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Cite this:Phys.Chem.Chem.Phys.,

2014, 16, 4071

Rotational spectroscopy with an opticalcentrifuge

Aleksey Korobenko,*a Alexander A. Milner,a John W. Hepburnb and Valery Milnera

We demonstrate a new spectroscopic method for studying electronic transitions in molecules with extremely

broad range of angular momentum. We employ an optical centrifuge to create narrow rotational wave

packets in the ground electronic state of 16O2. Using the technique of resonance-enhanced multi-photon

ionization, we record the spectrum of multiple ro-vibrational transitions between X3Sg� and C3Pg electronic

manifolds of oxygen. Direct control of rotational excitation, extending to rotational quantum numbers as

high as N \ 120, enables us to interpret the complex structure of rotational spectra of C3Pg beyond

thermally accessible levels.

The dynamics and spectroscopy of highly excited states of molecules

is an issue of great importance to chemical physics. Perturbative

approaches do not always work at high levels of excitation, where

coupling between degrees of freedom changes dramatically from

what is observed at thermal energies.1 As a result, interpreting

molecular spectra becomes increasingly difficult as the level of

excitation grows.2 Significant geometric changes in highly excited

molecules, when the level of excitation exceeds an isomerization

barrier, make understandingmolecular spectroscopy in these energy

ranges an ongoing challenge.4,5

This challenge can become more acute in the case of spectro-

scopic studies of a process, where product molecules can be

formed in highly excited states.6,7 To detect the low density

products, resonance-enhanced multiphoton ionization (REMPI)

is often employed due to its high sensitivity, spectral resolution

and versatility.8,9 This means that the electronic spectroscopy of

a highly rotationally excited molecule must be understood, both

the assignment of resonances and their strengths. This task can

be complicated by a predissociative coupling and decay behavior

in the intermediate excited electronic states.10

Assuming that the molecule of interest is reasonably stable,

REMPI spectra recorded at high temperatures can provide

information on the properties of highly excited states, but this

approach is limited both by the temperatures that themolecule can

tolerate before it dissociates, and by the difficulty of unraveling the

complex spectrum of a high temperaturemolecule, as illustrated by

the work done on the spectrum of high temperature water.2 In the

case of oxygen, reaching the high rotational states probed in

this paper (N > 100) would require a temperature ofE50 000 K.

Rotational excitation of oxygen with strong ultra-short laser

pulses is limited to N B 40 due to the rapidly increased

ionization rate with growing laser intensities.3 Even if a broad

thermal distribution of highly excited rotational states could be

produced in a diatomic molecule such as oxygen, the triplet

structure of the ground and excited states coupled with two-

photon selection rules (for the C3Pg (v0 = 2)’’ X3Sg

� (v00 = 0)

transition), would result in as many as 21 overlapping rotational

branches, making spectroscopic assignment challenging.11

Optical centrifuge is an alternative tool for exciting molecules

to extremely high rotational states by means of non-resonant laser

fields.12–15 In a recent study, we have shown that the centrifuge

can be used to produce and control the so-called ‘‘super rotor’’

states – coherent rotational wave packets with ultra-high angular

momentum N and narrow distribution width dN { N.16 Here we

utilize this unique capability of the centrifuge for the purpose of

obtaining and interpreting complex REMPI spectra of oxygen

super rotors (0o Nt 120). We excite oxygen to a narrow rotational

wave packet whose center is accurately tuned across the broad range

of well defined N values. The centrifuge excitation is then followed

by a REMPI measurement. Owing to the narrow N distribution, the

detected spectrum becomes significantly less congested, and identi-

fying rotational resonances is greatly simplified.

Following the original recipe by Karczmarek et al.,12 we utilize

the output of an 800 nm, 35 fs (full width at half-maximum,

FWHM), Ti:Sapphire regenerative amplifier. We split its spectrum

in half at around the central wavelength (Fig. 1a), in a Fourier

plane of a pulse shaper. Frequency chirps of equal magnitude

(0.26 ps�2) and opposite signs are applied to the ‘‘red’’ and ‘‘blue’’

arms of the centrifuge, as demonstrated by the cross-correlation

frequency-resolved optical gating (XFROG) measurement (Fig. 1c).

