frank filsinger et al- quantum-state selection, alignment, and orientation of large molecules using...

8/3/2019 Frank Filsinger et al- Quantum-state selection, alignment, and orientation of large molecules using static electric and laser fields

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3-aminophenol. 7 However, if focusing is not necessary, spa-tial dispersion of quantum states can still be achieved usingstatic electric elds in a SternGerlach-type deector. Thismolecular beam deection has been used extensively as a

tool to determine dipole moments and p olarizabilities of mo-lecular systems ra nging from diatomics 14 over clusters 34 tolarge biomolecules. 35

Recently, we d emonstrated the quantum-state selectionof large molecules 36 following the original proposal of Stern. 15 Here, the details of the electrostatic deection arepresented. It is shown how the rotational temperature of coldsupersonic jets can be determined with high precision fromdeection measurements and that indeed a small subset of quantum states can be addressed in deected samples of large molecules. In particular, the ground state has the largestStark shift and molecules residing in this state are deectedthe most. Our goal is to isolate and use rotational-ground-state molecules, or at least samples of molecules in the fewlowest-lying states as targets for various experiments. Sincethe deection does not change the initial state distributionbut merely disperses it, it is crucial that the population of ground-state molecules in the molecular beam is initially aslarge as possible. Therefore, the rotational temperature of themolecular beam is made as l ow as possible using a high-pressure supersonic expansion. 37 It is shown how the result-ing state-selected molecules can be used to improve one-dimensional 1D laser-induced alignment 4,38 and mixed-eld orientation. 36,39,40 Here, alignment refers to connementof a molecule-xed axis typically, the largest polarizabilityaxis along a laboratory-xed axis and orientation refers tothe molecular dipole moments pointing in a particular direc-tion. Alignment and orientation occur in the adiabatic limitwhere the laser eld, used to align the molecules, is turnedon and off slowl y compared to the inherent rotational periodsof the molecule. 41,42 The state selection leads to strong en-hancement in the degree of orientation and alignment of io-dobenzene IB molecules compared to that achieved whenno deection is used.

II. EXPERIMENTAL

A schematic of the experimental setup is shown in Fig.1. The molecular beam machine consists of three differen-

tially pumped vacuum chambers; The source chamber hous-ing a pulsed valve pumped by a 2000 l/s turbomolecularpump , the deector chamber pumped by a 500 l/s turbomo-lecular pump , and the detection chamber housing the ion/ electron spectrometer pumped by a 500 l/s turbomolecularpump . About 3 mbar of IB Sigma Aldrich, 98% purity orbenzonitrile BN, Sigma Aldrich, 98% purity is seeded in aninert carrier gas and expanded through a pulsed valve into

vacuum. In order to obtain optimal cooling of the mole cularbeam, a miniaturized, high pressure EvenLavie valve 37 isused operating at a backing pressure of 90 bar of He or20 bar of Ne, limited by the onset of cluster formation. Whilerotational temperatures down to 0.4 K have been achievedunder similar conditions, 43 the typical rotational temperaturein our experiments is 1 K. Two 1-mm-diameter skimmersplaced 15 cm separating the source and the deector cham-ber and 38 cm downstream from the nozzle collimate themolecular beam before it enters a 15-cm-long electrostaticdeector. A cut through the electrodes of the deector isshown in the inset of Fig. 1 together with the electric eldcreated. A trough with an inner radius of curvature of 3.2 mmat ground potential and a rod w ith a radius of 3.0 mm at highvoltage create a two-wire eld. 44 The vertical gap across themolecular beam axis is 1.4 mm, while the smallest distancebetween the electrodes is 0.9 mm. The two-wire eld geom-etry is ideally suited for molecular beam deection. The gra-dient of the electric eld along the vertical direction is largeand nearly constant over a large area explored by the mo-lecular beam, while the electric eld is very homogeneousalong the horizontal direction. Thus, a polar molecule expe-riences a nearly constant force in the vertical direction inde-pendent of its position within the deector, while the force inthe horizontal direction i.e., broadening of the beam in thehorizontal direction is minimized. In our setup, the deectoris mounted such that molecules in high-eld-seeking low-eld-seeking quantum states are deected upwards down-wards .

After passing through the deector, the molecular beamenters the differentially pumped detection chamber via athird skimmer of 1.5 mm diameter. In the detection area, themolecular beam is crossed by one or two laser beams that arefocused by a spherical lens with a focal length of f =300 mm. The lens is mounted on a vertical translationstage so that the height of the laser foci can be adjusted withhigh precision. In the rst part of the experiment, where thebeam deection of IB and BN is characterized, only one

laser, the probe laser, is used. This Ti:sapphire laser 25 fsfull width at half maximum FWHM pulses, 800 nm, beamwaist 0 =21 m is used to determine the relative densityin the molecular beam via photoionization. In the second partof the experiment, an additional laser pulse is included tostudy laser-induced alignment and orientation of IB. Forthese experiments, 10 ns FWHM long pulses from aneodymium-doped yttrium aluminum garnet Nd:YAG laser1064 nm, 0 =36 m are overlapped in time and space

with the probe laser pulses. While the YAG laser inducesadiabatic alignment and orientation, here the femtosecondlaser is used to determine the spatial orientation of the targetmolecules via Coulomb explosion. Ionic fragments produced

valve

deector

MCP

skimmers

probe

beam

YAG beam

CCD camera

phosphorscreen

x (mm)

12

0

0 1-2 -1

10 kV

ground-1

y (mm)

60

80

100

120E (kV/cm)

0. 1 5m

0. 4 1m

0. 2 2m

velocity map imagingelectrodes

FIG. 1. Scheme of the experimental setup. In the inset, a cut through thedeector is shown and a contour-plot of the electric eld strength is given.Details of the VMI spectrometer are shown in Fig. 7. See text for details.

