Journal of Molecular Spectroscopy 280 (2012) 77–84

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Journal of Molecular Spectroscopy

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Multi-resonance effects within a single chirp in broadband rotational spectroscopy:The rapid adiabatic passage regime for benzonitrile

David Schmitz, V. Alvin Shubert, Thomas Betz, Melanie Schnell ⇑Center for Free-Electron Laser Science, Notkestrasse 85, D-22607 Hamburg, GermanyMax-Planck-Institut für Kernphysik, Saupfercheckweg 1, D-69177 Heidelberg, Germany

a r t i c l e i n f o

Article history:Available online 14 August 2012

Keywords:Broadband rotational spectroscopyDouble resonanceChirped pulseRapid-adiabatic passage

0022-2852/$ - see front matter � 2012 Elsevier Inc. Ahttp://dx.doi.org/10.1016/j.jms.2012.08.001

⇑ Corresponding author at: Center for Free-Electron85, D-22607 Hamburg, Germany. Fax: +49 40899862

E-mail address: melanie.schnell@asg.mpg.de (M. S

a b s t r a c t

We report here pronounced, stepwise multi-resonance excitations in benzonitrile arising from a single1 ls broadband 2–8.3 GHz microwave chirp, observed with our new chirped-pulse broadband rotationalspectrometer, COMPACT. Such multi-resonance excitations significantly alter the relative intensity pat-terns and are a strong indication that, for the given experimental conditions and using benzonitrile asa polar test molecule (lA = 4.5152 D), the rapid adiabatic passage (RAP) regime for strong coupling mustbe applied. This finding is contrary to previous discussions of chirped-pulse rotational spectroscopy,where the linear fast passage regime of weak coupling has been assumed.

� 2012 Elsevier Inc. All rights reserved.

1. Introduction

Currently, the field of high-resolution rotational spectroscopy isbeing revolutionized, driven by recent major advancements in thetechnology of test and measurement equipment. In 2008, Pate andcoworkers reported a novel broadband rotational spectrometer de-sign employing a short, intense microwave chirp that allows forrecording the rotational spectra of complex, flexible moleculeswith a single acquisition [1]. With this new chirped-pulse Fouriertransform microwave (CP-FTMW) technique, broadband operationof up to 12 GHz has been demonstrated, therefore eliminating oneof the main disadvantages of conventional cavity-based FTMWspectroscopy, which has been its slowness. Depending on theexperimental parameters and the respective molecules understudy, the CP-FTMW technique is approximately 2–3 orders ofmagnitude faster than cavity-based FTMW spectroscopy forrecording spectra covering several GHz and with comparable sig-nal-to-noise ratios [1] while still offering a high spectral resolutionon the order of 40 kHz. As a comparison, the spectral resolution of acavity-based spectrometer is 1–3 kHz. The high speed of CP-FTMWspectroscopy, combined with its sensitivity, is accelerating themove of the field towards investigating the structure and dynamicsof larger and more complex molecules, including advanced double-resonance techniques such as dynamic rotational spectroscopy [2]and two-dimensional chirped-pulse Fourier transform microwavespectroscopy [3].

ll rights reserved.

Laser Science, Notkestrasse30.chnell).

In a typical experiment, within a chirp the microwave fre-quency is linearly swept over several GHz in a few hundrednanoseconds up to a few ls. The excitation power varies froma few Watts to kiloWatts. If the difference in energy betweentwo rotational energy levels of the molecules under investigationis resonant to a frequency within the chirp, the two respectiverotational energy levels will be coupled, i.e., a coherent superpo-sition is created. This excitation creates a macroscopic polariza-tion, and the free-induction decay (FID) of this macroscopicpolarization is recorded using a fast digital oscilloscope, after ithas been amplified with a low-noise microwave amplifier. Thedescription of the macroscopic polarization from a fast frequencysweep has been derived previously [1,4–7]. The important ad-vance of CP-FTMW spectroscopy compared to previous experi-ments (such as Stark sweeping) is that it is now possible toperform broadband chirped pulse excitation on a time scaleshorter than the transient emission time (T2) which is on the or-der of 10 ls. This advance became possible with the new gener-ation of arbitrary waveform generators (AWG), and it also allowsfor detecting the molecular emission in the absence of the polar-ization pulse.

Depending on the particular experimental conditions, a largechange in the population difference of the states in resonance(within the rapid adiabatic passage (RAP) regime for strong cou-pling) or in the coherence of the two-level ensemble (linear fastpassage (LFP) regime for weak coupling) can be achieved. For thelinear fast passage regime, Pate et al. discuss in Ref. [1] that themolecular signal from chirped pulse excitation has the form

S / x � l2 � Epulse � DN0 �pa

� �12; ð1Þ

78 D. Schmitz et al. / Journal of Molecular Spectroscopy 280 (2012) 77–84

with a being the sweep rate, x the frequency, l the transition di-pole moment, Epulse the electric field strength of the microwaves,and DN0 the population difference at equilibrium, assumed to beunchanged by the pulse. As discussed in Section 3, this conditionis true for the weak pulse limit within the linear fast passage re-gime. So far, this has been assumed to be applicable for high band-width measurements for all practical amplifier choices.

