Coherent multidimensional spectroscopy in the gas phase
Lukas Bruder, Ulrich Bangert, Marcel Binz, Daniel Uhl, Frank Stienkemeier
CCoherent multidimensional spectroscopy in the gasphase
Lukas Bruder , Ulrich Bangert , Marcel Binz , Daniel Uhl and Frank Stienkemeier , Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104Freiburg, Germany Freiburg Institute of Advanced Studies (FRIAS), University of Freiburg,Albertstr. 19, D-79194 Freiburg, GermanyE-mail: [email protected]
April 2019
Abstract.
Recent work applying multidimentional coherent electronic spec-troscopy at dilute samples in the gas phase is reviewed. The development ofrefined phase cycling approaches with improved sensitivity has opened up newopportunities to probe even dilute gas-phase samples. In this context, first resultsof two-dimensional spectroscopy performed at doped helium droplets reveal thefemtosecond dynamics upon electronic excitation of cold, weakly-bound molecules,and even the induced dynamics from the interaction with the helium environment.Such experiments, offering well-defined conditions at low temperatures, are po-tentially enabling the isolation of fundamental processes in the excitation andcharge transfer dynamics of molecular structures which so far have been maskedin complex bulk environments.
Keywords : multidimensional spectroscopy, nonlinear optics, ultrafast spectroscopy,molecular beams, cluster beams, helium nanodroplets
Submitted to:
J. Phys. B: At. Mol. Phys.
1. Introduction
The development of coherent multidimensional spectroscopy (CMDS) in the opticalregime has greatly improved the toolkit of ultrafast spectroscopy [1, 2, 3]. The methodmay be regarded as an extension of pump-probe spectroscopy, where pump and probesteps are both spectrally resolved, while maintaining high temporal resolution inthe sub 50 fs regime [4]. By spreading the nonlinear response onto multidimensionalfrequency-correlation maps, improved spectral decongestion is achieved and theanalysis of couplings within the system or to the environment is greatly simplified.The concept of CMDS was originally developed in NMR spectroscopy [5] andwas first implemented at optical frequencies about 25 years ago [6, 7]. Nowadays,routinely used methods in the optical regime comprise two-dimensional infrared a r X i v : . [ phy s i c s . a t m - c l u s ] S e p oherent multidimensional spectroscopy in the gas phase ≥ cm − [66, 67, 68] and very recently down to 10 cm − [69].These simple target systems, however, do not imply a generalization of the method’s oherent multidimensional spectroscopy in the gas phase -8 -6 -4 -2 -8 -6 -4 -2 S a m p l e den s i t y ( c m - ) Sample temperature (K) gas celleffusive beamssupersonic beamscluster isolationMOT
Condensed Phase
BEC ion traps
Gas Phase helium dropletstrappedmolecules
Figure 1.
Landscape showing typical temperatures and densities of gas phasesamples in comparison to the condensed phase. So far, CMDS has been exclusivelyperformed in the condensed phase and gas cells which cover only a small fractionof the available parameter space covered by nowadays available targets. Thework of our group extends this range to CMDS experiments on cluster-isolationand helium droplet targets. MOT: atoms in magneto-optical traps; BEC: Bose-Einstein condensate of atoms. applicability to more advanced systems. For rubidium vapors, also a high-resolution2D spectroscopy scheme based on frequency combs has been recently demonstratedcapable of even resolving the atomic hyperfine levels [70, 71]. Furthermore, high-resolution multidimensional spectroscopy in the frequency domain using nanosecondlasers has been performed on several molecular vapors [72]. Yet, considering the widerange of unique target systems available in the gas phase and the large parameterspace they cover, CMDS has been so far restricted to a small portion of targets.This is illustrated in Fig. 1 where the landscape of gas-phase samples provided bydifferent experimental techniques is plotted with respect to sample density and internaltemperature.Only very recently, the Brixner group and our group demonstrated the first 2DESstudies of gas-phase molecules and incorporated some of the afore mentioned newphotoionization detection schemes [73, 74]. Brixner and coworkers probed a thermalgas of NO molecules combined with selective mass spectrometry [73]. Our groupstudied cold ( T = 380 mK) Rb and Rb molecules prepared with matrix isolation in acluster beam apparatus, detected with photoelectron and ion-mass spectrometry [74].These experiments, in principle, continue the pioneering early work of Zewail andcoworkers [75], advancing the field of Femtochemistry to a new direction and extending oherent multidimensional spectroscopy in the gas phase
2. Principle of 2DES
The principle of CMDS is described in detail in several review articles and books [4,2, 76, 77, 25, 78, 3, 79, 80, 81, 82, 83, 84]. Here, we provide only a brief introductionto the basic concept of 2DES and highlight its most important features.In 2D spectroscopy, the sample (here approximated by a four-level model system,Fig. 2a) is excited with a sequence of three to four optical pulses (Fig. 2b) and the third-order nonlinear response of the system is probed as a function of the pulse delays τ, T and t . The time intervals τ and t (termed coherence times), track the evolution ofinduced electronic coherences. A Fourier transform with respect to these time variablesyields the 2D frequency-correlation maps (Fig. 2c) as parametric function of the thirdtime variable T (termed evolution time). Consequently, pump and probe steps areboth frequency-resolved with ω τ representing the pump/excitation frequency and ω t the probe/detection frequency axis, respectively.The detected signals are categorized in stimulated emission (SE), ground statebleach (GSB) and exited state absorption (ESA) each occurring as rephasing (RP)(photo echo) and non-rephasing (NRP) signals. GSB probes the time evolution onthe system’s ground state manifold whereas SE and ESA probe the dynamics of theexcited state. Thereby ESA involves the excitation to a higher-lying state (Fig. 2). Inmost cases, GSB and SE pathways appear as positive and ESA as negative signals inthe 2D maps which simplifies their identification and separation.Furthermore, peaks on the diagonal reflect the linear absorption/emissionspectrum of the sample, however, with the additional information of 2D lineshapesreadily dissecting homogeneous (along antidiagonal) from inhomogeneous (alongdiagonal) broadening [85]. This provides decisive information about static anddynamic inhomogeneities in the probed ensemble [82]. Off-diagonal features directlydisclose couplings among excited states of the system from which different typesof interaction and relaxation dynamics can be inferred, e.g. coherent excitonicinteractions or spontaneous decay pathways [14]. Excited state absorption (ESA) tohigher lying states may be also induced. These contributions typically appear withinverted (negative) amplitude which simplifies their identification and separation from oherent multidimensional spectroscopy in the gas phase g | a | b | c | a) Optical fieldsSignal Time τ T t b) I n t en s i t y Excitation frequency d)c) D e t e c t i on f r equen cy Excitation frequencyBAAB hom.inhom. T ω τ ω t AC B
Figure 2.
