Dynamics of molecules in extreme rotational statesLiwei Yuan, Samuel W. Teitelbaum1, Allison Robinson, and Amy S. Mullin2

Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742

Edited by F. Fleming Crim, University of Wisconsin, Madison, WI, and approved March 8, 2011 (received for review December 12, 2010)

Wehave constructed an optical centrifugewith a pulse energy thatis more than 2 orders of magnitude larger than previously reportedinstruments. This high pulse energy enables us to create largeenough number densities of molecules in extreme rotational statesto perform high-resolution state-resolved transient IR absorptionmeasurements. Here we report the first studies of energy transferdynamics involving molecules in extreme rotational states. In thesestudies, the optical centrifuge drives CO2 molecules into stateswithJ ∼ 220 and we use transient IR probing to monitor the subsequentrotational, translational, and vibrational energy flow dynamics.The results reported here provide the first molecular insights intothe relaxation of molecules with rotational energy that is compar-able to that of a chemical bond.

carbon dioxide ∣ rotational dynamics ∣ transient spectroscopy ∣high-energy molecules ∣ strong optical fields

Control of molecular energy for use in chemical and physicaltransformations requires tools for exciting specific degrees of

freedom in molecules. A number of methods exist for preparingmolecules with large, well-defined, and controllable amounts ofenergy in electronic, translational, and vibrational degrees offreedom, but until recently, it has been much more difficultto exert control over the rotational energy of molecules (1–14).Traditional methods for optically preparing rotationally hot mo-lecules are limited by strict selection rules that constrain angularmomentum changes to small values (15, 16). Microwave spectro-scopy has been used to a limited degree for walking molecules upa rotational ladder, but only small amounts of rotational energy(ΔJ ∼ 5) could be imparted to molecules with this approach (17,18). Static electric fields have been explored for orienting mole-cules, but this approach is impractical for rotating molecules intohigh-energy states due to the high angular velocity and voltagesrequired (19). Rotational motion in molecules can be inducedwith strong optical fields leading to rotational recurrences, butthe amount of rotational energy obtained with this method isfairly modest (19–25). In some cases, photochemical reactionsand inelastic collisions can be used to produce rotationally hotmolecules, but the products generally have broad and poorlycontrolled rotational energy distributions (26).

An important development in the area of light-matter inter-actions is the optical centrifuge for molecules (27, 28). In thisdevice, powerful ultrafast chirped laser pulses deposit rotationalexcitation in molecules that is comparable to, and in some caseseven exceeds, interatomic binding energies. The optical centri-fuge was proposed by Corkum and coworkers in 1999 and wasfirst demonstrated in 2000 (27, 28). They used an optical centri-fuge to spin Cl2 molecules into J ∼ 420 and used a time-of-flightmass spectrometer to detect Cl radicals that resulted from rota-tionally induced dissociation. The dissociation energy of Cl2 is3.5 eV, but rotational predissociation requires overcoming an an-gular momentum barrier that corresponds to a rotational energyof 4.5 eV and an angular momentum state of J > 420 (15, 29).

The observation of optically driven rotational predissociationshows that the optical centrifuge is an important tool for control-ling molecular behavior, but dissociation represents only oneoutcome of molecules that contain large amounts of rotationalenergy. It is known that centrifugal distortion induces bondlengthening in molecular rotors, but very little is known about

the extent of bond distortion for molecules in extreme angularmomentum states and how that distortion affects physical andchemical properties of molecules. To investigate molecules inextremely high rotor states, we have developed an instrumentthat couples an optical centrifuge with high-resolution transientIR absorption. High-resolution transient IR probing is a powerfultool for measuring time-dependent profiles for individual rota-tional quantum states following the optical centrifuge pulse andfor measuring how energy is partitioned among rotational, vibra-tional, and translational degrees of freedom.