In this work, we describe our new CP-FTMW spectrometerCOMPACT, that covers the 2–8.5 GHz frequency range and utilizesa 300 W Traveling Wave Tube (TWT) amplifier. Using benzonitrileas a test molecule (la = 4.5152 D [8]), we observe pronounced,stepwise multi-resonance excitations arising from a single micro-wave chirp that significantly change the obtained intensities. Theseobservations strongly indicate that the excitations take place with-in the RAP regime. In this work, we will first introduce our newspectrometer, COMPACT (Section 2), introduce the two limiting re-gimes LFP and RAP (Section 3), and discuss them along with ourexperimental results on benzonitrile (Section 4). These results havenotable implications for the future intensity treatment and analy-sis of chirped-pulse rotational spectra.

2. Experimental

Benzonitrile (98%, Sigma–Aldrich) was used without furtherpurification. It is a liquid at room temperature with a melting pointof �13 �C and a boiling point of 191 �C. Neon was used as the car-rier gas (with 2–3 bars backing pressure) and flowed through aheated reservoir (40 �C) containing benzonitrile. The molecules,seeded into the carrier gas, were introduced into the vacuumchamber through a pulsed valve (General valve Series 9) andcooled by supersonic expansion. The molecular jet propagated per-pendicular to the horn antennas and thus to the microwave excita-tion field.

Fig. 1 displays a scheme of our new chirped-pulse Fourier trans-form microwave spectrometer, COMPACT (compact-passage ac-quired coherence technique). It is a combination of the designspresented by Pate et al. [1,9] and of that proposed by Grabow[7]. For experiment control, the program FTMW++ of Grabow(Leibniz-Universität Hannover) is employed. The heart of the spec-trometer is an arbitrary waveform generator (Tektronix AWG7122A) that creates the microwave chirps. We use chirps spanningthe 2–8.5 GHz frequency range, i.e., within a short time (typically100 ns to 5 ls) the microwave frequency is swept linearly from 2to 8.5 GHz or vice versa. The operating frequency range of ourspectrometer is currently limited by the specifications of the trav-eling wave tube amplifier (Amplifier Research 300T2G8) and thehorn antennas (Advanced Technical Materials 250-441EM-NF).The frequency range was chosen for the investigation of largeand complex molecules with large moments of inertia and thussmall rotational constants, leading to low transition frequencies.

The low frequency chirped-pulse rotational spectrometer offersseveral interesting properties. In cavity-based FTMW spectroscopy,the physical size of the microwave cavity becomes an importantaspect at low frequencies. Microwave reflectors as large as 48 in.(about 122 cm) are used to access the low frequency range downto 1 GHz [10]. Physical size is less of a problem with chirped-pulsespectroscopy using horn antennas. Furthermore, in our experi-ments the ultimate line width scales linearly with frequency, sincethe dephasing time is related to Doppler motion. Thus, in principle,higher resolution can be achieved in the lower frequency range ascompared to the higher frequency range (7–18 GHz) employedmore often [1]. In addition, many molecular features, such as theK manifolds for asymmetric-top molecules, become more compli-cated with increasing rotational quantum number J, so having ac-cess to low J transitions is very valuable.

The microwave excitation chirp is amplified by the adjustabletraveling wave tube (TWT) amplifier with a maximum outputpower which is frequency-dependent and at least 300 W. Fig. 2shows a spectrogram of the excitation pulse after the TWT ampli-fier. The spectrogram was obtained by recording the output of theTWT at 6% gain with a 48 ls chirp spanning 1–9 GHz. Fast Fouriertransformations (FFTs) were performed on 100 ns slices and thenplotted together to give the frequency output as a function of time.A 48 ls chirp was chosen so that the full chirp could be recordedwith 5 million points at resolution of 10 ps with the oscilloscope.A setting of 6% gain was the maximum that could be used beforeportions of the chirp were too large in amplitude to be recordedby the oscilloscope. As described by Neill et al. [9], the amplifierintroduces spurious components, particularly the sidebands 2m(t)and 3m(t), with m(t) being the original chirp. These spurious partsare low in intensity relative to the primary chirp. Under certainexperimental conditions, however, they are sufficiently intense topolarize the molecular sample: With a 100% gain setting on theTWT amplifier and a linear chirp from 2 to 3 GHz to selectively ex-cite the 101 000 transition of benzonitrile located at 2.76 GHz, wealso saw that the 202 101, the 211 110 and the 212 111 transi-tions located between 5 and 6 GHz were significantly polarized bythe 2m(t) sideband (4–6 GHz) generated by the TWT amplifier, giv-ing rise to these transitions being observed in the spectrum. How-ever, usually sideband effects are assumed to be too weak tosignificantly influence the relative intensity accuracy of the ob-served molecular transitions, particularly when using less polarmolecules and when covering the whole frequency range of thespectrometer with the fundamental chirp m(t).