Principle of 2D spectroscopy. (a) Simplified four-level system. (b)Pulse sequence used in 2D spectroscopy. The sample is excited with 3 or 4 pulses(indicated by dashed pulse envelope). The blue trace indicates the signal, whichrepresents an oscillating dipole during the coherence times τ, t . In between pulse2 and 3 (time interval T ), the system’s time evolution (dashed trace) is probed.All three time variables τ, t, T are systematically scanned in the experiment. (c)2D frequency-correlation map obtained by a 2D Fourier transform of the data setwith respect to the coherence times τ, t directly correlating excitation ( ω τ ) anddetection ( ω t ) frequencies. Peaks A, B on the diagonal represent the | g (cid:105) ↔ | a (cid:105) , | b (cid:105) resonances, with inhomogeneous and homogeneous lineshapes along the diagonaland antidiagonal, respectively. Peak C denotes an excited state absorption from | a (cid:105) to the higher lying state | c (cid:105) (typically appearing with negative amplitude). ABand BA denote cross peaks, indicating couplings between states | a (cid:105) and | b (cid:105) . Thetime evolution of all features is tracked as a function of T .(d) Linear absorptionspectrum of the same system. Most spectral features overlap and are difficult toinfer from the data. Likewise, a characterization of the system’s inhomogeneitybecomes difficult. oherent multidimensional spectroscopy in the gas phase τ, t ) requiresinterferometric measurements with high phase/timing stability among the opticalpulses (typically ≤ λ/
50 [83]). This demand is slightly relaxed in 2DIR spectroscopy,since vibrational coherences evolve on roughly an order of magnitude lower frequencies.Second, the third-order 2D signals, subject to three to four light-matter interactions,are often weak and are covered by dominating background contributions, e.g. thelinear system response or scattered light. This calls for highly sensitive detection withlarge dynamic range.In the past 25 years, both issues have been experimentally solved. A numberof active and passive phase stabilization concepts have been developed to meet thedemands of interferometric stability [66, 88, 89, 90, 67, 91, 92, 93, 94, 95]. These arecombined with phase matching [7] or phase cycling [66, 96] schemes or combinationsof both [97, 30] to select the desired nonlinear signal contributions and providehighly sensitive background-free detection. An overview of the different experimentaltechniques has been recently published [79].Phase matching (Fig. 3a) relies on coherent four-wave-mixing (FWM), where thesample is excited with three laser pulses in the so-called boxcar geometry [4]. The thirdlight-matter interaction stimulates the coherent emission of the signal wave in phasematching direction, where it is background-free detected and frequency resolved withan optical spectrometer. Thereby, amplitude and phase of the signal are determinedby heterodyned detection with a fourth optical field (termed local oscillator) [83].In phase cycling (Fig. 3b), collinear pulse trains are used to induce four light-matter interactions, leaving the sample in a population state after the fourth pulse.The final population is detected with incoherent observables yielding the nonlinearresponse of the system. At the same time, specific phase patterns are imprinted onthe pulse trains by manipulating the carrier envelope phase (CEP) of each pulse,which results in a distinct phase signature of the detected signal [96]. By applying aunique set of phase combinations (typically 16 or 27), the desired nonlinear signal isidentified and isolated in the post processing while other contributions destructivelycancel. Here, the signal’s amplitude and phase are deduced by adequate combinationof extracted signal contributions.The development of these concepts has solved some important technical issues of2D spectroscopy experiments, having in recent years paved the way for widespreadimplementation in the condensed phase. Yet, other experimental issues exist thatare less discussed in literature. These include timing uncertainties due to chirpedoptical pulses [98], pulse overlap effects due to finite pulse durations [99], incompletespectral overlap with the sample [100], laser intensities beyond the weak perturbationregime [101], pulse propagation effects in the studied medium itself [102, 103], photo oherent multidimensional spectroscopy in the gas phase Figure 3.
Phase matching and phase cycling in 2D spectroscopy. (a)Phase matching of three incident pulses with different (cid:126)k i -vectors induce anonlinear polarization in the sample which radiates off in (cid:126)k s -direction where it isheterodyned with the local oscillator (LO) and isolated with a mask. (b) Phasecycling with four collinear pulses exciting a sample. The phase φ i of each pulseis modified throughout the experiment. (c), (d) Example Feynman diagramsshowing signal contributions selected with phase matching/cycling, respectively. bleaching of samples and scattering light contributions [104]. These points make2DES still a sophisticated experimental task requiring specialized expertise in ultrafastnonlinear optics and related fields.
3. Experimental implementation of gas-phase 2DES
The idea of gas-phase 2DES is to study isolated model systems, which implies very lowensemble concentrations (typically particle densities ≤ cm − [44]). This requiresorders of magnitude higher detection sensitivity than in condensed phase experiments(Fig. 1) and thus poses a severe technical challenge. The phase matching approachis ruled out by this criteria, as it relies on the coherent emission from a macroscopicpolarization induced in the sample. Therefore, the method cannot be scaled downto low target densities and, to the best of our knowledge, phase-matching 2DESexperiments have not been demonstrated for particle densities ≤ cm − [26]. oherent multidimensional spectroscopy in the gas phase Experimentally, phase cycling is implemented by pulse shaping based on spatial lightmodulators (SLMs)[114, 90, 93] or acousto-optical modulators (AOMs) [66, 95, 115].Alternatively, a phase modulation (PM) technique based on continuous phasemodulation with acousto-optical frequency shifters (AOFSs) is used [67, 107, 108,54, 109, 74, 69]. The latter may be regarded as shot-to-shot quasi-continuous phasecycling [107].Both approaches have their strengths and weaknesses depending on theapplication. Pulse shaping can drastically simplify the optical setups for 2DESexperiments [95, 115] and provide highest experimental flexibility. Amplitude, phaseand polarization shaping permit the generation of arbitrary pulse sequences to performa vast array of nonlinear spectroscopy experiments with a single apparatus [116].Another advantage of pulse shapers is their ability for inherent pulse compressionto yield transform-limited pulses in the 10-fs-regime [110].On the contrary, the PM approach requires larger assemblies of optics and ismore restricted in the manipulation of pulse properties. Yet, flexible signal selectionprotocols have been also implemented with the PM technique [117, 69] and pulsedurations <
20 fs have been reported [109]. The continuously operated AOFSs in thePM technique have the advantage of imprinting particularly clean, high purity phasemanipulation with very low distortion (reported artifacts ≤
50 dB [118, 119]), whereaspulse shapers require careful calibration and may produce artifacts due to space-timecouplings [120], thermal phase instabilities [121] or if operated at high update rates.In view of gas-phase experiments, the signal-to-noise performance and detectionefficiency are particularly important factors. In 2DES, it is recommended to usemoderate laser intensities to avoid the contribution of higher-order (larger thanthird order) signals to the data. Therefore, large statistics is best reached withlow laser intensities and high laser repetition rates. Here, the PM techniquehas the clear advantage of providing shot-to-shot phase manipulation up to laserrepetition rates in the MHz-regime [67] which is combined with highly sensitive lock-in detection [67, 117, 122]. Most pulse shapers are restricted to update rates of ≤ ≤
100 fs. Inthe gas phase, broadening effects are considerably smaller and electronic coherences oherent multidimensional spectroscopy in the gas phase ≤ Phase modulation 2DES combined with fluorescence detection is described in detailin the original publication from the Marcus group [67]. Here, we provide only abrief description of the technique with the focus on the photoionization gas-phaseexperiments performed in our laboratory.The experimental scheme and a sketch of the setup is shown in Fig. 4. A collinearpulse train of four phase-modulated laser pulses prepares a nonlinear populationstate in the sample, which is probed upon photoionization. The ionization is eitherperformed with a separate fifth pulse or by absorbing additional photons from pulse 4.Pulse 1-4 are generated in a nested three-fold optical interferometer fed by the outputof a noncollinear optical parametric amplifier (NOPA) (640-900 nm tuning range).Pulse 5 is produced from a second NOPA to enable independent wavelength tuning(540-900 nm) or from fourth harmonic generation (FHG) of the amplified oscillatorpulses to yield deep ultraviolet (UV) pulses (260nm). The relative pulse delays arecontrolled by motorized translation stages.The multipulse excitation sequence generally induces a large number of signals.The desired third-order rephasing (RP) and non-rephasing (NRP) signal contributionsare selected from the total signal by phase modulation of the excitation pulsescombined with lock-in detection. To this end, pulse 1-4 are passed through individualAOFSs (AOFS 1-4, Fig. 4b) which are phase-locked driven at distinct radio frequenciesΩ i . AOFS 1-4 shift the frequency of transmitted pulses by the value Ω =109 .