064309-2 Filsinger et al. J. Chem. Phys. 131 , 064309 2009

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in the Coulomb explosion are accelerated in a velocity fo-cusing geometry toward the detector. The detector can begated with a time resolution of 90 ns, which allows formass selective detection of individual fragments. A micro-

channel plate detector backed by a phosphor screen is em-ployed to detect the position of mass-selected ions. In par-ticular, I + fragment ions, formed in the Coulomb explosionof IB, are particularly useful experimental observables sincethey recoil along the CI symmetry axis of the molecule.Thus, two-dimensional 2D ion images of I + recorded with acharge coupled device camera provide direct informationabout the instantaneous molecular orientation of the CIbond axis with respect to the laboratory frame and are, there-fore, the basic observables in these experiments. All experi-ments are conducted at 20 Hz, limited by the repetition rateof the YAG laser.

III. RESULTS AND DISCUSSION

In the rst experiments shown in Sec. III A, a detailedanalysis of electrostatic beam deection is presented. It isshown that electrostatic deection of cold molecular beamscan be used to determine the rotational temperature of a su-personic jet. Furthermore, the degree of quantum-state selec-tivity that can be achieved with our setup is investigated. Asan application it is demonstrated how this quantum-stateselectivity of the deection process can be exploited to ob-tain an unprecedented degree of laser-induced alignmentSec. III B and orientation Sec. III C of IB molecules.

A. Electrostatic deection of cold molecular beams

In the rst experiment, the deection of benzonitrilemolecules BN,C 7H5N seeded in 90 bar of He is investi-gated. BN is an ideal candidate for electrostatic beam deec-tion due to its large permanent dipole momen t of 4.515 D.From the precisely known molecular constants 45 the energyof a given rotational quantum state can be calculated as afunction of the electric eld strength. The exact procedure isdetailed in the Appendix A 1. Figure 2 shows the Stark en-ergies for the lowest rotational states of BN. Due to the smallrotational constants and the resulting high density of rota-tional states, a large number of states is populated even under

the cold conditions in a supersonic expansion. At a rotationaltemperature of 1 K, the typical temperature in our experi-ments vide infra , 66 rotational quantum states with 419 M -components have a population larger than 1% relative tothe ground state. At the electric eld strengths present in thedeector, indicated by the shaded area in Fig. 2, all low-lyingquantum states are high-eld seeking. This is due to mixingof closely spaced states of the same symmetry and is typicalfor large asymmetric top molecules. The Stark shift and thusthe force a molecule experiences in an inhomogeneous elec-tric eld depend on the rotational quantum state. Moleculesin the ground state have the largest Stark shift and are, there-fore, deected the most. In general, the Stark shift decreaseswith increasing J quantum number. Thus, the lower the rota-tional temperature of the molecular beam, the more the beam

is deected.Figure 3 shows vertical intensity proles of BN for vari-ous high voltages applied to the deector. Vertical intensityproles are obtained by recording the BN + signal fromphotoionization by the femtosecond laser as a function of thevertical position of the laser focus. If no high voltage isapplied to the deector, the molecular beam extends overabout 2 mm. In this case, the size of the molecular beamin the detection region is determined by the mechanical ap-erture of the experimental setup, i.e., by the dimensions of the deector and the last skimmer before the detection re-gion. As the high voltage is turned on, the molecular beamprole broadens and shifts upwards. At a voltage of 10 kV, a

large fraction of the molecules is deected out of the origi-nal, undeected beam prole. A small fraction of the mol-ecules, however, is almost unaffected by the deector.

In order to understand these experimental ndings,Monte Carlo simulations are employed, which are describedin detail in the Appendix A 2. In brief, trajectory calculationsare performed for molecular packets of individual rotationalquantum states. These calculations yield single-quantum-state deection proles. Then, the single-state proles areaveraged according to the populations of the respective statesin the original molecular beam i.e., at the entrance of thedeector . From these simulations, it is obvious that the mol-ecules in the original beam are not rotationally thermalized,

A = 5655 MHz

B = 1547 MHz

C = 1214 MHz

= 4.515 D

FIG. 2. Energy as a function of the electric eld strength for the lowestrotational quantum states of benzonitrile. The shaded area indicates the ac-tual electric eld strength inside the deector. In the inset, the molecularstructure is shown together with the relevant molecular constants Ref. 45 .

C

H

C N

s i g n a l

( a . u . )

6

5

+

FIG. 3. The vertical spatial prole of the molecular beam for differentdeection voltages applied, measured by recording the BN + signal see text .The experimental data are shown as symbols together with the correspond-ing simulated proles lines .

064309-3 Quantum-state selection and orientation J. Chem. Phys. 131 , 064309 2009



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from the simulated deection proles. Table I provides anoverview of the most abundant quantum states present indifferent regions of the beam proles for IB at a rotationaltemperature of 1.05 K. For comparison, also the populationof each rotational quantum state in the undeected beam forthis rotational temperature is given. At the position of the

laser focus for the orientation experiments in Ne columnfour in Table I , the population of the lowest quantum statesis signicantly enhanced in the deected beam compared tothe undeected beam. The fraction of ground-state moleculesis enhanced by a factor of 5, for instance. About 97% of thepopulation resides in the quantum states listed in Table I with

TABLE I. Relative population of individual quantum states in the deected part of the molecular beam prole for T rot =1.05 K. Left: IB in He at 1% of peak intensity of undeected beam. Center: IB in Ne at 1% of peak intensity of undeected beam. Right: IB in Ne at 9% of peak intensity of undeected beam hereorientation images were taken . P M denotes relative population of individual M -sublevels in percent, P M % is the sum over all M -sublevels and P J K aK c

free is

the relative population of a given rotational quantum state in a free jet.

