00

Relativeionrate

C⁺⁺

H⁺

C⁺⁺ simulation H⁺ simulation

Figure 6.3.:Measured masked-VMI ion count rates of H⁺and C⁺⁺fragments as the major axis of the alignment laser’s polarization ellipse is rotated; see text for details. Solid lines indicate measured values, the dashed lines are simulations based on fitted atomic-ion contributions, see text for details.

and recoil axis of the ionic fragment with the total measured experimental distribution being the sum of all of these.

In order to quantify the 3D degree of alignment, the rotational dynamics of indole was simulated using RichMol [158], yielding time-dependent laboratory-frame 3D angular probability distributions of the molecule for all delay times. Rotational-probability-density distributions were computed for all seven hydrogen atoms and the eight carbon atoms of indole individually. Coulomb explosion of indole was modelled by assuming axial recoil of the hydrogen ions along the C-H and N-H bond vectors, whereas for carbon the vectors connecting the center of mass with each carbon atom were chosen as recoil axes. For direct comparison between experiments and simulations, 2D projections of the rotational probability densities onto the labory Y Z plane were carried out using a Monte-Carlo sampling routine. From these computed 2D momentum distributions, the time-evolution ofhcos²θ_2Di^sim_H+ was retrieved for all hydrogen atoms, choosing the same radial cuts that were used to retrieve the experimental hcos²θ_2Di^exp_H+. For the comparison with the angle-dependent masked VMI measurements for H⁺ and C⁺⁺, the rotational probability density att= 3.3 ps was rotated in steps of 1^◦ around the laboratory Y-axis.

At each angle, 2D projected momentum distributions were computed for all hydrogen and carbon atoms, and the signal withinr = 20 pixel of the centre was integrated.

Finally, for comparison with the measurements, a least-squares fitting procedure was employed. The contribution of individual hydrogen ions were determined by si-multaneously fitting the alignment revival trace and the angle-dependent masked VMI measurements. An eighth fit parameter was included to take account of non-axial recoil

6. Creating and Characterizing Strong Three-Dimensional Field-Free Alignment of Complex Molecules

within the indole plane. The parameter was the width of a single Gaussian with which the angular distributions were convoluted. Without this additional parameter, the fitted masked VMI yields did not satisfactorily reproduce the data. Non-axial recoil might arise from many body fragmentation and also a time-dependent charge distribution on the remains of the parent ion during the Coulomb explosion process, driven by the circularly polarized Coulomb explosion pulse [253,254]. Both of these processes result in spatially extended and time-dependent charge distributions within the indole plane from which the fragments are repelled. Intensity-dependent measurements of ionic fragments, when varying the energy of the Coulomb explosion laser (not shown), suggest H⁺ ions were only produced when 4 electrons were removed from indole. On the contrary, for the fit of the C⁺⁺ angular distributions, the axial recoil approximation yielded excellent agreement between the experiment and the simulation, and no convolution to model non-axial recoil was required. The resulting fit of the alignment revival trace of H⁺ is shown in Figure 6.2 and the resulting fits of the angular distributions of H⁺ and C⁺⁺ are shown in Figure 6.3.

The computed weights for the hydrogen and carbon atoms and more details about the simulations are given in the Supplementary Information.

The excellent agreement between the experiment and our simulations provides the required confidence to extract the ’real’ 3D degree of alignment of the polarizability frame of indole with α_zI > α_yI > α_xI with respect to the laboratory-fixed frame XY Z from our simulations. The planar alignment was quantified to be ∼0.84 at t = 3.3 ps, described by the two expectation valueshcos²θ_{Y yI}i= 0.85 andhcos²θ_XxIi= 0.83. These values are higher than the measured degree of alignment, which is due to non-axial recoil of the H⁺ fragments and different recoil axes that contribute to the measured ion-momentum distributions. A computed in-plane alignment of hcos²θ_ZzIi= 0.88 was obtained, in agreement with the experimentally determinedhcos²αi^exp_C++ = 0.88 from the angular distribution of C⁺⁺ in Figure 6.3. The simulated time-dependent alignment revivals, characterizing the 3D degree of alignment, can be found in the Supplementary Information. A single scalar metric [137], describing the overall degree of 3D alignment and defined by cos²δ= ¹₄(1 + cos²θ_ZzI + cos²θ_{Y yI} + cos²θ_XxI), is shown inFigure 6.2 c.

A maximum field-free alignment of hcos²δi= 0.89 was achieved.

The degree of field-free alignment demonstrated in our experiment is comparable to or even larger than the degree of alignment achieved in typical experiments employing adiabatic alignment for asymmetric top molecules [68, 88]. The achieved degree of alignment is, however, limited by the number of initially populated states in the molecular beam [62, 68] and the finite truncation time of ∼3 ps of the alignment laser field [247].

Improving the fall-off time of the field and the creation of colder molecular beams with a narrower initial state distribution could lead to an even higher degree of field-free alignment.

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