995 MHz, Ω = 110 .
000 MHz, Ω = 110 .
001 MHz and Ω = 110 .
009 MHz,respectively. This is equivalent to a shot-to-shot modulation of the CEP φ i ofeach pulse [107] in increments of ∆ φ i = Ω i /ν rep between consecutive laser shots( ν rep = 200 kHz denotes the laser repetition rate).The nonlinear mixing of the modulated electric fields in the sample leads tocharacteristic beat notes in the photoionization yield. According to the phase cyclingconditions for RP and NRP signals ( S RP and S NRP ), the modulation frequencies are: S RP : φ RP ( t ) = − φ + φ + φ − φ = 3 kHz (1) S NRP : φ NRP ( t ) = − φ + φ − φ + φ = 13 kHz . (2)The signals are extracted from the photoelectron/-ion count rates with lock-in detection. For the lock-in amplification, an external reference signal is usedconstructed from the optical interference of pulse 1-4. For this purpose, pulse pairs1,2 and 3,4 are split off at BS 4 and 5, respectively and are subsequently stretched intime with a monochromator (Fig. 4b). The pulse stretching ensures a non-vanishinginterference signal over sufficiently long scanning ranges of τ and t . The acquired beatsignals of both pulse pairs (Ω = 5 kHz and Ω = 8 kHz) are electronically mixed toyield sum- and difference frequency-sidebands at 3 and 13 kHz, respectively. oherent multidimensional spectroscopy in the gas phase Lock-in amp.
Sig.Ref. Δ SampleSample t T τΦ = Ω t' Φ = Ω t' Φ = Ω t' Φ = Ω t' a) τ tT AOFS1AOFS2AOFS3AOFS4BS1 BS2BS3 BS4 PD Ω - Ω NOPA 1NOPA 2 Mono 1Mono 2MZI2MZI1Amplified fs oscillator
Cluster beam SourcechamberDopingchamberDetectorchamber Ω + Ω Ω Ω PMT PMT
BS5
Sig.Ref. 1 Ref. 2Amp.
BS6 BC
FHG Δ LIA b) Figure 4.
Detection scheme and optical setup for phase modulation 2DESin the gas-phase combined with photoionization. (a) A sample is excited bya collinear pulse sequence consisting of four phase-modulated pulses (pulse 1-4) and an optional fifth pulse (indicated by dashed envelope). The phasemodulation of pulse 1-4 appears as characteristic beat notes in the detectednonlinear signals which are demodulated with a lock-in amplifier. A referencesignal is constructed from the optical pulses for the lock-in demodulation. (b)Experimental setup. Three-fold Mach-Zehnder interferometer (MZI) equippedwith four Acousto-optical frequency shifters (AOFSs) produces a collinear 4-pulsesequence (red). A fifth pulse (blue, not modulated) is collinearily overlapped withpulse 1-4 before focusing into the vacuum apparatus. Replicas of pulse pairs 1,2and 3,4 are picked-up after beam splitter (BS) 4 and 5. Their low-frequency beatsat Ω − Ω = Ω and Ω are detected in two monochromators (Mono 1,2) toconstruct the (Ω ± Ω ) sideband references (Ref. 1, 2) for the lock-in detection. τ, T , t , ∆: pulse delays, NOPA: noncollinear optical parametric amplifier, FHG:fourth harmonic generation, BC: beam combiner, PMT: photo multiplier tube.Adapted from Ref. [74], licensed under the Creative Commons Attribution 4.0International License. In the post processing, the sum of demodulated RP and NRP signals is Fouriertransformed with respect to the time delays τ and t to yield the complex-valued 2Dfrequency-correlation spectrum ˜ S ( ω τ , T, ω t ) as a parametric function of T . Its realpart represents the 2D absorption spectrum which is analyzed in the experiments.The here employed lock-in detection scheme has several advantages. RP andNRP signals are retrieved simultaneously in a single 2D scan of positive coherencetimes τ and t . Amplitude and phase of the signal are recovered through phase-synchronous lock-in detection. Heterodyning with the external reference leads torotating frame sampling which reduces the required delay sampling points by severalorders of magnitude. Phase/timing jitter introduced in the optical interferometersappears as correlated noise in the signal and reference and thus cancels out in thelock-in demodulation, resulting in a highly efficient passive phase stabilization of the oherent multidimensional spectroscopy in the gas phase Figure 5.
Performance advantage of the PM technique demonstrated in aquantum beat experiment. (a), (b): Time domain signal of electronic coherencesexcited in gaseous Rb atoms, with (a) and without (b) using the PM technique. In(a), rotating frame sampling leads to a downshift of the quantum beat frequencies.(c), (d): Respective Fourier transform spectra showing a clear SN advantage forthe PM case. Adapted from Ref. [54] - Published by the PCCP Owner Societies. setup. As such, a phase stabilization better than λ/
200 has been achieved in a deep-UVinterferometer ( λ = 266 nm) [123]. Eventually, the lock-in amplification considerablyimproves the general sensitivity of the setup. The signal-to-noise (SN) advantageof the PM technique is clearly demonstrated in an electronic quantum interferencemeasurement combined with photoionization which served as a precurser experimentto our gas-phase 2DES experiments (Fig. 5) [54]. There is a distinct difference between 2D spectroscopy experiments using phasematching and phase cycling. In case of phase matching, for each signal type (SE,GSB, ESA) exists one RP and one NRP pathway (and their complex conjugate).With phase-cycling, for each contribution exists an additional pathway whose signalis phase shifted by π . Example RP pathways, as detected in our photoionizationexperiments, are shown in Fig. 6. Here, the relative amplitude with which the pathwayscontribute to the signal strongly depend on the ionization probability. While SE1-ESA1 pathways are probed by two-photon ionization, the ESA2 process requiresonly one photon to the continuum and therefore dominates the ESA signal in thephotoionization 2D spectra. On the contrary, SE2 and GSB2 require three photons forionization and are usually negligible. As such, the net SE and GSB signals contributewith positive amplitude, whereas the net ESA signal strictly appears with negativeamplitude in the 2D absorption spectra. This is in analogy to phase matching based2D spectroscopy where the ESA amplitudes are also of opposite sign to SE/GSBsignals.The negative sign of ESA features in contrast to the other signal contributions,simplifies their identification, which is of advantage, in particular in congested spectra.Note that with other detection types the situation can differ. In fluorescence detection, oherent multidimensional spectroscopy in the gas phase RP SE1 T g | e | f | i | iieeegeegegg + Φ - Φ Φ - Φ RP GSB1 T g | e | f | i | iieeeggggegg + Φ - Φ Φ - Φ T g | e | f | i | iieefeeegegg + Φ - Φ - Φ T g | e | f | i | iifffeeegegg Φ - Φ - Φ RP ESA1 RP ESA2 Φ Φ τ Tt Δ tE T g | e | f | i | iiggegeegegg Φ - Φ Φ - Φ T g | e | f | i | iiggeggggegg Φ - Φ Φ - Φ RP SE2 RP GSB2 a)b)
Figure 6.