IB in He at 0 . 01 I peak IB in Ne at 0 . 01 I peak IB in Ne at 0 . 09 I peak undeected beamJ K a K c M P M (%) P M (%) P M (%) P M (%) P M (%) P M (%) P

freeJ K a K c

(%)

000 0 17.51 17.51 26.06 26.06 6.24 6.24 1.15

1010

1

0 . 02

7 . 697.71

3 . 90

9 . 7013.61 3.24

1110

1

1 . 92

15 . 6617.58

23 . 8423.84

2 . 37

5 . 437.79 1.55

1100

1

1 . 81

0 . 021.82

2 . 41

3 . 866.26 1.55

2021

2

0 . 57

7 . 177.74 4.75

212

0

1

2 3 . 22

3.22

0 . 23

3 . 51

4 . 16

7.90 2.28

303

0

1

2

3

0 . 01

6 . 17

23 . 5529.73

36 . 6136.61

2 . 93

7 . 17

8 . 01

0 . 89

19.00 5.47

3132

3

0 . 20

2 . 792.98 2.65

4040

3

0 . 01

3.98

3.992 . 12

5.56

7.68 5.43

413

1

2

3

2 . 17

8 . 35

10.52

13 . 49

13.49

2 . 12

2 . 60

2 . 87

7.58 2.54

505

1

2

4

0 . 19

3 . 24

3 . 30

6.73 4.80

5140

4 1 . 661.66

0 . 08

1 . 831.90 2.22

5233

4

0 . 06

5 . 61 5.67 1.92

6162

3

0 . 19

1 . 071.26 1.91

99.41 100.00 96.67 41.46




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the J K aK c =3 03 state being most abundant. Moving the laserfocus even closer toward the upper cutoff in the beam proleshould reduce the number of quantum states that are probedeven further. If a reduction in the beam intensity by twoorders of magnitude compared to the undeected beam canbe afforded, only four quantum states are predicted to beprobed with 37% of the molecules being in the J K aK c =3 03state. At rst glance, it is surprising that this state and not theabsolute ground state, which is expected to have the largest

eff , is populated most in the deected beam. In order tounderstand this, the Stark curves for the most deected quan-tum states of IB are shown in Fig. 6 a , together with theireffective dipole moments Fig. 6 b . Below the relevantelectric eld strengths, both the J K aK c M =3 032 and the J K aK c M =4 133 M -sublevels have avoided crossings withclose-by states of the same symmetry dashed lines in Fig.6 a . These avoided crossings lead to large local effectivedipo le moments that are comparable to the ground state

eff .79 Thus molecules in these quantum states are deected

as much as ground-state molecules. Furthermore, states with M 0 are doubly degenerate, whereas the ground state with M =0 is only singly degenerate. Therefore, the population of molecules in the J K aK c M =3 032 in the undeected beam isalready larger than the population in the ground state. 80 FromTable I, it is clear that it will be difcult to isolate the rota-tional ground state of IB in our setup. Nevertheless, giventhat the fraction of ground-state molecules could be in-creased from 1% in the undeected to 26% in the deectedbeam, dramatic effects are to be expected for a variety of further experiments.

We point out that we are assuming adiabatic following of

potential energy curves in all simulations. Nonadiabatic tran-sitions are unlikely in the strong elds inside the deector,since the number of avoided crossings and their energy gapsgenerally increase with electric eld strength. Moreover, theprobability for nonadiabatic following depends on the rate of change of the eld strength, which is only due to the slowtranslational motion of the molecules. However, nonadia-batic transitions have been observed in different Stark-decelerator beamlines at real 49 and avoided crossings 50 forsmall electric elds. Similarly, when the deected moleculesin the experiments reported here enter a eld-free region,scrambling of population over the various M components of their rotational state will occur.

For small molecules, like OCS or ClCN, the preparationof an ensemble of molecules, all in a single quantum statewill be feasible with the present setup. For these systems, thenumber of quantum states that are populated in a supersonic jet is signicantly smaller compared to large asymmetric topmolecules like IB or BN. The spacing between neighboringquantum states is larger and the number of avoided crossingssmaller. Thus, the differences in the effective dipole momentbetween individual quantum states are larger and, therefore,the degrees of their deection will vary considerably.

B. Laser-induced alignment of quantum-state-selectedmolecules

We now turn to studying alignment induced by the YAGpulse. The basic experimental observables are 2D I + ion im-ages recorded when the IB molecules are irradiated with boththe YAG pulse and the probe pulse. The geometry of thelaser pulse polarizations with respect to the velocity mapimaging VMI spectrometer is illustrated in Fig. 7. TheYAG pulse is linearly polarized along the vertical direction,i.e., in the detector plane. The probe pulse is linearly polar-ized perpendicular to the detector plane, which ensures thatthere is no detection bias on the molecular orientation in thatplane. This results in a circularly symmetric I + image, whenonly the probe pulse is used Fig. 8, image A1 . When the

YAG pulse is included Fig. 8, images A2 and A4 , the I+

images exhibit strong angular connement along the polar-ization of the YAG pulse.