The structure and electronic distribution of CO2 make it wellsuited for trapping in an optical centrifuge. CO2 has strong IRabsorption at λ ¼ 4.3 μm and its IR spectroscopy is well charac-terized for rotational states up to J ¼ 108 (30, 31). At 300 K, themost populated state of CO2 is J ¼ 16 and thermal population isdetected out to J ¼ 50 in our experiments. The current setup ofour optical centrifuge is estimated to be capable of exciting CO2

to J ∼ 220 but direct detection of the nascent high-J states is notpossible at this time because the spectroscopy of the very high-Jstates is unknown. Instead, we target transient populations ofCO2 in mid-J states (J ¼ 62–88) that are induced by the opticalcentrifuge. These states have rotational energies of Erot ¼ 1;440–3;050 cm−1 and are essentially unpopulated at 300 K. The actionof the optical centrifuge is characterized by the appearance anddepletion of population in these states and by their rotational andtranslational energy distributions. These data provide a detailedlook at the dynamics of molecules in extremely high rotationalstates. The ability to optically interrogate the dynamics of ex-treme rotational states opens an unexplored frontier in the studyof energetic molecules.

The optical centrifuge traps molecules using the electric fieldsof intense optical pulses. Angular acceleration of the field rotatesthe trapped molecules (27). When a molecule with a nonuniformpolarizability is placed in a linearly polarized, ac electric fieldfrom a nonresonant ultrafast laser pulse, the most polarizable axisof the molecule tends to align along the polarization vector of thefield, as shown in Fig. 1A. This process is analogous to Ramanscattering, in that the electric field creates an induced dipole mo-ment in the molecule that in turn interacts with the electric field.The energy of the interaction depends on the polarizability ani-sotropy (Δα) of the molecule times the square of the electric field,and the laser pulse creates a potential well for the molecule. Foran angle θ between the laser polarization and the axis of maxi-mum polarizability of the molecule (Fig. 1A), the potential energyis given by

U0 ¼ −1

4ΔαE2 cos2ðθÞ: [1]

The optical centrifuge is generated using two counterrotating,oppositely chirped laser pulses. The net field of the two pulses

Author contributions: L.Y., S.W.T., and A.S.M. designed research; L.Y., S.W.T., and A.R.performed research; L.Y., S.W.T., A.R., and A.S.M. analyzed data; and A.S.M. wrotethe paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1Present address: Department of Chemistry, Massachusetts Institute of Technology,Cambridge, MA 02139-4307.

2To whom correspondence should be addressed. E-mail: mullin@umd.edu.

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~Eoc is determined by the instantaneous frequencies of the twopulses, ω1 and ω2. The angular frequency of the optical trapΩoc is determined by the bandwidth of the optical pulse whereΔω ¼ ω1–ω2 withΩoc ¼ 1

2½ω1ðtÞ − ω2ðtÞ�. Initially, the wavelength

of the two reverse-chirped pulses is the same, and ω1 ¼ ω2. Overthe time of the centrifuge pulse (approximately 50 ps), ω1 goes tohigher frequency and ω2 goes to lower frequency, resulting in anincreasing frequency difference Δω. The optical pulses start atλ ¼ 803 nm and have maximum chirp of Δλ ¼ �20 nm. The rateof angular acceleration is chosen to balance being slow enoughto trap thermal molecules and fast enough to keep them in thetrap once they are rotationally excited. Fig. 1B shows the labframe angle ϕ of the optical field as it accelerates over the first20 ps of the centrifuge pulse. The field undergoes the first fullrotation in 4.4 ps. By 20 ps, the number of rotations has increasedto 20 and by the end of the 50-ps pulse, the field has undergone127 complete rotations.

The rotational energy of molecules in the optical centrifuge isErot ¼ 1

2I Ωoc

2, where Ωoc is the rotational frequency of the trapand I is the moment of inertia. Based on the bandwidth of ouroptical centrifuge, we estimate that CO2 molecules are drivento high rotational energies of about 19;000 cm−1, correspondingto the J ∼ 220 rotational state. Fig. 2 shows the calculated CO2

rotational energy during the optical centrifuge pulse. The quan-tum mechanical picture for this process is that molecules undergoa series of Raman transitions induced by the pair of chirpedpulses (32). At the beginning of the pulse, λ1 ¼ λ2. As the pulseevolves, the wavelength difference sweeps through sequentialRaman transitions with ΔJ ¼ þ2, ultimately leaving CO2 in theJ ∼ 220 state. The maximum extent of the wavelength spreadcorresponds to an energy difference of approximately 620 cm−1.The chirped energy difference is sufficient for CO2 rotationaltransitions near J ¼ 220, but is insufficient for the Raman-allowed vibrations, the (1000) and (0220) states at 1,285 and1;388 cm−1.