RP excitation pathways in photoionization-2DES. (a) Simplified levelscheme with | g (cid:105) ground, | e (cid:105) , | f (cid:105) excited states and | i (cid:105) ionic state along withSE, GSB and ESA excitation pathways. Interaction by pulse 1-4 (red), pulse5 (green). Solid arrows indicate interaction on ket-side, dashed on bra-side ofthe system’s density matrix operator. (b) Corresponding double-sided Feynmandiagrams. Common notation is used: Time evolves from bottom to top. Eachentry denotes an element of the density matrix | i (cid:105)(cid:104) j | . Arrows indicate the light-matter interaction leading to de-/excitation of the system. Double-arrows indicatetwo simultaneous interactions. φ i indicates the phase imprinted onto the signalby each interaction. Plus/minus signs below each diagram indicate the sign withwhich the processes add to the 2D response function. Adapted from Ref. [74],licensed under the Creative Commons Attribution 4.0 International License. the sign of the ESA peaks depends on the degree of quenching of fluorescence fromthe | f (cid:105) state [124]. Related to the phase shift among signal contributions is the general phasing issue in2D spectra [125, 126]. The correct phase information can only be retrieved if the totalphase of the complex-valued 2D response function S ( τ, T, t ) is correctly determined.Otherwise the absorptive and dispersive line shapes are not correctly separated inthe 2D absorption spectrum leading to distorted or even inverted peak shapes whichmight be interpreted incorrectly.While phasing of the 2D signals is intricate in FWM-based 2D spectroscopy, itis much simpler in collinear 2D spectroscopy experiments. Pulse shaper setups areintrinsically phased through the calibration of the device. In the phase modulationapproach, phasing is done by calibrating the phase offset between the signal andreference in the lock-in detection. To this end, at coherence times set to zero( τ = t = 0 fs), the phase of the demodulated RP/NRP signal is adjusted to zerothrough adjusting a global phase factor applied in the lock-in electronics or in the postprocessing [67]. With this procedure, phase shifts between the signal and the referenceaccumulated in the different electronic circuits of the setup are compensated.This procedure is required for the initial calibration of any PM-2DES setup,or whenever electronics are changed. Any reference sample may be used for thecalibration. In our experiments, we phased the setup with photoionization signalsof gaseous Rb atoms which provide a simple, well-defined 2D spectrum with isolated oherent multidimensional spectroscopy in the gas phase ESASE/GSB b) E c) S P P D D D D ESA transition a) Figure 7.
Reference measurement to phase the setup. (a) Photoelectron-detectedabsorptive 2D-spectrum of gaseous Rb. Used to phase the setup according to theexpected peak shape and sign: positive, absorptive GSB/SE features and negative,absorptive ESA features. (b) Different color-coding to amplify weak contributions.Homogeneous/inhomogeneous broadenings are beyond the spectral resolution ofthe measurement, explaining the absence of peak elongations along the diagonal.(c) Relevant energy levels of atomic Rb for the reference measurement. Probedare the D line transitions (via GSB/SE) as well as the 5 P / → D / , / transition (via ESA). sharp peaks that allows for direct examination of any phase offset (Fig. 7).
4. Preparation of gas-phase samples
A great variety of experiments on atoms, molecules and molecular complexes areperformed on gas phase samples, driven in particular by two main characteristicsof such targets: (a) probing systems without the interaction between individualconstituents or/and without the interaction with an environment; (b) establishinglow temperature conditions and corresponding quantum state selectivity.With respect to (a), already gas cells containing a vapor pressure of the samplemay evolve only weak perturbations in spectroscopic measurements. Albeit, thecoherent excitation of molecular vapors (molecular densities ∼ cm − ) may leadto cascading effects which compromise the nonlinear response of the sample [127].Likewise, propagation effects may occur in gas cells [102, 103]. Experiments on particlebeams prepared in high or ultra-high vacuum (UHV) environments circumvent theseissues and in addition provide conditions (pressures below ≈ − mbar) where themean free path for extracting ions and electrons is suitable for an unperturbeddetection. Furthermore, detection methods employing electron multipliers andcorresponding high voltages cannot be operated at higher vacuum pressures.With respect to (b), in the gas phase a variety of cooling and trapping methodsare at hand to reach temperatures even down to nanokelvin temperatures (cf. Fig.1) [128]. A central technique is based on the cooling by means of a supersonicexpansion in molecular beams [45], reaching temperatures in the low Kelvin range.Ultracold temperatures (below mK) mostly involve laser cooling methods, as well asevaporative cooling in shallow traps [128]. Low temperatures are for many experimentsinstrumental for guaranteeing quantum state selectivity, preferable in all degrees offreedom, as well as providing well-defined structural properties. Finally, in comparisonwith ordinary gas targets, molecular beam as well as trapping methods are in manycases a prerequisite for providing an interaction volume having a distinct higher oherent multidimensional spectroscopy in the gas phase SkimmerDroplet/clusterbeamHeateddoping cell p ∼ -4 mbar a) Carrier gas(He, Ar,...)Heatedreservoir Nozzle Δ p ≥ bar p ∼ b) Figure 8.
Gas-phase sample preparation. (a) Skimmed seeded supersonic beamgeneration. (b) Cluster isolation technique. target density in comparison to the background gas inside the vacuum apparatus.Furthermore, Doppler broadening is minimized even in fast molecular beams whenintersected perpendicularly by the laser beams.It is intriguing that independent of the very different experimental techniquesproviding gas-phase targets, like e.g. size-selected molecular or cluster ion beams,decelerated molecular beams [129], helium droplet isolation, or ultracold atoms inmagnetooptical traps (cf. Fig. 1), the target density typically is in the range ofabout 10 cm − . Of course, such densities are many orders of magnitudes belowcorresponding bulk target densities. However, the sensitivity and selectivity ofsignals detecting angular resolved and energy resolved single electrons or mass-selected ions even in sophisticated coincidence methods, in combination with generallyfast regenerating targets offer unique options of experimental techniques not beingavailable on bulk liquid or solid systems.The most commmon molecular beam technique is the generation of a skimmedseeded supersonic beam, (Fig. 8a). In an adiabatic expansion of high-pressure raregases (He, Ar, Kr, Xe) into vacuum an internally cold beam traveling at supersonicspeed is formed [45, 130], seeded with target molecules at much lower pressure, e.g.from a heated reservoir. In this way the molecules adapt in many collisions duringthe expansion process to the narrow speed distribution and the low temperature of oherent multidimensional spectroscopy in the gas phase Beam creation Doping Laser interaction & detection
CryocoolerRare gas Laser interaction CEM
TOFMS LT
NozzleSkimmerChopperPick-up cells1200 l/s
300 l/s
300 l/s 300 l/s 80 l/sRe-wire
LIF MB
PMT2300 l/s Ion+e-MCP B -8 mbar2x10 -8 mbar8x10 -9 mbar7x10 -8 mbar7x10 -7 mbar9x10 -5 mbar a)b) Doping inside Doping on surface "Microsolvation"AkHe N He N He N Surface doping,low mobility
Figure 9.