The I + ions appear as two pairs of radially localizedregions, corresponding to two different fragmentation chan-nels of the Coulomb explosion. The radius of the outermostand weakest pair of rings is approximately 2 times larger

than the radius of the innermost and brightest pair of rings.Since the radius is proportional to the velocity of the ions,the I + ions from the outermost pair of rings originate from aCoulomb explosion channel that releases twice as much ki-netic energy as the channel producing the I + ions in the in-nermost pair of rings. As pointed out in several previous

0 0 0 0

1 1 1 1

3 0 3 2

4 1 3 3

0 00 0

1 1 1 1

3 03 2

4 13 3

a) b)

FIG. 6. a Energy as a function of the electric eld strength for selectedquantum states of IB. Solid lines represent quantum states that are presentclose to the upper cutoff of the molecular beam prole for IB seeded in Ne.The respective J K aK c quantum numbers are given in the gure. b Effectivedipole moment for selected quantum states of IB. The shaded area representsthe range of electric eld strengths in the deector at 10 kV.

repeller extractor ground

detector

Estat

Eprobe

EYAG

FIG. 7. Illustration of the polarization state of the YAG and the probe pulsewith respect to the static electric eld and the detector plane used to char-acterize alignment. The dashed line represents the propagation directions of the laser beams. A sketch of the resulting molecular alignment is included aswell. Repeller, extractor, and ground refers to the electrostatic plates of theVMI spectrometer.




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studies from our group see for instance Ref. 51 , this is onlyconsistent with the innermost pair of rings originating fromIB being doubly ionized by the probe pulse and fragmentinginto an I + +C 6H5

+ ion pair, and the outermost pair of ringsoriginating from I + ions formed by triple ionization and frag-mentation into an I + +C 6H5

2+ ion pair. The pronounced angu-

lar connement observed in images A 2 and A 4 is quantiedby calculating the expectation value of cos 2 2D , where 2Dis the angle between the YAG pulse polarization and theprojection of the I + recoil velocity vector onto the detectorplane. In this paper, cos 2 2D values are calculated onlyfrom ions detected in radial region corresponding to the I +

+C 6H52+ channel. By doing so, the YAG intensities probed

are restricted to a narrow range close to the maximum value,as the high nonlinearity of the multiphoton process occursefciently only in the spatial regions close to the focal pointof the YAG beam.

Image A1, recorded with only the probe pulse present,should correspond to a target of randomly oriented mol-ecules. As expected the image is circular symmetric andcos 2 2D =0.515. When the YAG pulse is included image

A2 a pronounced angular connement is observed along thepolarization of the YAG pulse and cos 2 2D is increased to0.947. These ob servations are in complete agreement withprevious studies. 38 When the deector is turned on and thelaser foci moved to the edge of the most deected moleculesat the position marked in Fig. 5 a , corresponding to mol-

ecules in the lowest rotational states, the angular connementis further enhanced image A3 leading to a cos 2 2D valueof 0.968. By contrast, when the experiment is conducted onthe least deected molecules in the depleted region image

A4 , corresponding to molecules in the highest rotationalstates, the alignment is weakened and cos 2 2D =0.900.We repeated the alignment measurements when IB was

seeded in Ne. The results are displayed in Fig. 9. Like in theHe case a pronounced improvement is observed when de-ected rater than undeected molecules are employed. Fig-ure 9 shows images of I + recorded at three different intensi-ties of the YAG laser for both undeected and deectedmolecules seeded in Ne. The effect of the deector is clearlyseen when comparing, for instance, image B1 deected andA1 undeected . At this low YAG intensity 2.3

1010 W / cm 2 weak alignment is obtained in the nonde-ected beam with cos 2 2D =0.695. Going to the edge of

the deected molecular beam position indicated in Fig. 5 ba clear enhancement is observed image B1 with thecos 2 2D value rising to 0.869. Also, at high YAG intensity1.2 1012 W / cm2 the difference in angular connement

comparing the undeected image A3 to the deected mol-ecules image B3 is visible. While cos 2 2D =0.929 repre-sents the limit of the degree of alignment of IB seeded in Nein the undeected beam, employing the deector leads to anunprecedented degree of laser-induced alignment of cos 2 2D =0.972. We note that cos 2 2D =1 would corre-

spond to the quantum mechanically unfeasible situation of perfectly 1D-aligned molecules.

To quantify the angular information of the images,cos 2 2D values are plotted as a function of YAG intensity;

the results are displayed in Fig. 10. Even at very low laserintensities, a high degree of alignment can be obtained froman ensemble of quantum-state-selected molecules. The ten-dency shown in this graph with a steep rise and early satu-ration of the degree of alignment agrees with previous resultsinvestigating the dependence of alignment on the rotational

probe only no deection deection depletionA1 A2 A3 A4

0.5

1

0

a.u.

FIG. 8. I + ion images illustrating alignment, recorded when the probe pulseCoulomb explodes the IB molecules seeded in He. The polarizations of the

YAG and the probe pulses are kept xed as illustrated in Fig. 7. The labelsno deection, deection, and depletion correspond to images re-corded at lens position y=0.0, 1.0, and 0.9 mm, respectively, the latter twowith the deector at 10 kV see Fig. 5 . The intensities of the YAG andprobe pulse are 8 1011 and 5 1014 W / cm 2, respectively. The color scaleindicates the relative number of ions. This color scale is the same for allsubsequent gures showing ion images.

2.3 10 10 W/cm 2 2.3 10 11 W/cm 2 1.2 10 12 W/cm 2

n o

d e

e c t i o n

d e

e c t i o n

B1

A1

B2

A2

B3

A3

FIG. 9. I + ion images illustrating alignment at different intensities of theYAG pulse, recorded when the probe pulse Coulomb explodes IB moleculesseeded in 20 bar Ne. The labels no deection and deection correspondto images recorded at lens position y =0.0 mm deector turned off and2.15 mm deector at 10 kV , respectively. The intensity of the probe pulseis 5 1014 W / cm 2.

0 2 4 6 8 10 12

0.5

0.6

0.7

0.8

0.9

1.0

deectionno deection

YAG intensity (1011

W/cm2)

2 D

FIG. 10. Degree of alignment as a function of the YAG intensity for IBseeded in 20 bar Ne. The labels no deection and deection correspond toimages recorded at lens position y=0.0 mm deector turned off and2.15 mm deector at 10 kV , respectively. The intensity of the probe pulseis 5 1014 W / cm 2.