After amplification, the excitation chirp is transmitted into thevacuum chamber using horn antennas. In our setup, the distancebetween the horn antennas is approximately 42 cm. The moleculesare supersonically expanded into the vacuum chamber, where theyinteract with the microwave excitation pulse. If a frequency of thechirp is resonant with a molecular transition, the molecular sampleis polarized, i.e., a macroscopic dipole moment is formed. Its decayis monitored as a function of time as a free-induction decay (FID).The rotational spectrum is obtained via fast Fourier transformationof the FID, after it has been amplified with a low-noise microwaveamplifier (Miteq Amplifier AMF-5F-0200080-15-10P). All fre-quency sources and the oscilloscope (Tektronix DPO 71254A) arephase-locked to a 10 MHz Rb-disciplined quartz oscillator (Stan-ford Research FS 725). On the receiver end, a high-power diodelimiter (Aeroflex ACLM-4535) and a solid-state, single-pole sin-gle-throw (SPST, Advanced Technical Materials S1517D) switchare integrated to protect the sensitive receiver electronics fromthe high-power excitation pulse (Fig. 1). In our current setup, theresolution is mainly determined by Doppler broadening and thelength of the recorded FID (typically 30–50 ls), and it is about40 kHz.

Fig. 3a shows the 2–8 GHz rotational spectrum of our test mol-ecule, trifluoroiodo methane (CF3I), after 1, 10, 100, and 1000 FIDacquisitions obtained with our COMPACT spectrometer using neonas a carrier gas and two simultaneously operated valves. CF3I is asymmetric top with rotational energy levels that can be describedby the rotational quantum numbers J,K,F = jJ + Ij, jJ + I � 1j, . . . , jJ � Ijand the nuclear spin I. The individual rotational transitions arehyperfine-split due to nuclear quadrupole coupling of the iodinenuclear spin (I = 5/2) with the total angular momentum. Theresulting splitting pattern and its intensities are very characteristicand can facilitate the spectral assignments. As can be seen, themain features of the rotational spectrum are already seen afterone FID acquisition. After 1000 acquisitions (about 9 min recordingtime), all of the spectral features are resolved with a good signal-to-noise ratio. Fig. 3b displays a comparison of the experimentaland the calculated rotational spectrum for the J + 1 J: 2 1

Fig. 1. Schematic of the Hamburg COMPACT microwave spectrometer covering the 2–8.5 GHz range. Both trigger lines and microwave cables are indicated.

Freq

uenc

y (G

Hz)

0 5 10 15 20 25 30 35 40 45

2

4

6

8

10

12

14

16

18

Time (µs)

Fig. 2. Time–frequency analysis of the chirp after TWT amplification indicating thespectral range of the excitation pulse as well as spurious components due to theamplifier. The intensity is plotted on a square-root scale.

D. Schmitz et al. / Journal of Molecular Spectroscopy 280 (2012) 77–84 79

transition of CF3I. The intensities for the various hyperfine transi-tions can be calculated following text book procedures (see, forexample, Ref. [11]). The experimental intensities of chirped-pulseFTMW spectroscopy, when working in the linear-fast passage re-gime, are accurate over the relevant frequency range and agreewell with the calculated ones. This feature is extremely useful forthe assignment of new species, in determining relative dipole com-ponents, and in estimating the relative populations of differentspecies that contribute to the spectrum. The occurrence of step-wise multi-resonance effects can significantly alter the observedintensities and is the main topic of this article. In the experiments

described in the following, we study the multi-resonance excita-tions in benzonitrile arising in chirped-pulse rotational spectros-copy by using different gain settings on the TWT amplifier,ranging from a few percent gain to full power (gain = 100%).

3. The linear fast passage vs. the rapid adiabatic passage regime

In the experiments, the microwave frequency is swept througha molecular resonance in a short time compared to the relaxationtime (fast passage). Consequently, spontaneous decay and dephas-ing will be neglected throughout the discussion. The sweep rate ais defined as

a ¼ @Dxab

@t; ð2Þ

with Dxab being the detuning of the sweep frequency from themolecular resonance, xab. Fast passage can be rationalized as tran-sient absorption during the sweep, followed by transient emissionafter the sweep. Although the molecules are in resonance only fora very short time, a large change in the population difference ofthe states in resonance or in the coherence of the two-level ensem-ble can be achieved, strongly depending on the particular experi-mental conditions. Here, the coupling of the molecules to themicrowave field is particularly important. It is characterized bythe Rabi frequency, X0, the frequency of the population oscillatingbetween the two states of the resonance. It parameterizes thestrength of the interaction of the molecule with the electromagneticfield. According to