The effectiveness of the optical centrifuge depends on thepulse characteristics and the properties of the molecule (27, 33,34). The key elements are the angular acceleration of the trap,the laser intensity Eoc

2, the polarizability anisotropy Δα, and

the moment of inertia I. There are two important constraintsthat must be met for the efficient creation of highly rotationallyexcited molecules. The first criterion arises directly from Eq. 1:The product of the laser intensity (Eoc

2) and the polarizabilityanisotropy (Δα) must be significantly larger than the thermalenergy of rotation in order to create an effective trap. The secondcriterion concerns the rate of optical acceleration δ that willeffectively excite a sample of molecules. The rotating linearpolarization has an angular velocity that defines a turn-on timeof the trap. Molecules that are to be trapped start with a randomdistribution of orientations, and it is therefore necessary that thepolarization cover an angle of at least π while the beam is turningon. If the polarization rotation accelerates too quickly duringturn-on, the molecules cannot be trapped. These two criterialead to the following inequality that must be met in order for anoptical centrifuge to be effective:

8πδ

Eoc2<

ΔαI

: [2]

The left side of Eq. 2 corresponds to experimental parametersand the right side to molecular parameters. Simulations haveshown that the population of optically trapped molecules declinesprecipitously if this inequality is not met (27, 33, 34).

Molecules that can be optically centrifuged in an efficientmanner are identified by their values of Δα and Δα∕I. The valuesfor Cl2 and CO2 are listed in Table 1. These two molecules havebeen successfully centrifuged and they serve as reference pointsfor other candidates for the optical centrifuge.

The scheme for probing molecules in the optical centrifugeis depicted in Fig. 3. The optical centrifuge pulse drives CO2 mo-lecules at 300 K to rotational states near J ∼ 220. The centrifugedmolecules undergo a collisional cascade that induces transientpopulations in lower states. The transient populations in indivi-dual rovibrational states are interrogated using high-resolutiontransient IR absorption. The IR laser frequency is tuned to CO2

transitions that start from the vibrational ground state (0000) orthe (0330) state with 3 quanta of bend.

The optical centrifuge-IR absorption spectrometer is shownschematically in Fig. 4. The two centrifuge pulses are generatedfrom an amplified 10-Hz Ti:sapphire laser system. The oppositelychirped pulses are combined in a polarizing beam cube and coun-terrotating linear polarization is induced with a λ∕4 plate. Thecombined beams are focused to a 14-μm beam waist in a gas cellcontaining CO2 and the arrival of the pulses in the cell is madecoincident with a delay line. This setup provides energies up to100 mJ per pulse in the cell. The IR probe source is a continuouswave (cw) lead-salt diode laser operating at λ ¼ 4.3 μm with aspectral resolution of Δν ¼ 0.0003 cm−1. A single-mode of theIR laser passes through the gas cell and transient absorption iscollected with an InSb detector.

Results and DiscussionEvidence for Optically CentrifugedMolecules.We performed a seriesof tests to verify that molecules are driven to high-J states in theoptical centrifuge. For the trap to accelerate rotationally, both

Fig. 1. Behavior of molecules in rotationally accelerating strong opticalfields. (A) Molecules with nonuniform polarizability tend to align with theelectric field vector. (B) Trajectory of the lab frame angle for the electric fieldduring the optical centrifuge pulse, showing the angular acceleration of thefield.

Fig. 2. The calculated CO2 rotation energy and quantum number during theoptical centrifuge pulse.

Table 1. Molecular parameters for the optical centrifuge

Molecule Δα,* a03 I, 10−46 kgm2 Δα∕I‖, 1015 m∕kg Erot,

† cm−1

Cl2 18.74 11.6 2.4 30,507CO2 14.25 7.3 2.9 19,286

Molecular parameters for Cl2 and CO2 in an optical centrifuge are Δα (thepolarizability anisotropy), I (the moment of inertia), and the ratio of Δα to I.The rotational energy for these molecules is based on the moment of inertiaand the characteristics of our optical centrifuge.*The Bohr radius is a0 ¼ 5.29 × 10−11 m.†Based on the characteristics of our optical centrifuge.