Helium nanodroplet isolation technique. (a) HENDI beam apparatusfor 2DES measurements. Three different detection schemes can be used to gaincomplementary information: laser-induced fluorescence detector (LIF), magneticbottle-type electron time-of-flight spectrometer (MB), ion time-of-flight massspectrometer (TOF MS). A Langmuir-Taylor detector (LT) and a quadrupol-massspectrometer (not shown) are used for beam diagnostics. PMT: photo multipliertube. MCP: microchannel plate. CEM: channeltron electron multiplier. Typicalpressure readings for the different chambers when operating the droplet beam,and pumping speed vacuum pumps are indicated below. (b) Doping of raregas clusters. Most species immerse into the liquid He droplets and formationof larger atomic or molecular aggregates is possible. Co-doping of other atomsor molecules (microsolvation) allows for a precise tuning of the environmentalparameters. Alkali (Ak) atoms and molecules are only weakly bound to the Hedroplet and reside on the droplet surface. Large clusters of Ne, Ar and Kr aresolid and hence the dopants attach to the cluster surface exhibit a low mobility. the seed gas. In this way, both the directionality and density in the target volume ismuch higher, and the internal temperature is much lower in comparison with e.g. aneffusive gas beam (molecules exiting a reservoir though a pin hole without collisions).In our first studies on 2DES in molecular beams we used the helium nanodropletisolation (HENDI) technique, detailed out in the next section, because of itsprospects and options for generating specific larger molecular structures at millikelvintemperatures.
Rare gas (Rg) clusters of variable sizes (Rg N , < N < ) can be readily condensedin supersonic expansions at appropriate conditions. Depending on the rare gas, oherent multidimensional spectroscopy in the gas phase −
100 bar, and low temperatures, down to4 K in case of He have to be applied [131, 132, 133]. Because of the low bindingenergies of rare gas atoms to the clusters and the high surface-to-volume ratio, theclusters very efficiently evaporatively cool to specific low temperatures. In helium, theterminal temperature is 380 mK [134] which is well below the transition temperatureto superfluidity. The liquid state and the superfluidity provides peculiar properties,in particular frictionless flow and efficient cooling which has been confirmed in manyhelium cluster studies, [135, 136] and explain why such clusters are appropriately calleddroplets. All rare gas clusters can be loaded with atoms and molecules by the pickuptechnique [137, 138], where during inelastic collisions, e.g. in a cell containing a lowvapor pressure of the dopant atoms or molecules, these are attached to the clusters. Incomparison with seeded beams the needed partial pressure for doping a large clusterwith unit probability is on the order of 10 − − − mbar, significantly extending therange of molecules suitable for establishing such low densities without fragmentation.One can dope large clusters even with thousands of atoms or molecules [139]. A varietyof doping techniques has been developed, including laser ablation [140, 141, 142] anddopants from electrospray (ESI) sources [143, 144, 145]. In this way, also chargedparticles have been doped. In combination with ion traps, cluster-isolated spectroscopyof large bio-molecules up to 12000 Dalton has been performed [143].In helium, generally, dopants aggregate inside the liquid droplet and in this wayone can specifically synthesizes even larger atomic or molecular structures (Fig. 9b)and/or model solvation effects by adding specific solvent molecules. On the otherhand, the larger clusters of heavier rare gas atoms (Ne, Ar, Kr, Xe) all form solidclusters. For such solid clusters, it has been shown that larger molecules upon dopingdo not submerge and are immobile [146, 147]. In this way, multiple doping leads to avariable surface coverage of the doped molecules (cf. Fig. 9b) [148, 149].All kinetic energy from the doping process as well as internal energy of the formedaggregates are dissipated via the evaporated cooling of the cluster. In this way, lowtemperature targets are formed, e.g., for helium droplets at millikelvin temperatures.Since the rare gas clusters are transparent at all wavelength down to the VUV,the dopants are selectively probed in laser experiments operating at IR, VIS or UVwavelengths [138, 153].Fig. 10 demonstrates the advantage of helium droplet isolation in the comparisonof linear absorption spectra of PTCDA molecules at different conditions. Thespectrum in a room temperature solvent shows the typical broad absorption bandsof the S ← S first singlet-to-singlet transition (red curve in Fig. 10). Even the gas-phase absorption in a heated vapor cell does not lead to better-resolved details (purplecurve in Fig. 10) because of the large number of thermally populated states. Thehelium droplet isolated spectrum, however, clearly resolves in detail the vibrationalstructure of the molecule.With the latter technique, the broadening of lines in vibronic spectra typically isabout 1 cm − [150]. The main source of broadening often is the Pauli repulsion ofthe electron density with the surrounding helium. For atoms having low ionizationpotentials and corresponding extended electron density distributions, large blue-shiftsand repulsive interactions may appear upon excitation of electronic states. Therepulsive nature of helium with respect to electrons can even lead to the formation ofso called “bubbles” [154], i.e. a helium void around e.g. atomic dopants. For the samereasons alkai atoms, dimers and trimers do not submerged in helium but are locatedat dimple-like structures on the surface of helium droplets (cf. Fig. 9b) having binding oherent multidimensional spectroscopy in the gas phase Figure 10.
Comparison of linear absorption spectra of PTCDA (3, 4, 9,10-perylenetetracarboxylicdianhydride) in different environments. Purple: gas-phase absorption in a heated vapor cell,[150]. Red: measurement in a roomtemperature solvent (dimethyl slufoxide)[151]. Black: helium droplet isolatedmonomer spectrum [152]. energies only on the order of 10 cm − [155, 156].The just introduced peculiar binding properties of alkali-doped helium dropletspreferably leads to the formation of high-spin states upon the formation of alkalimolecules or clusters (Fig. 11) [46, 157, 158]. Dissipation of binding energy uponthe formation of molecules leads to high desorption rates of strongly bound entitiesduring the doping process. In this way, in particular weakly bound molecules can bestudied, which might be very difficult to form by other techniques. Alkali molecules inweakly-bound high-spin states have been probed in the first 2DES studies on heliumdroplets.During the last 20 years, helium droplet isolation has been applied to a largevariety of spectroscopic techniques. The results have been reviewed in variouspublications and we refer to these for further information [159, 150, 47, 153, 136,160, 139, 161]. A typical helium nanodroplet apparatus is depicted in Fig. 9a. Helium droplets(He N ) with an average size of N ≈ P = 50 bar stagnation pressure and about T = 15 K nozzletemperature. The molecular beam machine consists of a differentially pumped linearchain of HV/UHV vacuum chambers guiding the initially formed helium droplet beamvia the doping unit to different detection chambers. Laser pulses can be introducedalternativly into a fluorescence detector, a magnetic bottle-type electron time-of-flight (TOF) spectrometer or a ion-TOF mass spectrometer, respectively. The mildly oherent multidimensional spectroscopy in the gas phase Heliumdroplet Doping Evaporative cooling Molecule formation Laser interaction
Rb atom Rb quartet LaserHe N He N He N He N He N Figure 11.