X0 ¼ la � EPulse=�h; ð3Þ

it is proportional to the molecular transition dipole moment la.Two different regimes of fast-passage phenomena should be

mentioned here: For strong coupling (large X0), it is necessary towork in the rapid adiabatic passage (RAP) regime in order to de-scribe the transient effects during the course of the chirp [12,13],

Fig. 3. Rotational spectrum of trifluoroiodo methane (CF3I) obtained with the Hamburg COMPACT spectrometer after 1, 10, 100 and 1000 acquisitions using two valvessimultaneously and neon as carrier gas (a). The J + 1 J: 1 0 (around 3 GHz) and the J + 1 J: 2 1 (around 6 GHz) rotational transitions are displayed. Both transitionsare split due to nuclear quadrupole coupling arising from the iodine nucleus. Part (b) shows a comparison of the experimental spectrum (J + 1 J: 2 1 rotational transition)with a simulation indicating the very good agreement for both the frequencies and the intensities of the quadrupole hyperfine transitions.

80 D. Schmitz et al. / Journal of Molecular Spectroscopy 280 (2012) 77–84

while the linear fast passage (LFP) regime should be used for weakcoupling (small X0). We first consider the case of RAP, which is awell-known technique in atomic physics to selectively prepareatoms in specific states, i.e., to allow for a controlled and efficientpopulation transfer to a specific state using, for example, chirpedlasers [13].

During the sweep process, the molecules are initially in a pop-ulation distribution of states cooled into during the supersonicexpansion and the electromagnetic field is far below resonance.In the Bloch vector representation (Fig. 4) assuming the rotating-wave approximation, the situation can be described with the Blochvector H and the driving vector X being nearly aligned with the w-axis (Fig. 4a). As is worked out in more detail in Ref. [7], the drivingvector X is defined as

Xðr; tÞ ¼X0ðr; tÞ

0xab

0B@

1CA; ð4Þ

see Fig. 4b.Then, H precesses on a very narrow cone about X. This preces-

sion is very rapid with an angular frequency given by

XabðrÞ ¼ X20ðrÞ þ Dx2

ab ð5Þ

(single frequency case), with X0 being the Rabi frequency (vide su-pra) and Dxab the detuning of the microwave frequency frommolecular resonance xab (vide supra) [7]. For the fast passage exper-iment, with the detuning being time-dependent (Dxab(t)), we have

Xabðr; tÞ ¼ X20ðr; tÞ þ Dx2

abðtÞ: ð6Þ

According to Eq. (3), if the coupling X0 of the molecular system tothe electromagnetic field is strong, the precession is very rapid evennear resonance, where Dxab vanishes. If we now start to sweep thefrequency towards resonance, the angle h between X and the w-axisincreases. However, if the reorientation is small compared to theprecession frequency, i.e., if dh/dt�Xab(t), the Bloch vector H fol-lows the driving vector X smoothly (Fig. 4a). Within a doubly rotat-ing framework [7], the RAP experiment can be described as follows.Initially, at h = 0, the Bloch vector H and the driving vector X areparallel. Then, with dh/dt – 0, the experiment starts. As long as

dh/dt�Xab(t), the precession continues at a small angle until, ath = p, the experiment is stopped. Thus, within the strongly coupledRAP regime, performing a linear frequency sweep, that is equivalentto h = 0 ? p in the Bloch representation, can result in a large popu-lation transfer from one diabatic state to another diabatic state andeven to complete population inversion wab ¼ �wð0Þab at a rather smallremainder of coherence, as seen in Fig. 4. The term adiabatic refersto the Bloch vector H, which follows its precession axis X smoothly.The effect is not adiabatic in the sense that no transitions are made.

We now consider the case of weak coupling and weak fields, theso-called linear fast passage (LFP) regime. If the coupling X0(t) tothe electromagnetic field is less strong, the precession describedby Eq. (6) becomes slow near resonance, where Dx2

abðtÞ vanishes.If, in the experiment, we now start to sweep the frequency towardsresonance, the reorientation might no longer be small compared tothe precession frequency, and dh/dt�Xab(t) loses its validity. Con-sequently, the Bloch vector H cannot smoothly follow the drivingvector X anymore (see Fig. 4d + e). This problem can be solved ana-lytically with the simplification that the sweep rate a is much fas-ter than the Rabi frequency (a�X0(t)2, low-power regime), whichis the basic assumption of the LFP regime. In its pure form, it im-plies that dh/dt�Xab(t). In this regime we assume that the popu-lation difference is only insignificantly affected when the externalmicrowave field is swept through resonance (see also the discus-sion associated with Eq. (1) in the introduction). In the linear fastpassage regime, as shown in Fig. 4f, maximum coherence is ob-tained rather than the population inversion observed in the RAPregime.