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chirped pulses must be present. Fig. 5A shows the transientabsorption for CO2 (0000) in J ¼ 76 when each chirped beam(54 mJ) was independently introduced to the sample and whenboth beams were introduced together. Transient signal is seenonly when both beams of the centrifuge pulse are present indi-cating a two-photon response. When either of the oppositelychirped pulses was introduced alone, no signal was seen. Power-dependent measurements show that the transient signals increaselinearly with the optical centrifuge power. The maximum inten-sity occurs when the two chirped beams arrive in the sample cellconcurrently. The two-photon dependence rules out spontaneousRaman excitation of CO2 vibration with a single 800-nm photon.

The depletion of several thermally populated states of CO2

was measured in the optical centrifuge. We used isotopicallylabeled 13CO2 for these measurements, because ambient 12CO2

in the atmosphere and gas cell completely absorbs the IR light.The depletion was measured under low-pressure conditions(∼4 mtorr) where the average collision time is approximately20 μs. Fig. 5B shows that population is lost from the J ¼ 14 stateimmediately after the optical centrifuge pulse and that the statedoes not repopulate on the timescale of the measurement. Thedepletion is prompt and the rise time is limited by the detectorresponse time of 100 ns. The depletion signals are sensitive to theIR polarization and are maximized when the IR polarization isin the plane of rotation in the centrifuge. These results show thatthe depletion signals directly probe centrifuged molecules.

Transient population in the J ¼ 62–88 states of CO2 (0000) isinduced by the optical centrifuge. Transient signals for the J ¼ 76state are shown in Fig. 6. Fig. 6A shows prompt appearanceof population is followed by slower decay. Unlike the depletionsignals, the appearance of the J ¼ 60–88 states is not directly in-duced by the optical centrifuge. Instead, population in thesestates comes from a collisional cascade following the centrifugepulse. The CO2 pressure in these measurements is 10 torr, givingan average collision time of approximately 10 ns based on a 300-Ksample. Fig. 6B shows that the rise time of the appearance isslower than the detector response time and that the appearancerate increases when an He buffer gas is added. The decay signalsare also collision-induced with lifetimes that decrease as a func-tion of He pressure. In addition, transient signals for the J ¼ 62–88 states show no preference for IR polarization, consistent withorientational scrambling due to collisions.

Energy Evolution in the Optical Centrifuge. State-resolved transientabsorption is a window to view the evolution of the centrifugeenergy. In 50 ps, the optical centrifuge prepares CO2 moleculesin high rotational states with J ∼ 220 or higher. Centrifuged mo-lecules cool through collisions with uncentrifuged molecules at300 K and redistribute their rotational energy among the avail-able degrees of freedom: rotation, translation, and vibration.

The transient IR signals (such as in Fig. 6) for the J ¼ 62–88states of CO2 (0000) show that the population in these statesreaches a maximum at 360 ns, corresponding to approximately36 collisions. The population in these states includes uncentri-fuged molecules that are heated by collisions and centrifugedmolecules that are cooled by collisions. It is likely that the initialappearance of these states is dominated by energy gain in uncen-trifuged molecules because the energy and angular momentum ofthese states is closer to that distribution than to the distributionfor the centrifuged molecules.

The translational energy of molecules in the centrifuge wasdetermined by measuring Doppler-broadened transient line pro-files for individual rotational states of CO2. Transient absorption

Fig. 3. Scheme for measuring high-resolution transient IR absorption ofmolecules in extreme rotational states.

Fig. 4. Schematic of the optical centrifuge-transient IR absorption spectro-meter.

Fig. 5. Spectroscopic verification of optically centrifuged molecules. (A)Transient IR absorption of CO2 (0000) J ¼ 76 is observed only in the presenceof both beams of the optical centrifuge. (B) Transient IR absorption signalshowing prompt depletion of 13CO2 in the optical centrifuge.