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temperature of the ensemble of molecules. 38 Effectively, thequantum-state selection corresponds to a colder albeit non-

thermal beam see Sec. III A .Note that the contrast between the undeected and thedeected beam is expected to be greater if Ne is used insteadof He as a carrier gas. In the undeected beam the maximumdegree of alignment that can be achieved is smaller in Nebecause the rotational cooling in the supersonic exp ansion isless effective due to the lower stagnation pressure. 37 Addi-tionally, in the deected beam, a better degree of alignmentis expected for Ne, as the efciency of the quantum-stateselection in the present setup is signicantly enhanced due tothe longer residence time in the deector see Sec. III A .

C. Laser-induced orientation ofquantum-state-selected molecules

Next, we discuss orientation due to the combined actionon the molecules by the YAG pulse and the static electriceld E stat from the VMI electrodes.

5,6 Figure 11 illustratesthe polarization state of the YAG and the probe pulse withrespect to the static electric eld of the VMI electrodes. The

important difference compared to the alignment data is thatthe YAG polarization is rotated away from the axis perpen-dicular to the static eld. Thus, the orientation data resultfrom geometries where the angle between the YAG polar-ization the CI bond axis and the static electric eld isdifferent from 90, see Fig. 11. To image orientation a circu-larly polarized probe pulse is used. This ensures that anymolecule will be ionized and thus detected with the same

probability independent of . This circularly polarized probewill induce some bias on the angular distribution of the I +

ions see Fig. 12 A1 and C1 , however, importantly, it isup/down symmetric. Figure 12 shows I + ion images for dif-ferent values for both deected and undeected moleculesseeded in He. As mentioned, the circularly polarized probealone gives rise to an image that exhibits some angular con-nement with cos 2 2D =0.70 Fig. 12, A1 . Consequently,including the YAG pulse at =90, results in an image Fig.12, B1 that appears slightly different from the correspond-ing image with a linearly polarized probe Fig. 8 A2 , butstill shows that the molecules are tightly aligned.

Focusing rst on the nondeected data of Fig. 12 rowsA and B two prominent changes are observed as the polar-ization of the YAG pulse is gradually rotated away from thedetector plane images A2A6 and B2B6 . First, the loca-tion of the I + rings shifts closer to the center of the images.This is due to the fact that the CI axis alignment and thusthe emission direction of the I + ions follows the YAG pulsepolarization. When the CI axis is aligned at an angle , themagnitude of the I + velocity vector recorded on the detectorwill be reduced by the factor sin . The detrimental effecton the radial velocity resolution is obvious at =135 / 45 image A5 and B5 and 30/150 image A6 andB6 , where the two I + explosion channels, I + +C 6H5

+ and I +

+C 6H52+

, become indistinguishable as they merge in the 2Dprojection onto the detector plane.

Second, as the YAG pulse polarization is turned awayfrom 90, the up/down symmetry of the images, characteris-tic for the alignment data described in Sec. III B and Fig. 12column 1 is broken. For images with 90 180 im-ages B2B6 , more I + ions are detected in the upper part,

repeller extractor ground

detector

E stat

E

E YAG

FIG. 11. Illustration of the polarization state of the YAG and the probe pulsewith respect to the static electric eld and the detector plane used to char-acterize orientation. The dashed line represents the propagation direction of the laser beams. A sketch illustrating the molecular orientation is included aswell.

n o

d e

e c t i o n

d e

e c t i o n

D1

C1

B1

A1

D2

C2

B2

A2

D3

C3

B3

A3

D4

C4

B4

A4

D5

C5

B5

A5

D6

C6

B6

A6

90o 100o 110o 120o 135o 150o

probe 80 o 70o 60o 45o 30o

90o 100o 110o 120o 135o 150o

probe 80 o 70o 60o 45o 30o

FIG. 12. I + ion images illustrating ori-

entation for different values of , re-corded when the circularly polarizedprobe pulse Coulomb explodes the IBmolecules seeded in 90 bar He. Thelabels no deection and deection cor-respond to images recorded at lens po-sition y=0.0 mm deector turnedoff and 1.0 mm deector at 10 kV ,respectively. The intensity of theYAG and the probe pulse is 8 1011

and 5 1014 W / cm 2, respectively. E stat =594 V / cm.




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whereas for 0 90 images A2A6 , more I + ions aredetected in the lower part. The asymmetry becomes morepronounced as the YAG polarization is rotated closer to theaxis of the static eld. We interpret these observations asorientation due to the combined effect of the YAG laser eldand the projection of the static electric extraction eld E staton the YAG polarization axis. This projection numericalvalue: cos E stat increases as is rotated toward 0 or180, which is expected to cause an increase in theorientation, 5,6 in agreement with the experimental ndings.

As discussed in Sec. III A, all states of IB are high-eldseeking, hence the orientation is expected to place the I-endof the molecules toward the repeller plate see Fig. 11 ,where the electrical potential is highest, because the dipolemoment of IB is directed along the CI axis pointing fromiodine negative end toward the phenyl ring positiveend . The expected resulting molecular orientation at agiven angle of is shown in Fig. 11. Thus, for 0

90, the I + ions are expected to preferentially be ejecteddownward and, for 90 180, they will be ejected up-ward. This is in agreement with the up/down asymmetry inthe images.