He droplet assisted formation mechanism of the investigated Rbmolecules. By picking up several atoms, molecules are formed on the clustersurface. Evaporation of He atoms efficiently dissipates the released binding energyand cools the formed molecule to its vibrational ground state. Due to thismechanism, the formation of the Rb molecules in their lowest weakly-bound high-spin state is preferred. The higher binding energy of the low-spin electronic groundstate molecules leads to desorption or droplet destruction, due to which thesemolecular configuaritons are normally not detected in the experiments. Furtherdownstream, the prepared doped droplets are probed via 2DES. Graphic takenfrom Ref. [74], licensed under the Creative Commons Attribution 4.0 InternationalLicense. focussed laser and the droplet beam intersect perpendicularly. Since the droplet beamis travelling at about 400 m/s and the repetition rate of the laser is 200 kHz, each setof 2DES laser pulses acts on a fresh section of the target beam. Typical signal ratesare one ion/electron per laser shot at target densities of about 10 droplets per cm − .The magnetic bottle spectrometer for photoelectron spectroscopy has a resolution∆ E/E ≈
5. Gas-phase 2DES of isolated, cold molecules
Recently, we have combined PM-2DES with HENDI and studied Rb and Rb molecules prepared in their weakly-bound high-spin states. These experimentsconstitute the first 2DES study of isolated, cold molecules prepared at sub-Kelvintemperatures.Fig. 12 shows the potential energy curves (PECs) of the molecules. Both moleculeshave been previously studied with HENDI using high resolution steady-state laserspectroscopy [163, 164, 165] and femtosecond quantum beat spectroscopy [166, 167,168]. The steady-state laser absorption and emission spectra are shown in Fig. 13a, b.The Rb molecule shows a pronounced absorption at the 1 Π g ← a Σ +u excitation withresolved spin-orbit (SO) couplings of the excited state. Note, that the 1 g absorptiondoes not appear in HENDI experiments. In the Rb molecule, the 1 A (cid:48)(cid:48) , ← A (cid:48) absorption peak is observed. Emission spectra have been only reported for the Rb molecule (Fig. 13b). 2D spectra taken of the same molecules attached to heliumdroplets are shown in Fig. 13c for photoion detection and in (d) for photoelectrondetection. Both are taken under different ionization conditions with the purpose toselectively amplifying certain features (see discussion below).The 2D frequency-correlation maps exhibit high quality, in particular ifconsidering the challenging experimental conditions. They show sharp, well-separated oherent multidimensional spectroscopy in the gas phase Figure 12.
PECs of Rb triplet (a) and Rb quartet (b) manifolds. Arrowsindicate the probed transitions. In (a), the perturbation of the 0 +g state bythe helium environment is schematically shown as dashed curve. The Rb PEC graphic is adapted from Ref. [74], licensed under the Creative CommonsAttribution 4.0 International License. The Rb PEC graphic is adapted bypermission from Springer Nature: Ref. [162], License Number: 4606941432839. spectral features, which is not common in condensed phase studies, indicating theresolution advantage of the gas-phase approach. Remarkably, these spectra weretaken for very small number densities of doped droplets being only n ≈ cm − which corresponds to roughly 300 absorbers inside the laser interaction volume.For these conditions, the integral optical density (OD) of the sample estimates toOD = − log ( I/I ) ∼ − [74]. This is several orders of magnitude lower than inprevious 2D spectroscopy studies, where the OD typically ranges between 0.1 and 1.Our experiments thus indicate a drastic improvement in sensitivity and open up newpossibilities for an expansion to other fields, e.g. ultra cold atom clouds [169] and ioncrystals [170] or towards single-molecule studies [105].In comparison with the previous 1D spectroscopy measurements of the molecules,the advantages and additional information gained by 2D spectroscopy becomeapparent. While the 2D spectra show the same absorption lines as in the 1D steady-state spectroscopy, correlated to the absorption bands, additional ESA pathways(negative peaks) and cross-peaks (red shifted positive peaks) are revealed. TheESA features expose the different ionization pathways as a function of the molecularexcitation and show the position of respective Frank-Condon (FC) windows to higher-lying states [74]. This information was not available in previous photoionization studiesof these molecules [166], but, in principle, may be gained by narrow-band two-colorpump-probe ionization experiments. The advantage of the 2DES approach is, that oherent multidimensional spectroscopy in the gas phase Figure 13.
Comparison of Rb and Rb spectra obtained with 1D and2D spectroscopy methods. (a,b) Absorption and emission spectra from highresolution laser spectroscopy (black) and 2D spectroscopy (red), obtained from ahorizontal/vertical cuts through the 2D spectra in (d,c), respectively. The laserspectrum used in the 2DES experiments is shown in the background (gray). (c)Photoion-detected 2D spectrum at population time T = 200 fs, excitation pulse1-4 center wavelength: 722 nm, ionization pulse: 670 nm. (d) Photoelectron-detected 2D spectrum at population time T = 700 fs, excitation pulse 1-4 centerwavelength: 732 nm, measured without additional ionization pulse. Color scale issaturated by a factor of 1.3. Adapted from Ref. [74], licensed under the CreativeCommons Attribution 4.0 International License. high spectral resolution is gained even when using broadband femtosecond pulses (seepulse spectra in Fig. 13a,b), that cover all transitions simultaneously and also permitfemtosecond temporal resolution.Furthermore, in Fig. 13a, we show a direct comparison of line shapes obtainedfrom steady-state spectroscopy and 2DES. To this end, the 2D spectra were integratedalong certain horizontal/vertical spectral intervals [74]. We find a remarkably goodmatch of absorption and emission profiles and equal spectral resolution for bothmethods, confirming that the Fourier transform concept of 2D spectroscopy indeedachieves optimum spectral resolution. Note that the relative amplitude missmatch inthe absorptive profiles of Rb corresponds to different ionization probabilities of therespective states.For the Rb emission spectrum, the situation is slightly different. The steady-state spectroscopy captures mainly the emitted fluorescence of free gas-phase moleculeswhich tend to desorb from the droplet surface after their excitation [171, 172]. Thisexplains the absence of the ESA resonance (negative peak at 13 250 cm − ) and thewell resolved vibronic features around 13 300 cm − .In contrast, the 2DES measurements provide spectral information withfemtosecond time resolution (as a function of the evolution time T ) and reproducethe spectrally broadened response of the Rb molecules while being still attachedto the droplet surface. As such, an almost identical pump and probe profile of the a Σ +u → Π g transition is observed. The absence of a Stokes shift is due to a verynarrow FC window between the shallow ground state potential and the 1 Π g state [74]. oherent multidimensional spectroscopy in the gas phase ω τ (x10 cm -1 ) ω t ( x c m - ) -1.0-0.50.00.51.0 T=0fs 225020001750150012501000750500250
GSBSE a) b) S i gna l ( a r b . un i t s ) Figure 14.