Fig. 6. Transient IR absorption signals for CO2 (0000) J ¼ 76 following theoptical centrifuge pulse. (A) Rapid appearance of population followedby slow decay. Decay times decrease with increasing He buffer gas pressure(Inset), showing that collisions induce the relaxation. (B) Early time signalfor appearance of population. The rate of appearance increases with Hepressure (Inset), indicating the population in the J ¼ 76 state is part of acollisional cascade initiated by the optical centrifuge pulse.

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signals collected as a function of IR wavelength provide a mea-sure of the line profile as a function of time. The line profile forCO2 (0000) J ¼ 76 at t ¼ 350 ns following the centrifuge pulse isshown in Fig. 7A. The line profile is broadened relative to the300-K profile, indicating that the scattered molecules have gainedtranslational energy. For the J ¼ 76 state, the translational tem-perature at 350 ns is Ttrans ¼ 1;130 K. The line profiles narrow asfunction of time due to collisional cooling, as shown in Fig. 7B.The translational energy decays with a lifetime of 1.3 μs and levelsout at Ttrans ¼ 450 K. This result shows that rotation-to-transla-tion energy transfer takes place promptly after the centrifugepulse and that by about 130 collisions the translational energyhas equilibrated locally. This local equilibrium persists for severalhundred microseconds. Eventually diffusion and subsequentrelaxation return the system to 300 K before the next centrifugepulse.

The evolution of rotational energy in the optical centrifuge wasinvestigated by measuring the rotational distribution for the J ¼62–88 states as a function of time. Relative populations of CO2 inindividual J states were determined from transient signals col-lected at line center. A semilog plot of the degeneracy-weightedpopulations at t ¼ 350 ns is shown in Fig. 8A as a function ofrotational energy. The slope yields a rotational temperature ofTrot ¼ 840 K. The rotational temperature for these states initiallydrops as a function of time, as shown in Fig. 8B, and then showsa slow increase to a final temperature of Trot ¼ 600 K. The dataare fit to the sum of an exponential decay and an exponentialgrowth. The fit reveals a rapid initial cooling that takes placein approximately 57 collisions and has a final Trot ¼ 460 K.The slower increase in rotational energy takes approximately1,200 collisions and results in a local equilibrium with Trot ¼600 K. The observation of prompt rotational heating of popula-tion in J ¼ 62–88 followed by rapid cooling is consistent withthe collisional cascade that relaxes the centrifuged molecules.The rotational heating that takes place on longer timescales in-dicates the presence of an energy bottleneck in the collisionalcascade.

It is likely that the energy bottleneck in the rotational coolinginvolves the relaxation of CO2 vibrational modes that are excitedin the centrifuge. To test this idea, we measured transient absorp-tion signals for a state with 3 quanta in the ν2 bending mode,(0330). The state has a vibrational energy of 1;951 cm−1 and isnot populated at 300 K. Transient absorption for the (0330) J ¼43 state indicates the appearance of population in the centrifuge.Fig. 9A shows the transient line profile for this state which has atranslational temperature of Ttrans ¼ 1;147 K at 500 ns after thecentrifuge pulse. The translational energy decays with time, asshown in Fig. 9B, and eventually levels out to Ttrans ¼ 540 Kin 3.3 μs (approximately 330 collisions). Fig. 9C shows that thepopulation in (0330) J ¼ 43 decays in 5.1 μs (approximately510 collisions) to about 25% of the value at 500 ns.

The relatively slow decay of the (0330) state is consistent withthe long-time appearance of rotation in (0000). The relaxationtimes for the (0330) state are somewhat faster (3.3 μs) thanthe rotational appearance (12 μs) in (0000), but the (0330) stateis just one of the vibrations likely to be excited in the centrifuge.The lower energy bending states, (0110), (0200), and (0220), arelikely to be populated as well, and their one-quantum relaxationrates should be slower than that of the (0330) state. For dipole-mediated relaxation that involves single-quantum changes invibration, the probability for (0330) relaxation is 3 times greaterthan that for the (0110) state, based on the coupling matrix ele-ments. Additional contributions from the higher frequencystretching modes may contribute as well.