The alignment image D1 and orientation imagesC2C6 and D2D6 improve signicantly when the deectoris turned on and the foci of the lasers are moved to theposition of the most deected molecules position marked inFig. 5 a . The markedly better orientation resulting in a

much more pronounced up/down asymmetry is clearly vis-ible even when the YAG pulse is only turned slightly awayfrom perpendicular, i.e., comparing deected and undeectedimages for =100 images C2 and A2 and =80 imagesD2 and B2 . From the previous discussion it appears that thehighest degree of orientation is achieved when is rotatedtoward 0 or 180. This is clearly seen from the images inrows C and D and, again, the improvement obtained withdeected molecules is striking compare image C6 to A6, orD6 to B6 .

Similar orientation measurements were conducted for IBseeded in Ne instead of in He. Figure 13 shows I + images ata series of values for two different intensities of the YAG

pulse recorded with the deector at 10 kV at the positionmarked in Fig. 5 b . Compared to the images displayed inFig. 12 rows A and B, although recorded at slightly differentintensities of the YAG pulse, a signicant improvement isobserved. Furthermore even at low intensity of the YAG ahigh degree of orientation for IB seeded in Ne is achieved.At the same time some loss in the angular connement, i.e.,in the alignment degree, is visible. We assign the clear im-provement in the up/down asymmetry to the more stringentstate selection in Ne compared to He as described in Sec.III A, hence, manifesting itself in a higher degree of orienta-tion.

To quantify the up/down asymmetry, i.e., the degree of orientation, we determine for each image the number of I +

ions, N I+up

, in the upper part of the I + +C6H

5

+ and I +

+C 6H52+ channels i.e., ions detected in the upper half of

the images as well as the total number of ions, N I+ total

A def. (Ne) 1.2 1012

W/cm2

B def. (Ne) 1.2 1011

W/cm2

C def. (He)D no def. (He)

20 40 60 80 100 120 140 1600.2

0.3

0.4

0.5

0.6

0.7

0.8

N u p

/ N t o t a l

(O)

FIG. 14. Orientation of IB, seeded in either He or Ne, represented by thenumber of I + ions in the upper half of the image N up divided by the totalnumber of I + ions in the image N total as a function of . For the experi-ments conducted with He as a carrier gas, curves C lens position y=1.0 mm and deector at 10 kV and D lens position y=0.0 mm anddeector off , the intensity of the YAG pulse was 7.8 1011 W / cm 2. For theNe carrier gas, curves A and B lens position y =2.25 mm and deector at10 kV , the intensities of the YAG pulse are displayed in the insert. Theintensity of the probe pulse for all curves was xed at 5 1014 W / cm 2, E stat =594 V / cm.

1 . 2

1 0 1 2 W / c m

2

1 . 2

1 0 1 1 W / c m

2

D1

C1

B1

A1

D2

C2

B2

A2

D3

C3

B3

A3

D4

C4

B4

A4

D5

C5

B5

A5

D6

C6

B6

A6

90o 100o 110o 120o 135o 150o

probe 80 o 70o 60o 45o 30o

90o 100o 110o 120o 135o 150o

probe 80o 70o 60o 45o 30o

FIG. 13. I + ion images of deected IBseeded in 20 bar Ne, illustrating orien-tation at two different intensities of theYAG pulse. The images are recordedat lens position y=2.25 mm with thedeector at 10 kV. The intensity of theprobe pulse is 5 1014 W / cm 2. E stat=594 V / cm.




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=N I+ up +N I+ down . This ratio, as a function of , is dis-played in Fig. 14. Focusing rst on curves C and D, repre-senting IB seeded in He, the difference between the data forthe deected molecules and the data obtained with the de-ector turned off is striking and shows the advantage of se-lecting the lowest-lying rotational states for strongly increas-ing the degree of orientation. The further improvement whenNe is used instead of He is clear from curves A and B. These

two curves also show that the pronounced degree of orienta-tion is maintained when the intensity of the YAG pulse islowered by an order of magnitude compared to the maximumvalue of 1.2 1012 W / cm 2.

IV. CONCLUSION AND OUTLOOK

In conclusion, we have shown that deection of coldmolecular beams with an inhomogeneous static electric eldenables the selection and the spatial separation of the mostpolar quantum states, i.e., the lowest-lying rotational states.The method demonstrated here is complementary to stateselection for small molecules using a hexapole focuser,which has been suggested to be applied for improved align-ment and orientation ex periments 52 and recently been experi-mentally demonstrated. 53 While a hexapole focuser onlyworks for small molecules in low-eld-seeking quantumstates, beam deection will apply broadly to a wide range of molecules, from diatomics to large biomolecules. The deec-tion is strongest for molecules with a large permanent dipolemoment to mass ratio. For a given molecule the deection isoptimized by employing stronger deection elds, increasingthe length of the deector, or lowering the speed of the mol-ecule, for instance, by using neon rather than helium as acarrier gas. For small molecules, the preparation of an en-

semble of molecules all in a single quantum state should befeasible. As an application of the state-selected molecules,we showed that selection of IB in low-lying rotational statesallows achievement of unprecedented degrees of laser-induced adiabatic alignment and mixed laser- and static-eldorientations. In particular, we demonstrated that strongalignment and orientation can be maintained even when theintensity of the alignment pulse is lowered to the1010 10 11 W / cm 2 range. This can reduce unwanted distur-bance from the laser eld in future applications of adiabati-cally aligned or oriented molecules. We note that it should bepossible to improve the degree of orientation obtained heresimply by increasing the static electric eld. Due to experi-

mental constraints this was not implemented in the presentwork.