System-bath dynamics in the Rb He N system. (a) Time evolution ofspectral features correlated to the Rb A (cid:48) → A (cid:48)(cid:48) , absorption. (b) Schematicof the Rb -He N interaction potentials. Steps 1-3 sketch the repulsion of the heliumdensity following the impulsive excitation of the Rb molecule. The excited staterelaxation process is traced by SE signals, whereas GSB signals probe the groundstate where no system-bath dynamics occur. Adapted from Ref. [74], licensedunder the Creative Commons Attribution 4.0 International License. The femtosecond time resolution of the 2DES study, furthermore, has revealedthe coherent WP dynamics of the Rb molecule (not shown), which permitted arefined interpretation of the Stokes peak appearing at 12 900 cm − . While thisfeature was previously interpreted as the emission from vibrationally relaxed free gas-phase Rb molecules [163], the 2DES experiments point to an ultrafast intramolecularrelaxation into the outer potential well of the 1 Π g state, catalyzed by the heliumperturbation. This population transfer shows a remarkable efficiency, taking placewithin <
100 fs [74].
Using the helium nanodroplets as a matrix to isolate and cool down molecules, hasthe advantage of forming enclosed nanometer-sized model systems in an ultra highvacuum environment. This allows us to expand our studies beyond pure intramoleculardynamics towards intermolecular effects and the exploration of system-bath couplingsinduced by well-controlled environmental parameters.For instance, different types of system-bath interactions can be modeled by co-doping of the droplets with rare gas atoms or solvent molecules (Fig. 9b) [173, 174].Alkali-metals show here an exceptional behavior and induce already a significantinteraction with the pure helium droplets. This is explained by the strong Pauli-repulsion between the loosely-bound valence electrons of the alkali-metal atomswith the closed-shell 1 s configuration of the helium atoms [158]. Alkali atoms andmolecules thus serve as ideal probes to sense the interaction potentials and dynamicalbehavior of the superfluid droplets and allow us to explore the properties of thequantum fluid itself.An example of static guest-host interaction has been already discussed above forthe perturbation of the Rb (1) Π g , +g potential, opening up an ultrafast molecularrelaxation channel which is not observed in the gas phase. The Rb excitationreveals, on the contrary, an example of the ultrafast dynamic droplet response whenimpulsively pumping energy into the system through an impurity (Fig. 14).Upon excitation of the Rb molecule, its electron density distribution expands,causing a repulsion of the surrounding helium atoms on a few-picosecond time scale, oherent multidimensional spectroscopy in the gas phase a) NO mass + b) NO mass + Figure 15.
Ion-mass detected 2DES of gaseous NO molecules. Absorptive 2Dcorrelation spectra extracted from the NO +2 parent ion in a) and the ion fragmentNO + in b). Adapted from Ref. [73], licensed under the Creative CommonsAttribution 4.0 International License. while the heavy Rb molecule effectively remains in position and slowly desorbs fromthe droplet surface on a much longer time scale (estimated to be >
10 ps).The 2DES experiment allows us to directly follow the initial fast repulsion of thequantum liquid. Here, we observe a dynamic Stokes shift along the probe-frequencyaxis of the 2D spectra (Fig. 14a), which reflects the system’s relaxation on the excitedstate of the Rb -He N interaction potential (Fig. 14b). Our time-resolved study revealsa rearrangement of the helium density towards the Rb ∗ He N equilibrium state within2.5 ps. Note, that the Rb peak on the diagonal position reflects the dynamics on thesystem’s ground state where the Rb -He N interaction is of static character.The here discussed example of system-bath dynamics represents a unique casewhere a single, isolated molecule interacts with a homogeneous environment. It allowsus to directly probe the system-bath interaction potential without inhomogeneousbroadening. This is in contrast to condensed phase studies, where a statisticalensemble of molecules is probed in an inhomogeneous environment. There, local bathfluctuations typically lead to a diffusion of the lineshape over time [20, 22] rather thanresolving a dynamic Stokes shift. As such, our experimental approach provides aninteresting alternative route to elucidate the influence of environmental parameterson molecular processes.
6. Photoionization as a selective and versatile probe
One benefit of the photoionization is the vast array of highly developed electron/iondetectors enabling for instance energy- or mass-resolved spectroscopy. Dependingon the detection method, one hereby is able to add extra dimensions to the 2Dspectroscopy measurements which permits further disentanglement of excitation andreaction pathways.
A first demonstration of 2D spectroscopy combined with ion-mass detection has beenrecently reported by Brixner et al. [73]. Here, a warm effusive beam of gaseous oherent multidimensional spectroscopy in the gas phase molecules was studied. Multiphoton excitation and ionization of the samplewas induced by four collinear VIS pulses produced by an acousto-optical pulseshaper. Rapid shot-to-shot phase cycling was incorporated to improve signal to noiseperformance [95] and to isolate the nonlinear response from NO +2 and NO + ion yields(Fig. 15).Both ion signals reveal clear differences in their line shape and sign of amplitudes,which points to different excitation pathways leading to the ionic products. Inaccordance with their hypothesis, a laser intensity analysis shows different high-ordermultiphoton processes for the detected cationic signals (8’th order for NO +2 and 10’thorder for NO + ). The high-order nonlinearity reveals the challenging experimentalconditions in this study, however, also leads to ambiguities due to many overlappinghigh-order pathways that cannot be discriminated. This might be resolved in thefuture by incorporating additional phase cycling steps or extended pulse sequences.In general, the multiphoton ion-mass-detected 2D spectroscopy approach showsthe potential to study ionization pathways and ultrafast autoionization processes inhighly excited Rydberg manifolds of gaseous molecules, where 2D spectroscopy mayprovide additional information about transient intermediate states and improves theanalysis of complex high-order multiphoton processes.In the same fashion to this study, we have combined ion-mass detection withthe phase modulation approach. In an early demonstration, we combined phase-modulated quantum interference measurements with a quadrupole ion mass filter forsensitive detection of RbHe excimer formations [54]. For our 2DES experiments, weused instead an ion-TOF spectrometry arrangement (Fig. 16). The 2D spectra ofspecific masses are recorded by means of TOF-gating using boxcar integrators. Tothis end, boxcar windows are placed on the respective mass peaks in the ion-TOFtransients and the boxcar output is fed into the lock-in detection and processed asdiscussed in section 3.For the above discussed study of Rb molecules, the ion-TOF distribution(Fig. 16a) shows three significant peaks, which correspond to the Rb + , Rb +2 and Rb +3 species. Examples of obtained 2D spectra (for population time T = 700 fs) are shownin (Fig. 16c,d) along with a 2D spectrum recorded without mass-gating as a reference(Fig. 16b). From these measurements, we can learn more details about the photo-induced dissociation dynamics and can identify specific dissociation channels.For the used laser frequencies, Rb atoms may only be ionized via off-resonantthree-photon excitation, which is a negligible process for the applied low laserintensities. Thus, the Rb + cations reflect the dissociation products of Rb and Rb molecules and carry the nonlinear response of both parent molecules, respectively, asreflected in the 2D spectrum of Fig. 16c. Here, we directly see, that the ESA pathway inthe Rb molecule leads to a dominant production of Rb + ions, whereas neither dimer(Fig. 16d) nor trimer ions (not shown) are detectable for this excitation/ionizationchannel. This stands in contrast to the photodynamics in the Rb molecule, whereexcitation to the (1) Π g manifold and subsequent ionization leads only to a smallproduction of Rb + fragments and most signal is detected in the Rb +2
2D spectrum.Interestingly, the Rb ESA excitation pathway is absent in all ion-detectedmeasurements but can be clearly observed in photoelectron measurements (Fig. 13d).This may be explained by a direct transition into the ion continuum or an ultrafastautoionization induced via the ESA pathway. Both processes would lead to immediateionization by pulses 3, 4 before desorption of the excited molecule from the dropletsurface has taken place. This is followed by the solvation of the cation into the helium oherent multidimensional spectroscopy in the gas phase ω τ (x10 cm -1 ) ω τ (x10 cm -1 ) ω τ (x10 cm -1 ) ω t ( x c m - ) ω t ( x c m - ) ω t ( x c m - ) I on y i e l d ( a r b . un i t s ) Ion TOF ( μ s) S i gna l ( a r b . un i t s ) -1.0-0.50.00.51.0 a) b)c) d) Rb + Rb + Rb + Rb Rb Integral ion yieldRb + mass Rb mass + Figure 16.