The latter was carried out by overlapping the centrifuge pulse

with a reference Fourier-transform limited pulse on a 20 mm-thick

BaB2O4 crystal. The bandwidth of the reference pulse was reduced

aDepartment of Physics & Astronomy, University of British Columbia,

2036 Main Mall, Vancouver, BC, Canada V6T 1Z1. E-mail: korobenk@phas.ubc.cabDepartment of Chemistry, University of British Columbia, 2036 Main Mall,

Vancouver, BC, Canada V6T 1Z1

Received 30th October 2013,

Accepted 9th January 2014

DOI: 10.1039/c3cp54598a

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to about 1 nm in a separate pulse shaper to increase the spectral

resolution. The spectrum of the frequency mixing signal was

measured as a function of the relative time delay between the

centrifuge and reference pulses.

The two centrifuge arms are combined with a polarizing

beam splitter cube, and polarized with an opposite sense of

circular polarization. Optical interference of the two circularly

polarized frequency-chirped laser fields results in a pulse with

rotating linear polarization (inset to Fig. 1c). Because of the

anisotropic polarizability, molecular axes line up along the axis

of laser polarization, and then follow it adiabatically as

the plane of polarization rotates with increasing angular

frequency. Quantum-mechanically, this process corresponds to

the rotational ladder climbing, executed as a series of consecutive

Raman transitions between the rotational levels separated by

DN = 2. Each step consists of absorbing a photon from the blue

centrifuge arm and emitting a photon into the red arm. The

frequency difference between the two photons (2O) grows in

time following the rotational line separation. Opposite circular

polarization of the two centrifuge arms ensures DMN = 2

selection rule, resulting in unidirectional rotation. Given the

available spectral bandwidth, the accelerating centrifuge

can reach angular frequencies on the order of 10 THz, which

in the case of oxygen corresponds to the rotational quantum

number N E 119.

As we have demonstrated in ref. 16 truncating the spectrum

of the centrifuge in a Fourier plane of the pulse shaper by a

movable shutter (see inset to Fig. 1a, and field spectrum in

Fig. 1b) enables accurate control of the rotational state of the

centrifuged molecules. Characterizing the centrifuge field with

XFROG allowed us to calibrate the final rotation speed of the

centrifuge, and hence the corresponding molecular angular

momentum, as a function of the shutter position.

REMPI detection was carried out using narrowband nano-

second probe pulses tunable from 279 nm to 288 nm (0.1 cm�1

line width, 500 mJ per pulse, 50 Hz repetition rate). The probe

beam was combined with a centrifuge beam (5 mJ per pulse) on

a dichroic mirror (Fig. 2), and focused with a 35 mm focal length

spherical aluminium mirror on a supersonically expanded mole-

cular jet passing between the charged plates of the time-of-flight

(TOF) mass spectrometer. We estimate the peak centrifuge field

intensity at the focal spot around 1013 W cm�2. The jet was

generated by an Even-Lavie pulsed valve (25 ms opening time,

150 mm nozzle diameter) located 20 cm away from the detection

region. Ion current was detected with a microchannel plate

(MCP) detector. The initial rotational temperature of the sample,

extracted from the REMPI spectrum taken without the centrifuge

field (Fig. 3a), was about 10 K.

The main result of this work is shown in Fig. 3, where

the detected ion count is plotted against the probe energy

(horizontal axis) and the final rotation speed O of the truncated

centrifuge (vertical axis). The latter is expressed in terms of the

angular momentum N of an oxygen molecule rotating with the

angular frequency O, according to:

O = 2pc[E(N) � E(N � 1)],

E(N) = BN(N + 1) � DN2(N + 1)2,

where E is the energy of state |Ni, c is the speed of light in

vacuum, B = 1.438 cm�1 and D = 4.839� 10�6 cm�1.18 The validity

of Dunham expansion of rotational energy to second order in

Fig. 1 Optical centrifuge. (a) Broadband laser pulses from a Ti:S chirped pulse amplifier (10 mJ, 35 fs, 1 KHz repetition rate) are dispersed with a

diffraction grating and split in the center of the spectrum in a Fourier plane of the focusing lens into ‘‘red’’ and ‘‘blue’’ arms, whose chirps are individually

controlled by two separate ‘‘chirp boxes’’. The chirp of the ‘‘red’’ arm is reversed, while that of the ‘‘blue’’ arm is left unchanged. Movable shutter on a

motorized linear stage (inset) allows precise truncation of the ‘‘blue’’ arm bandwidth. (b) Spectrum of the centrifuge pulse after shaping. Solid red (dashed

black) line corresponds to the truncated (full) centrifuge. (c) Cross-correlation frequency-resolved optical gating (XFROG) spectrogram of the truncated

centrifuge field, schematically shown below the XFROG plot. O is the angular frequency at which molecules are released from the centrifuge.