Getting access to cold molecules in the gas phase typi-cally involves using a molecular beam from a supersonicexpansion that usually consists of more than 99% carrier gasand less than 1% of the specic molecules. In several typesof experiments the atomic carrier gas can contribute to, oreven completely overshadow, the particular signal measured.The electrostatic deection naturally separates the polarmolecules from the unpolar carrier gas and thus removes thisunwanted background. We estimate the density in the origi-nal molecular beam to be 10 11 molecules / cm 3. In the experi-ments presented here the density in the deected part of the

beam is approximately 10 10 molecules / cm 3. We foresee thisdensity to be sufcient for a variety of applications, such asphotoelectron spectroscopy with vacuum-ultraviolet VUV ,extreme-ultraviolet EUV ,54 or x-ray light sources, includ-ing attosecond pulses, or high harmonic generation experi-ments with femtosecond laser pulses. 55 For all of these ap-plications the separation of the molecular target from thecarrier gas might be of great relevance.

Additionally, brute-force orientation,1,2

that is, the spatialorientation of polar molecules using strong dc electric elds,will benet from the state-selected samples similar to whatwas demonstrated here. In fact, the states that are deectedthe most are also oriented the most in a dc electric eld. Toillustrate the achievable orientation, we calculated theensemble-averaged orientation in a homogeneous electriceld of 250 kV/cm for IB for a thermal ensemble of 1 K. Forthis ensemble cos =0.757 is obtained. For a deected,quantum-state-selected sample of IB molecules at 1% of theundeected peak intensity see Table I , an increasedensemble-averaged orientation of cos =0.905 is pre-

dicted. For nonadiabatic alignment,56,4

it was demonstratedthat the dynamics and, importantly, the degrees of alignmentand orientation depend strongly on the initial rotational-statedistribution. 5761 Selection of rotational states is, therefore,highly advantageous for nonadiabatic laser-induced schemesto control the spatial orientation of molecules, as recentlydemonstrated for NO molecules. 53 In general, completeelimination of the rotational tumbling of an asymmetric topmolecule requires that all three principal axes are connedalong laboratory xed axes. This is the area of three-dimensional 3D alignment and orientation, subjects thathave been treated theoretically and experimentally. 6267 Astraightforward extension of the current work would be sig-nicantly improved 3D alignment and orientation of polarmolecules by employing state-selec ted molecules and we re-cently performed such experiments. 67

For large bio- mo lecules, typically multiple structuralisomers conformers 68 are present even at the low tempera-tures in a supersonic jet. 69 These conformers often exhibitlarge and largely different dipole moments, which can beexploited to spatially separate them using inhomogeneouselectric elds. This separation has recently been demon-strated in an alternating gradient focusing selector for the cis -and trans -conformers of 3-aminophenol. 7 However, also thestatic eld of a deector can be used to spatially isolate in-

dividual conformers.70

In general, the ability to achieve veryhigh degrees of alignment and orientation is of great interestfor a number of applications. We therefore believe state-selected molecules could be very benecial for areas such asphotoelectron angular distributions from xed-in-spacemolecules, 71 ultrafast diffraction with electron or x-raysources, 8,9 and time-resolved studies of light-induc edstereochemistry. 72 Furthermore, Janssen and co-workers 26

have shown that the ability to select a single rotational statewith a hexapole focuser enables new possibilities for study-ing directional dynamics of fragments in photodissociationof small molecules. The deection method strongly increasesthe number of molecules to which single rotational state




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selection and subsequent orientation can be applied. In par-ticular, it will offer access to studies of photoinitiated pro-cesses in oriented targets of larger asymmetric tops.

ACKNOWLEDGMENTS

We thank Henrik Haak for expert technical support. Thiswork is further supported by the Carlsberg Foundation, the

Lundbeck Foundation, the Danish Natural Science ResearchCouncil, and the Deutsche Forschungsgemeinschaft withinthe priority program 1116.

APPENDIX A: SIMULATION OF BEAM PROFILES

In this Appendix, the simulations of the experimentaldeection proles are described in detail. First, the calcula-tion of the Stark effect for asymmetric top molecules is ex-plained in Appendix A 1. Appendix A 2 describes howsingle-quantum-state deection proles are obtained fromtrajectory simulations using the calculated Stark curves. Fi-nally, the single-quantum-state proles are averaged in a

suitable way to simulate a thermal ensemble for a given ro-tational temperature, which is described in Appendix A 3 andtted to the experimental data Appendix A 4 .

1. Stark effect calculations

In order to calculate the adiabatic energy curves forasymmetric top molecules, the Hamiltonian matrix is set upin the basis of symmetric top wave functions. In the presenceof an electric eld, only M is a good quantum number for anasymmetric rotor. J , which is a good quantum number in theeld-free case, is mixed by the eld, whereas K is mixed bythe molecular asymmetry. Thus, the adiabatic energy curvescan be calculated for the different M levels individually bysetting up and diagonalizing the M matrices including all J and K levels. An accurate description of higher rotationalquantum states also requires including centrifugal distortionconstants. The Hamiltonian H of an asymmetric rotor mol-ecule with dipole moment

in an electric eld of strength E can be written as the sum of the Hamiltonian H rot of anasymmetric rotor in free space in Watsons A-reduction 73 andthe contribution due to the Stark effect H Stark as

H = H rot + H Stark . A1

Followin g Refs. 73 and 74, the corresponding matrix ele-ments are 81

JKM H rot JKM = B + C

2 J J + 1 K 2 + AK 2

J J 2 J + 1 2 JK J J + 1 K

2 K K 4 ,

A2

JK 2 M H rot JKM

= B C

4 J J J + 1

K

2K 2 2 + K 2

J J + 1 K K 1 J J + 1 K 1 K 2 ,

A3

JKM a JKM = MK

J J + 1 a E , A4

J + 1KM a JKM = JKM a J + 1KM

= J + 1 2 K 2 J + 1 2 M 2

J + 1 2 J + 1 2 J + 3a E ,

A5

JK 1 M b JKM = M J K J K + 1

2 J J + 1 b E , A6

J + 1K 1 M b JKM

= JK 1 M b J + 1KM

= J K + 1 J K + 2 J + 1 2 M 2

2 J + 1 2 J + 1 2 J + 3b E , A7

JK 1 M c JKM = i M J K J K + 1

2 J J + 1c E , A8

J + 1K 1 M c JKM

= JK 1 M c J + 1KM

= i J K + 1 J K + 2 J + 1 2 M 2

2 J + 1 2 J + 1 2 J + 3c E . A9

For the correct assignment of the states to the adiabaticquantum number labels J K aK c M