Thus, the rapid adiabatic passage in its pure form leads to a ‘‘p-pulse’’ analogue (population inversion), while the LFP produces re-sults which can approach the ‘‘p/2-pulse’’ analogue, as illustratedin Fig. 4c and f.

A feature of broadband rotational spectroscopy is that anymolecular transition b a in the band passed by the frequencychirp xab(t) will be polarized. Since it is possible that the passageincludes transitions that share a common level, multi-resonanceeffects must be considered. In the LFP regime, as stated above,d(DNab)/dt � 0 and thus population effects that modify DNab arenegligible. Similarly, coherence effects which might alter thecoherence terms of the first resonance being excited are minor in

u

v

w

Θ

Δωab >> Δωab<

u

v

w

Θ Δωab

u

v

w

Θ

−Δωab>>

u

v

w

Θ

u

v

w

Θ

−Δωab >>

u

v

w

Θ

−Δωab>>

(a) (b) (c)

(d) (e) (f)

Rapid Adiabatic Passage (RAP) regime

Linear Fast Passage (LFP) regime

0

Fig. 4. Bloch vector representation of the fast passage procedures in the rapid adiabatic passage (a–c) and in the linear fast passage regime (d–f). (a) Initial detuning of theexternal field far below resonance. (b) RAP of the external field; the Bloch vector H follows the driving vector X adiabatically. (c) Population inversion at final detuning of theexternal field far above resonance, achieved in the RAP regime. (d) Linear fast passage of the external field. (e) Molecular coherence at final detuning of the external field farabove resonance. (e) Optimal coherence at final detuning of the external field far above resonance, when p/2 conditions are employed.

D. Schmitz et al. / Journal of Molecular Spectroscopy 280 (2012) 77–84 81

the LFP regime. Thus, an LFP across molecular resonances in suffi-ciently short time with respect to the relaxation times, i.e.,1=a� T2

2, can uniformly excite all transitions in a broad band forsimultaneous observation with the chirp FTMW spectroscopy tech-nique. To date, across a range of several GHz broad chirps swept ina few ls and amplified with high-power traveling wave tube(TWT) amplifiers in investigations of molecules with dipole mo-ments of up to a few Debye, no indications of multi-resonance ef-fects have been observed. For example, Neill et al. showed in theirstudy of the broadband rotational spectrum of iodobenzene(la = 1.6250(20) D) very good intensity agreement between exper-iment and simulation (Fig. 5 of Ref. [9]). Thus, the LFP regimeseems to be a good approximation for these experiments.

In the RAP regime of strong coupling, where large populationtransfers and even population inversion can occur, the situationis significantly different. Here, stepwise multi-resonance effectscan alter the relative intensities of the observed rotational transi-tions. We experimentally observed these effects for benzonitrile(la = 4.52 Debye), as discussed in the following section.

4. Results

The concept of adiabatic passage is not limited to two-state sys-tems, but can be extended to multiple levels, which is essential forthe effects observed in this work. For example, in atomic physics,adiabatic passage using a single pulse has been extended to athree-state ladder system, using the example of the 5s � 5p � 5dtransition in rubidium [14–17]. In this approach, virtually com-plete population transfer from the 5s state to the 5d state wasachieved. In addition, coherent population transfer was demon-

strated by chirped microwave pulses in the sodium s–p Rydbergladder [18]. In a related experiment using lithium, control overthe electron orbits using microwave radiation was achieved, i.e.,the increase or decrease of the velocity of the orbital motion ofthe electron by increasing or decreasing the microwave frequency[19].

Let us now have a closer look at the observed multi-resonanceeffects for benzonitrile induced by a single chirp, that can be de-scribed and understood within the rapid adiabatic passage regime.

Benzonitrile, displayed in the inset of Fig. 5a, is a near-prolatesymmetric top with the rotational constants A = 5655.2654(72)MHz, B = 1546.875864(66) MHz and C = 1214.40399(10) MHz, anda dipole moment la=4.5152 D [8]. Due to the symmetry of the mol-ecule (only la – 0), only a-type transitions with the selection rulesDKa = 0, (±2,±4, . . .) and DKc = ±1, (±3,±5, . . .) are allowed, whichfacilitates both the spectrum and its analysis. Furthermore, due tothe nuclear spin of the nitrogen nucleus (IN = 1), a characteristic nu-clear quadrupole splitting occurs.