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N(N + 1) at extremely high values of N has been demonstrated

in our previous study.16

Each peak in the two-dimensional REMPI spectrogram of Fig. 3b

corresponds to a two-photon transition between a rotational

level in the electronic ground state, X3Sg�, and a rotational level

of C3Pg. The finite horizontal width of the observed peaks

stems from the predissociation line width (as in conventional

‘‘1D REMPI’’ detection), whereas finite vertical spread reflects

the narrow width of the excited rotational wave packet created

by the centrifuge.

The complexity of the two-photon absorption line structure

in rotationally hot oxygen gas is illustrated by red and yellow

lines in Fig. 3a which correspond to the hot thermal ensemble

(simulated numerically) and the ensemble of centrifuged mole-

cules (experimentally observed 2D spectrogram integrated along

its vertical dimension), respectively. In sharp contrast to conven-

tional 1D REMPI spectroscopy, controlled centrifuge spinning

offers direct assignment of rotational quantum numbers to the

observed REMPI peaks, as well as significantly better peak separa-

tion due to their distribution along the added second dimension.

Vertical traces originating from bright resonance peaks in

Fig. 3b (examples are marked with white arrows) correspond to

molecules which ‘‘leaked out’’ of the weakened centrifuge potential

before reaching the terminal angular frequency of the centrifuge.

After escaping the centrifuge, these molecules continue their free

rotation while the trap is accelerating further. The three bright

vertical stripes reproduce the initial cold beam spectrum (blue line

in Fig. 3a) and correspond to the molecules which were not trapped

by the centrifuge. The width of the final rotational wave packets can

be readily extracted as dN E 7 (FWHM), from the vertical cross

sections, shown in Fig. 3c. Here, we detected rotational states withN

as high as B80. Rotational line broadening above N E 60 can be

attributed to the increasing Rydberg-valence interaction (governed

by the Franck–Condon (FC) overlap with the continuum wavefunc-

tions) similarly to the previously observed rotational broadening in

the lower vibrational states (v0 = 0,1) of the excited potential.11

Fig. 2 Detection setup. Centrifuge beam is combined with a tunable UV

laser pulse and focused inside a vacuum chamber on a supersonically

expanded oxygen jet between the charged plates of a time-of-flight (TOF)

mass spectrometer. The ionization rate is measured with a multi-channel

plate (MCP) detector.

Fig. 3 2D REMPI spectrogram for a linearly polarized probe. (a) Experimental spectra of cold (10 K, blue) and centrifuged molecules (yellow), along with a

simulated spectrum of a ‘‘hot’’ thermal ensemble (3000 K, red) calculated with pgopher software.17 (b) Ion signal as a function of the probe laser two-

photon energy and molecular angular momentum defined by the centrifuge final rotation speed. Different areas of the 2D plot were measured with

different sensitivities and probe intensities and are displayed with different color scales to compensate for the broad dynamic range of the data. (c)

Vertical cross-sections of several consecutive peaks from one particular branch, shown in the inset to b. The peaks are regularly separated with a distance

of DN = 2 reflecting 16O2 nuclear spin statistics.

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One can see that the peaks in Fig. 3 are grouped in regular

patterns, resembling Fortrat parabolas corresponding to different

rotational branches. Within a single branch, the center of each

consecutive resonant peak is shifted by DN = 2 (Fig. 3c), reflecting16O2 nuclear spin statistics. Circularly polarized light can be used

to further simplify the spectrum. As shown in Fig. 4, the signal

strength of different rotational branches depends on the handed-

ness of probe polarization. This is due to the highly non-uniform

population distribution among the magnetic sub-levels in the

centrifuged wave packet, withmost of the population concentrated

at MNC N (or MNC �N).12

To identify different rotational branches, we use three sets of

molecular constants (for F1,F2 and F3 spin–orbit components of

the excited state) from the previous studies on thermally excited

ensembles.7,19 The three components correspond to L + S = 0

(F1), 1 (F2) and 2 (F3), with L and S being the projections of the

orbital and spin components of the total angular momentum

on the molecular axis, respectively. These constants are listed

in Table 1. For F2 and F3 components, our results are well

described by the constants provided by Lewis et al.19 On the

other hand, the observed F1 peaks do not agree well with the

suggested numerical values (n0 = 69366 cm�1 and B0 = 1.6 cm

�1),

as shown in Fig. 5. This can be attributed to the complexity of

the broadened and highly overlapping structure of F1 lines,

which makes it hard to interpret and fit the data from a

thermally populated ensemble. Centrifuge spectroscopy enables

us to correct the values of F1 molecular constants (Table 1)

by performing the fit of the most pronounced DN = �2

branch (Fig. 5).