, i.e., to the adiabaticallycorresponding eld-free rotor states, one has to classify thestates accord ing to their character in the electric eld sym-metry group .75,76 This symmetry classica tion can be per-

formed by applying a Wang transformation 77 to the Hamil-tonian matrix. If the molecules dipole moment is along oneof the principal axes of inertia, the matrix will be block di-agonalized by this transformation according to the remainingsymmetry in the eld and the blocks can be treated indepen-dently. For arbitrary orientation of the dipole moment in theinertial frame of the molecule, the full matrix must be diago-nalized. In any case, this process ensures that all states ei-genvalues and eigenvectors obtained from a single matrixdiagonalization do have the same symmetry, and, therefore,no real crossings between these states can occur. Therefore,sorting the resulting levels by energy and assigning quantumnumber labels in the same order as for the eld-free states of the same symmetry yields the correct adiabatic labels. Thesecalculations are performed for a number of electric eldstrengthstypically in steps of 1 kV/cm from 0 to 200 kV/ cm, and the resulting energies, W Stark E , are stored for lateruse in simulations using the LIBCOLDMOL programpackage. 78

2. Monte Carlo simulations of a molecular beam

Simulations of the electrostatic beam deection in oursetup are per formed with the home-built software packageLIBCOLDMOL .78 Trajectories for individual molecules in agiven rotational quantum states are obtained from numerical




12/13

integration of the 3D equations of motion using a RungeKutta algorithm. The initial phase-space distribution of themolecular packet in the transverse spatial coordinates, x and y, is described by the mean values and widths of circularuniform distributions. For the velocity coordinates, Gaussiandistributions characterized by their mean values and FWHMsare used. Also, the initial time spread of the molecular beam,which corresponds to the opening time of the valve, is de-

scribed by a Gaussian distribution centered around t 0. Fromthe initial phase-space distribution, the position of a mol-ecule in phase space is randomly chosen. Then, it is propa-gated through the beamline, which includes all mechanicalapertures of the experimental setup. From the electric eld inthe electrostatic deector, which is calculated in two dimen-sions using nite element methods COMSOL MULTIPHYSICS3.4 and the Stark energy see Appendix A 1 , the force actingon the molecule in the transverse directions is obtained: F

=

W Stark E . The electric eld is taken to be constant along z. Finally, the deected molecules are propagated througheld-free space to the detection region. For each quantumstate, 10 5 trajectories are calculated yielding single-quantum-state deection proles I s y .

3. Deection proles

The spatial deection prole for an ensemble of mol-ecules at a given rotational temperature, I y, T rot , is calcu-lated from the single-quantum-state deection proles, I s y ,as follows:

I y,T rot =1w s=1

N

ws T rot I s y . A10

Here, N is the number of quantum states included in the

simulations and ws T rot is the population weight for a givenquantum state:

ws T rot = g M gnseW 0W s/ kT rot , A11

with W 0 being the eld-free potential energy of the groundstate and W s the eld-free energy of the current state; g M =1 for M =0 and g M =2 otherwise. gns accounts for thenuclear spin statistical weight of the current state. For bothbenzonitrile and IB, gns =5 for K a even and gns =3, otherwise.The normalization is given by w = s=1

N ws.In some cases, a molecular beam canno t be accurately

described by a single rotational temperature. 46 Therefore, atwo-temperature model is implemented in our simulations. In

the two-temperature model, the low-temperature part of themolecular beam is calculated as described above. In order torealistically simulate the high-temperature component in themolecular beam, a very large number of quantum stateswould have to be included in the simulations for large asym-metric top molecules. Because these Monte Carlo simula-tions are very time consuming, the high-temperature compo-nent is approximated by adding a small fraction of undeected molecules to the deected beam prole. This ap-proximation is well justied, because typical rotational tem-peratures for the high-temperature component in a molecularbeam are on the order of 10 K and, for these temperatures,most of the molecules reside in high rotational quantum

states that have a small Stark shift and, therefore,remain almost undeected. Thus, the deection prole, I 2T y, T rot , q , in the two-temperature model is calculated as

I 2T y,T rot,q = qI y,T rot + 1 q I ud y , A12

where 0 q 1 and I ud y denotes the undeected spatialbeam prole that is obtained when both electrodes aregrounded.

4. Fit of rotational temperature

In order to calculate the rotational temperature of themolecular beam, the simulated deection proles are tted tothe experimental data using a NelderMead simplex algo-rithm. In the tting procedure, the difference between simu-lated and measured deection proles is minimized, wherethe rotational temperature T rot of the low-temperature com-ponent, the fraction q of molecules in this low-temperaturecomponent, and a general intensity scaling factor s of thedeected proles with respect to the undeected beam pro-le are used as tting parameters. All deection curves mea-

sured for different high voltages are tted simultaneously todetermine the rotational temperature.

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80 In principle, deection of the quantum states that are coincidentally polarfor the range of electric eld strengths in the deector could be reducedby operating the deector at a different high voltage. However, due to thelarge number of quantum states populated and the resulting large numberof avoided crossings, other quantum states might be conincidentally polarfor these operation conditions.

81 Note that in the Ref. 74 representation I l is used.

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