Fig. 5a presents the rotational spectra of benzonitrile in the2–8.3 GHz frequency range obtained using a chirp-up pulse(2–8.3 GHz, upper trace) and a chirp-down pulse (8.3–2 GHz, lowertrace) and a low-gain setting on the TWT amplifier (50%, corre-sponding to about 75 W output power). The individual rotationaltransitions are labeled using the JKa ;Kc

quantum numbers. Azoom-in of this overall scan, showing the quadrupole hyperfinestructure, is displayed in Fig. 6 and discussed in more detail below.In Fig. 5a, the relative intensities are nearly identical in both spec-tra (chirp up and chirp down). Thus, with the described experi-mental settings, the chirp has a negligible effect on the relativepopulations of the rotational states. As described by the linear fast

frequency (GHz)

sign

al in

tens

ity (µ

V)(a)

frequency (GHz)

sign

al in

tens

ity (µ

V)

(b)

000

101

202

303

111

212

313

110

211

312

221

322

220

321

ω3

ω2

ω1

(c)

linear fast passage regime rapid adiabatic passage regime

101 000

212 111

202 101

211 110

313 212

303 202

Fig. 5. Broadband rotational spectra (2–8.3 GHz frequency range) for benzonitrile with reduced microwave power and thus in the linear fast passage regime (50% gain for theTWT amplifier (a)) and with full microwave power (rapid adiabatic passage regime, 100% gain (b)). The upper traces correspond to chirp-up measurements (2–8.3 GHz) whilethe lower traces correspond to chirp-down measurements (8.3–2 GHz). In (c), an energy level scheme for the rotational states, labeled with the JKa ;Kc

quantum numbers ofbenzonitrile, neglecting hyperfine structure, is shown (see text).

82 D. Schmitz et al. / Journal of Molecular Spectroscopy 280 (2012) 77–84

passage regime discussed in Section 3, the population DN0 remainsnearly unchanged by the chirp.

Fig. 5b, on the other hand, presents the rotational spectra ofbenzontrile obtained with the same chirps as in Fig. 5a, but withthe gain setting of the TWT amplifier at 100%, which correspondsto at least 300 W and up to about 600 W of output power (fre-quency dependent). Two important points should be noted: (a)the relative intensities of the individual transitions are clearly af-fected by the direction of the chirp, and (b) the relative intensitiesdiffer from those obtained in the low-power measurements forwhich the linear fast passage regime is valid (see Fig. 5a). Thesefindings can be explained with stepwise multi-resonance effectsas described within the rapid adiabatic passage regime.

Fig. 5c displays an energy level scheme for the rotational statesof benzonitrile, neglecting hyperfine splitting for the moment. Theallowed a-type transitions are indicated by the sorting. Three pro-gressive series of stepwise multi-resonance transitions are possiblein the relevant frequency range from 2 to 8.3 GHz. The energy lev-els labeled with the rotational quantum numbers JKAKC

, namely 000,101, 202, and 303 are connected by a-type transitions as are the 111,212, 313 and the 110, 211, 312 rotational energy levels. The rotationalstates 221, 322, 220, and 321 are at higher energies and are cooled outby the supersonic expansion, and thus are not sufficiently popu-lated anymore under the conditions of our experiment.

As discussed in Section 3 and displayed in Fig. 4, the population ofthe respective energy levels within a progressive series can be signif-icantly influenced by the chirp. For example, for a chirp-up measure-ment within the J0Kc¼J series (Fig. 6c), the population of the 101

energy level will be enriched in the course of the chirp via the

101 000 transition at 2.76 GHz. This change will then be probedby the same chirp when approaching resonance for the 202 101

transition at 5.5 GHz. As a result, the 202 101 transition is stronglyenhanced compared to the 101 000 transition. This change in turnleads to an increase of the population of the 202 level, within the RAPregime, and thus to an enhancement of the 303 202 transition at8.2 GHz. These effects become particularly clear when comparingthe transition intensities of the J0Kc¼J series with (a) the chirp-downmeasurements (lower trace) and (b) the 211 110 transition at5.85 GHz. Its intensity cannot be affected by multi-resonance transi-tions since the connected transition 312 211 is located outside thefrequency range of our spectrometer.

A similar multi-resonance effect is observed for the 313 212

transition at 7.7 GHz, which is enhanced by population transferfrom the 211 110 transition at 5.19 GHz, whose intensity is sim-ilar to the one for the chirp-down measurement, in line with theprevious discussion for the 101 000 transition at 2.76 GHz.

As mentioned above, each rotational energy level of benzoni-trile is split due to nuclear quadrupole coupling (F = J + IN) of thenuclear spin (IN) of the nitrogen atom with the overall angularmomentum (J) of the molecule. A schematic representation of theenergy level diagram for the J0Kc¼J series is shown in Fig. 6e. Thus,the occurring multi-resonance effects are a mixture arising fromthe progressive J series and the regressive hyperfine structurescheme.