The lowest vibrational level of C3Pg electronic state of

oxygen known to exhibit well-resolved rotational structure is

v = 2.11 Predissociation to the closely lying valence state 13Pg

broadens the rotational spectrum of the lower vibrational states

v = 0,1. This broadening is weakened in the case of v = 2

because the repulsive potential crosses the level near the node

of the vibrational wavefunction, lowering the Franck–Condon

overlap.11 The FC overlap, however, increases with the increasing

degree of rotational excitation. At high values of N, we observe a

significant line broadening which results in a completely unresol-

vable rotational structure at N\ 60 (see Fig. 3).

At even higher centrifuge frequencies, corresponding to

the extreme rotational levels with 99 o N o 125, we observe

the re-appearance of narrow resonances shown in Fig. 6. Their

line width drops down to a well-resolvedB7 cm�1, as shown in

Fig. 7. Similar non-monotonic N-dependencies were previously

Fig. 4 2D REMPI spectrogram for a circularly polarized probe. Electric field vector is counter-rotating (a) and co-rotating (b) with the centrifuged

molecules. The directionality of laser-induced rotation results in the sensitivity of the measured signal to the handedness of probe polarization. The

results of fitting the data to the theoretical model are shown with colored lines and markers for different branches and resonances, respectively (see text

for details). Branch nomenclature is the same as in ref. 11.

Table 1 Molecular constants used to fit the data in Fig. 4

Spin–orbit branch v0/cm�1 B0/cm

�1 D/cm�1

3P0(F1) 69 375 1.585 2.5 � 10�7

3P1(F2) 69 445 1.648 1.0 � 10�5

3P2(F3) 69 550 1.685 1.3 � 10�5

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observed in OD21 where they were used to analyze the repulsive

state. Indeed, according to the Fermi Golden Rule, the line

width is proportional to the predissociation matrix elements

between the bound and the continuum eigenstates, as well

as the density of states in the continuum. As shown in ref. 21

the behavior of both quantities with N can be calculated

numerically and used for extracting the parameters of the

repulsive state from the experimentally observed dependence

on the rotational quantum number.

Our analysis showed that, unlike the previously discussed

branches of C3Pg (v0 = 2) ’’ X3Sg� (v00 = 0), the observed

ultra-high narrow lines originate from the v0 = 1 state, which

displays no resolvable rotational structure at lower rotational

levels, but re-appears at higher J’s. Well described by Hund’s

Fig. 5 Comparison of the observed REMPI data for the perturbed F1spin–orbit component with the calculations based on molecular constants

from this work (red circles), White et al.7 (blue triangles) and Lewis et al.

19

(purple squares).

Fig. 6 Ultra-high rotational resonances of O2. The two panels correspond to two possible ways of fitting the observed resonant branches (apparent

along white dashed lines) to the calculated Hund’s case (b) structure (labeled with markers). In panel a, the upper branch corresponds to DN =�1, and the

lower one to DN = 3, resulting in Bv = 1.620 cm�1 and Dv = 4.4 � 10�6 cm�1. In panel b, the upper branch overlaps with DN = �2, whereas the lower one

with DN = 2, yielding Bv = 1.664 cm�1 and Dv = 5.7 � 10�6 cm�1.

Fig. 7 Observed linewidths of J0 = N0 � 1 (triangles) and J0 = N 0 (squares)

spin–orbit sublevels of C3Pg (v0 = 1) level as functions of rotational

quantum number N0. Inset demonstrates a fit of experimental data (solid

red) to a sum of lorentzians (dashed black) in order to extract line widths.

Absolute position, absolute area and the widths of two peaks were fitted

for each doublet individually, with the areas ratio fixed to a value extracted

from the best resolved N0 = 115 doublet and with a doublet line separation

equal to a calculated one.

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case (b) at such high degree of rotational excitation, the observed

rotational structure consists of a series of spin–orbit multiplets.

Out of 9 possible DN branches, we have observed only

two (dashed lines in Fig. 6). Given this limited amount of

information, fitting the data by a single set of molecular

constants proved difficult. Our analysis resulted in two possi-

bilities shown in panels a and b of Fig. 6. The retrieved

molecular constants are Bv = 1.620 cm�1 and Dv = 4.4 �

10�6 cm�1 for plot a, and Bv = 1.664 cm�1 and Dv = 5.7 �

10�6 cm�1 for plot b. To choose between the two possibilities,

we note that in Hund’s case (a), an effective rotational constant

B0 for F2 spin–orbit component is equal to the true Bv value.20

This implies that at v = 2, Bv = 1.648 cm�1 (see Table 1). Since we

expect Bv to decrease with v, Fig. 6b should reflect the correct

branch assignment.