The observation that CO2 molecules have increased rotationaland translational energy from relaxation of centrifuged moleculesprovides a measure of the energy imparted by the centrifugepulse. The quasi-equilibrium distributions of CO2 (J ¼ 62–88)have rotational and translational temperatures near 450 K fol-lowing the collisional cascade of centrifuged molecules. Eq. 3describes the total energy in the optical centrifuge before andafter the collisional cascade:

Fig. 7. Transient absorption measurements of translational energy distribu-tions for CO2 (0000) J ¼ 76. (A) Doppler-broadened line profile at t ¼ 350 nsfollowing the optical centrifuge pulse. The broadening corresponds to atranslational temperature of 1,130 K. (B) Translational temperaturesdecrease as a function of time due to collisional cooling. The translationenergy remains elevated after many collisions due to the energy added byoptical centrifuge.

Fig. 8. Transient absorption measurements of the rotational energy for CO2

(0000) J ¼ 62–88 following the optical centrifuge pulse. (A) Semilog plotof the degeneracy-weighted population as a function of rotational energy.The rotational temperature is 840 K at t ¼ 350 ns. (B) Time dependence ofthe rotational temperature. Initially, large amounts of rotational energy arepresent following the centrifuge pulse and collisions rapidly reduce therotational energy spread. At longer times, the rotational temperature gra-dually increases, due to an energy bottleneck in the collisional cascade. It islikely that vibrational cooling is responsible.

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ErotNJ þ kTiðNtot −NJÞ þ3

2kTiNtot ¼

5

2kTfNtot: [3]

The first two terms on the left side of Eq. 3 account for the initialrotational energy prior to collisional relaxation. Erot is the centri-

fuge-induced rotational energy and NJ is the number density ofcentrifuged molecules. Ntot is the total number density in the cell,k is Boltzmann’s constant, and Ti ¼ 300 K. The third term is theinitial translational energy. The term on the right side of Eq. 3describes the quasi-equilibrated distribution. For a final tempera-ture Tf ∼ 450 K for rotation and translation and Erot of the J ¼220 state of CO2, we find that NJ is approximately 2% of the totalnumber density along the IR probe volume.

Concluding RemarksUntil recently, there has not been a way to produce and studymolecules in extremely high rotational states. Our combinationof an optical centrifuge with high-resolution transient IR probingprovides detailed insights into the dynamics of molecules inextreme rotational states. This work paves the way for lookingat reactivity, structure, rotation-vibration coupling, and otherunique aspects of molecules with rotational energies comparableto chemical bond energies. This approach has the potential fordeveloping different types of chemistry and providing insightsinto molecular motion, structure, and interactions.

Materials and MethodsAn ultrafast (40 fs) Ti:sapphire laser system (Coherent) is the core of theoptical centrifuge system. An 80-MHz Ti:sapphire laser pulse is stretchedto 50 ps and positively chirped. The pulse enters a regenerative amplifierand its power is amplified to 1.2 mJ at a 1-kHz repetition rate. The opticalpulse is split in half spectrally and a negative chirp is induced in one beamusing a pair of gratings. The power for each beam is increased to 50 mJ witha four-pass Nd:yttrium/aluminum-garnet-pumped amplifier, operating at10 Hz. A delay line controls the time delay between the two pulses. The ne-gatively chirped pulse passes through a λ∕2 plate to rotate the polarizationby 90°. The two beams are combined in a polarizing cube, passed througha λ∕4 plate to induce opposite circular polarization, and then focused to a28-μm diameter beam waist. The focal point of the chirped pulses is posi-tioned in a cell containing 10 torr or less of gas. A high-resolution cwmid-IR diode laser (Laser Photonics) operating at λ ¼ 4.3 μm is crossed withthe optical centrifuge beam and transient signals are collected on an InSbdetector. The IR transitions correspond to one-quantum absorption of ν3antisymmetric stretch transitions ð0000Þ → ð0001Þ. The single-mode lead-saltdiode laser has sub-Doppler resolution (ΔνIR ¼ 0.0003 cm−1) that allowsboth state and velocity-resolved transient absorption. The CO2 is 99.99%purity (Matheson Tri-gas).

ACKNOWLEDGMENTS. We thank Profs. Paul Corkum and John Fourkas formany helpful discussions. Generous research support was provided by theUniversity of Maryland and The Arnold and Mabel Beckman Foundation.S.W.T. was a Beckman Scholar during this research.

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