In Fig. 6a and b the J + 1 J = 101 000 transition is displayed,measured with 100% gain and 50% gain of the TWT amplifier,respectively. Again, the upper traces correspond to chirp-up mea-surements (2–8.3 GHz) while the lower traces correspond to

101 000

202 101

5501 5502 5503 5504 5505 5506

-50

0

50

100

150

200100% gain

(c)

5502 5504 5506

-50

0

50

50% gain(d)

frequency (MHz)

frequency (MHz) frequency (MHz)

frequency (MHz)5501 5503 5505

2759 2760 2761 2762 2763 2764 2765-30

-20

-10

0

10

20

30100% gain

(a)

sign

al (µ

V)

2759 2760 2761 2762 2763 2764 2765-100

-50

0

50

10050% gain

(b)

sign

al (µ

V)si

gnal

(µV)

sign

al (µ

V)

1 1

2 1

0 1

1 12 1

0 1

2 1

1 11 02 2

3 21 2 2 1

1 11 02 2

3 2

1 2

000, 1

101, 1

101, 2

101, 0

202, 2

202, 3

202, 1

303, 3

303, 4

303, 2

JKa,KC, F

(e)

Fig. 6. Zoom into the broadband spectra displayed in Fig. 5 to investigate the multi-resonance effect on the quadrupole hyperfine structure of benzonitrile for theJ + 1 J = 101 000 transition (100% gain (a) and 50% gain (b)) and for the 202 101 transition (100% gain (c) and 50% gain (d)). The upper traces correspond to chirp-upmeasurements (2–8.3 GHz) while the lower traces correspond to chirp-down measurements (8.3–2 GHz). The individual hyperfine transitions are labeled with theirrespective quantum numbers F0 F. In part (e), a schematic energy level diagram of the individual hyperfine transitions for the J0;Kc¼J series is shown.

D. Schmitz et al. / Journal of Molecular Spectroscopy 280 (2012) 77–84 83

chirp-down measurements (8.3–2 GHz). In the full-power mea-surement (a), the intensities differ significantly between the mea-surements with chirp-up and chirp-down. The effect is mostpronounced for the 1 1 hyperfine transition, which is reducedin the chirp-down experiment, and the 2 1 hyperfine transition,which is reduced in the chirp-up measurement. This differencecan be explained with the energy level diagram displayed inFig. 6e. In the chirp-up experiment, a significant amount of pop-ulation will be transferred from the JKaKc

; F ¼ 000; 1 ground stateto the 101,1 state, which has the lowest excitation energy. As aconsequence, the obtained intensity for the 101, 2 000, 1 transi-tion is reduced. The same holds for the 101, 0 000, 1 transition,but less pronounced. For the chirp-down experiment, both the101, 2 000, 1 and the 101, 1 000, 1 transitions should be re-duced, while the 101, 0 000, 1 transition (which has the highestexcitation energy of this group) is unaffected. In the reducedpower measurements (50% gain, part (b)), such effects are not ob-served. The relative intensities of both measurements (chirp-upand chirp-down) are very much comparable. A similar observa-tion can be made for the 202 101 measurements displayed inFig. 6c and d.

5. Conclusions

In this report, the design and performance of our new broad-band chirped-pulse FTMW spectrometer COMPACT covering the2–8.5 GHz frequency range is discussed. The measurements ofthe rotational spectra of CF3I and benzonitrile (reduced powermeasurements) demonstrate the sensitivity and relative intensityaccuracy of our spectrometer, which is especially designed for

the low-frequency range appropriate for large and complex mole-cules and complexes.

Interestingly, we observed stepwise multi-resonance excitationfor benzonitrile excited by a single chirp for full-power measure-ments. We could demonstrate that, for a polar molecule such asbenzonitrile (la = 4.5152 D), we can deliberately choose betweenthe linear fast passage and the rapid adiabatic passage regime. Inthe first, the initial population of the energy levels is practicallyunaffected, but maximum coherence is obtained, while in the latter,the population of the energy levels is strongly influenced. In the ex-treme case, this can even lead to a complete population inversion.We observed pronounced changes in the relative intensities of thevarious rotational transitions of benzonitrile, that fall into our fre-quency range (2–8.5 GHz). These changes are strong indicationsthat the RAP regime of strong coupling must be applied.

Our results suggest that for molecules with large dipole mo-ments and high-power TWT amplifiers (in our case maximum out-put power (100% gain) with at least 300 W and up to 600 W), itshould be possible to routinely work in both the RAP and the LFPregime. The observed changes of intensities can facilitate the spec-tral assignment when changing from the LFP to the RAP regime andwhen performing both chirp-up and chirp-down experiments.

Acknowledgments

M.S. gratefully acknowledges financial support from the Fondsder Chemischen Industrie via a Dozentenstipendium, and T.B.acknowledges support from the Austrian Science Fund (FWF) pro-ject J3315-N19 via a Schrödinger grant. Additionally, the authorsthank Prof. Dr. Brooks H. Pate and his group for valuable

84 D. Schmitz et al. / Journal of Molecular Spectroscopy 280 (2012) 77–84

discussions on the chirped-pulse technique. The authors alsoacknowledge electronic and technical support by André Hömkeand Carlo Schmidt, and thank Prof. Dr. Jens-Uwe Grabow fromthe Leibniz-Universität Hannover for various fruitful scientificand technical discussions and for providing them with the experi-ment control program FTMW++.