In conclusion, we have demonstrated a new spectroscopic

method for studying the rotational structure of electronic

transitions in molecules. The method is based on controlled

molecular spinning with an optical centrifuge. We have applied

this technique to C3Pg’’ X3Sg� (v00 = 0) in O2. By varying the

level of rotational excitation, we have observed rotational line

broadening and narrowing associated with the dependence of

predissociation rates on the molecular angular momentum.

In case of v0 = 2, resolved at lower rotational states (N t 60),

we showed an agreement with previously reported molecular

constants for F2 and F3 spin–orbit components and, owing to

the higher resolution of the implemented method, refined

those for the strongly perturbed F1 component. In case of

v0 = 1, extreme rotational excitation (N \ 100) resulted in the

suppression of predissociation and enabled us to determine

previously unknown rotational constants.

Acknowledgements

This work has been supported by the CFI, BCKDF and NSERC,

and carried out under the auspices of the Center for Research

on Ultra-Cold Systems (CRUCS). We gratefully acknowledge

stimulating discussions with R. Krems, V. Petrovic, M. Shapiro

and E. Grant. We would also like to thank one of the reviewers

of this manuscript for pointing out that the dependence of the

rotational line width on N could be used for mapping out

the repulsive potential responsible for the molecular pre-

dissociation. The analysis presented in Fig. 7 is a result of this

valuable suggestion.

References

1 J. C. Keske and B. H. Pate, Annu. Rev. Phys. Chem., 2000, 51,

323–353.

2 O. L. Polyansky, N. F. Zobov, S. Viti, J. Tennyson,

P. F. Bernath and L. Wallace, Science, 1997, 277, 346–348.

3 H.-M. Frey, P. Beaud, T. Gerber, B. Mischler, P. P. Radi and

A. P. Tzannis, Appl. Phys. B: Lasers Opt., 1999, 68, 735–739.

4 M. P. Jacobson, C. Jung, H. S. Taylor and R. W. Field,

J. Chem. Phys., 1999, 111, 600–618.

5 J. Ma, D. Xu, H. Guo, V. Tyng and M. E. Kellman, J. Chem.

Phys., 2012, 136, 014304.

6 A. S. Mullin, C. A. Michaels and G. W. Flynn, J. Chem. Phys.,

1995, 102, 6032–6045.

7 M. G. White and R. J. Beuhler, J. Chem. Phys., 2004, 120,

2445–2455.

8 V. S. Letokhov, Laser photoionization spectroscopy, Academic

Press, 1987.

9 M. N. R. Ashfold and J. D. Howe, Annu. Rev. Phys. Chem.,

1994, 45, 57–82.

10 M. N. R. Ashfold, J. M. Bayley and R. N. Dixon, Chem. Phys.,

1984, 84, 35–50.

11 A. Sur, C. V. Ramana, W. A. Chupka and S. D. Colson,

J. Chem. Phys., 1986, 84, 69.

12 J. Karczmarek, J. Wright, P. Corkum and M. Ivanov, Phys.

Rev. Lett., 1999, 82, 3420–3423.

13 D. Villeneuve, S. Aseyev, P. Dietrich, M. Spanner, M. Ivanov

and P. Corkum, Phys. Rev. Lett., 2000, 85, 542–545.

14 L. Yuan, S. W. Teitelbaum, A. Robinson and A. S. Mullin,

PNAS, 2011, 108, 6872–6877.

15 L. Yuan, C. Toro, M. Bell and A. S. Mullin, Faraday Discuss.,

2011, 150, 101–111.

16 A. Korobenko, A. A. Milner and V. Milner, arXiv preprint

arXiv:1304.0438, 2013.

17 PGOPHER, a Program for Simulating Rotational Structure, C. M.

Western, University of Bristol, http://pgopher.chm.bris.ac.uk.

18 K. P. Huber and G. Herzberg, NIST Chemistry WebBook, NIST

Standard Reference Database, National Institute of Standards

and Technology, Gaithersburg MD, 2012, vol. 69.

19 B. R. Lewis, S. T. Gibson, J. S. Morrill and M. L. Ginter,

J. Chem. Phys., 1999, 111, 186.

20 G. Herzberg, Molecular spectra and molecular structure, Krieger

Publishing Co., Malabar, Florida, 2nd edn, 1950, vol. I.

21 J. Czarny, P. Felenbok and H. Lefebvre-Brion, J. Phys. B: At.

Mol. Phys., 1971, 4, 124.

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