References

[1] Gordon G. Brown, Brian C. Dian, Kevin O. Douglass, Scott M. Geyer, Steven T.Shipman, Brooks H. Pate, Rev. Sci. Instrum. 79 (2008) 053103.

[2] Brian C. Dian, Gordon G. Brown, Kevin O. Douglass, Brooks H. Pate, Science 320(5878) (2008) 924–928, http://dx.doi.org/10.1126/science.1155736. <http://www.sciencemag.org/cgi/content/abstract/320/5878/924>.

[3] David S. Wilcox, Kelly M. Hotopp, Brian C. Dian, J. Phys. Chem. A 115 (32)(2011) 8895–8905, http://dx.doi.org/10.1021/jp2043202. <http://pubs.acs.org/doi/abs/10.1021/jp2043202>.

[4] J.C. McGurk, T.G. Schmalz, W.H. Flygare, J. Chem. Phys. 60 (1974) 4181–4189,http://dx.doi.org/10.1063/1.1680886.

[5] F. Wolf, J. Phys. D: Appl. Phys. 27 (8) (1994) 1774. <http://stacks.iop.org/0022-3727/27/i=8/a=029>.

[6] V.V. Khodos, D.A. Ryndyk, V.L. Vaks, Eur. Phys. J. – Appl. Phys. 25 (03) (2004)203–208, http://dx.doi.org/10.1051/epjap:2004008. <http://dx.doi.org/10.1051/epjap:2004008>.

[7] Jens-Uwe Grabow, Walther Caminati, Microwave spectroscopy, in: F. Merkt,M. Quack (Eds.), Handbook of High-Resolution Spectroscopy, Wiley, 2011.

[8] K. Wohlfart, M. Schnell, J.-U. Grabow, J. Küpper, J. Mol. Spec. 247 (2008) 119–121.

[9] Justin L. Neill, Steven T. Shipman, Leonardo Alvarez-Valtierra, Alberto Lesarri,Zbigniew Kisiel, Brooks H. Pate, J. Mol. Spec. 269 (2011) 21–29, http://dx.doi.org/10.1016/j.jms.2011.04.016.

[10] Stephen G. Kukolich, Laszlo C. Sarkozy, Rev. Sci. Instrum. 82 (2011), http://dx.doi.org/10.1063/1.3627489. ISSN 0034-6748..

[11] C.H. Townes, A.L. Schawlow, Microwave Spectroscopy, Dover Publications,New York, 1975. ISBN 048661798X.

[12] C. Liedenbaum, S. Stolte, J. Reuss, Inversion produced and reversed by adiabaticpassage, Phys. Rep. 178(1) (1989) 1–24. http://dx.doi.org/10.1016/0370-1573(89)90018-5. ISSN 0370-1573. <http://www.sciencedirect.com/science/article/pii/0370157389900185>.

[13] N.V. Vitanov, T. Halfmann, B.W. Shore, K. Bergmann, Annu. Rev. Phys. Chem. 52(2001) 763–809.

[14] B. Broers, H.B. van Linden van den Heuvell, L.D. Noordam, Phys. Rev. Lett. 69(1992) 2062–2065, http://dx.doi.org/10.1103/PhysRevLett.69.2062. <http://link.aps.org/doi/10.1103/PhysRevLett.69.2062>.

[15] B. Broers, L.D. Noordam, H.B. van Linden van den Heuvell, Phys. Rev. A 46(1992) 2749–2756, http://dx.doi.org/10.1103/PhysRevA.46.2749. <http://link.aps.org/doi/10.1103/PhysRevA.46.2749>.

[16] P. Balling, D.J. Maas, L.D. Noordam, Phys. Rev. A 50 (1994) 4276–4285, http://dx.doi.org/10.1103/PhysRevA.50.4276. <http://link.aps.org/doi/10.1103/PhysRevA.50.4276>.

[17] D.J. Maas, C.W. Rella, P. Antoine, E.S. Toma, L.D. Noordam, Phys. Rev. A 59(1999) 1374–1381, http://dx.doi.org/10.1103/PhysRevA.59.1374. <http://link.aps.org/doi/10.1103/PhysRevA.59.1374>.

[18] H. Maeda, J.H. Gurian, T.F. Gallagher, Phys. Rev. A 84 (2011) 063421, http://dx.doi.org/10.1103/PhysRevA.84.063421. <http://link.aps.org/doi/10.1103/PhysRevA.84.063421>.

[19] H. Maeda, D.V.L. Norum, T.F. Gallagher, Science 307 (5716) (2005) 1757–1760,http://dx.doi.org/10.1126/science.1108470. <http://www.sciencemag.org/content/307/5716/1757.abstract>.