Mass-resolved 2DES. (a) Ion time-of-flight (TOF) trace ofphotoionized rubidium molecules desorbed from helium nanodroplets (recordedwith additional, delayed ionization laser). (b) 2D spectrum recorded without massselection. (c-d) 2D spectrum recorded at masses Rb + and Rb +2 , respectively. droplet accompanied by the formation of a surrounding high density shell of He atoms( snowball formation), which can be detected at large masses ( >
500 amu) [171]. Incontrast, the lower-lying ESA transition can be observed in ion-detected spectra atcertain population times (Fig. 13c), which indicates the absence of a coupling to theion continuum for slightly lower-lying states.Eventually, the sum of the 2D spectra recorded for individual mass-species(Fig. 16c,d) matches with the spectrum obtained from integral ion yields (Fig. 16b),confirming that no signals are omitted in the mass-selective detection.Both examples, from the Brixner group and our group, show the addedinformation, one may gain by combining coherent 2D spectroscopy with massspectrometry. As an advantage over conventional pump-probe mass spectrometry,2DES provides spectral information for pump and probe steps and is able to trackthe coherent molecular dynamics. This information may help to decipher complexultrafast photoreactions including involved dissociative dynamics. A crucial point in all action-detected 2DES is the modulation contrast. Themeasurements rely on the detection of small modulations of a nonlinear population,induced by the coherent interactions of four optical pulses. Systematic modulation ofthe pulses’ phase induces an alternation of the probability to reach the final populationstate. By applying well-defined phase patterns on the excitation pulses, the desiredthird-order nonlinear response of the system can be isolated from population signals oherent multidimensional spectroscopy in the gas phase Figure 17.
Comparison of photoionization schemes and modulation contrast. a)Oscillation of the population probability in a two-level system as a function of therelative delay and phase of excitation pulses. b,c) Mapping of populations to theion continuum by photoionization. A nonlinear population state is induced bythe 4-pulse sequence used in action-detected 2D spectroscopy (red arrow), whichis detected via multiphoton ionization (a) or one-photon ionization (b). Theionization of ground ( | g (cid:105) ) and excited states ( | e (cid:105) ) is shown by green/blue arrows.Dashed lines indicate resonant or virtual intermediate states in the multiphotonionization. modulated at different patterns and non-modulated background contributions.The sensitivity of this detection concept critically depends on the detectioncontrast between the final excited population state and the complementary state (e.g.the ground state). This becomes clear when considering the simple case of a two-levelsystem, where a coherence induced between both states leads to a complementary(antiphase) oscillation of the excited and ground state population as a function ofthe relative pulse delay/phase (Fig. 17a). If excited and ground state populations aredetected with equal probability, the modulation contrast is lost and a constant signalis measured. Hence, a high contrast between the detection efficiency of both states isimportant.An alternative explanation is given by the Feynman diagrams in Fig 6b. For eachprocess, always two complementary pathways exist (denoted as 1 and 2), which differin the final population state (being | e (cid:105) and | g (cid:105) or | f (cid:105) and | e (cid:105) ). Both pathways areidentical except for the 4’th interaction, leading to an antiphase modulation of thesignal yield. If both contributions (i.e. final population states) are detected with thesame efficiency, the modulations cancel each other leading to a depletion of the signal.In case of multiphoton ionization of the sample, a reasonably strong modulationcontrast is naturally given, since complementary states require different numbers ofphotons for the ionization (Fig. 17b). Here, care must be taken to avoid saturationand hence loss of modulation contrast due to an intense ionization laser which is closeto resonance with the probed transition ( | g (cid:105) → | e (cid:105) ). The least photons are requiredfor the ionization of ESA pathways ending in a high-lying population state (ESA2 inFig 6b), due to which these signals are generally amplified in mulitphoton detection.Likewise, any state may be selectively amplified by suitable choice of ionization laserwavelength and consideration of resonant intermediate levels. This property might beexploited to amplify and discriminate certain features in the 2D spectra in order tofurther disentangle overlapping spectral features from different species (Fig. 13). oherent multidimensional spectroscopy in the gas phase
7. Outlook
In conclusion, action-detected 2DES has already demonstrated a high degreeof sensitivity in measurements including both high spectral resolution and fullfemtosecond dynamics, thereby facilitating the combination with extremely dilutesamples like molecular beams at target densities down to 10 cm − or even below. Thecombination with HENDI yields studies at millikelvin temperatures and unprecedentedhigh resolution enabling a new level in the interpretation of dynamics in comparisonwith theory. The HENDI technique provides a plethora of tailored model systemsranging from weakly-bound van der Waals molecules, microsolvated systems up tospecifically designed large organic complexes. Other prospective targets like size-selected free ions or charged clusters may open alternative avenues where 2DES couldprovide new insight, thus, being the ideal playground to study photoinduced ultrafastprocesses.Furthermore, with the capabilities demonstrated already, coherent spectroscpoymay find its way into new disciplines. E.g., the field of Quantum Optics could pivotallygain from corresponding new approaches. Ultracold ensembles in optical lattices orcold Rydberg gases might be studied with respect to the full dynamics of all coupledstates, or Markovian vs. non-Markovian dissipation when probing interactions withexternal modes. On the other hand, high sensitive detection methods, as introducedabove, are prerequisite for experiments on non-trivial quantum effects exploitinge.g. correlation experiments with single photon light sources. With the ongoingdevelopment of high repetition rate and high photon flux sources, exciting experimentshave come into reach. The photoionization detection proved to be a valuable extension in 2DES. Thevariety of detection schemes available at UHV conditions grants a high control ofthe detection process, thereby simplifying 2D spectra through precise selectivity, andadding a considerable amount of complementary information. The incorporation offurther detection schemes will open extra dimensions in multidimensional spectroscopyschemes. Velocity-map-imaging combined with sophisticated online data processingoffers not only selected photoelectron energies but also electron emission angles asextra dimension. VMI ion images can provide directionality in dissociation processes. oherent multidimensional spectroscopy in the gas phase
The introduced phase-cycling methods inherently enable the detection of higherharmonic processes, e.g. in high-harmonic demodulation at phase-modulationexperiments [117]. Apart from studying multiple quantum coherences (MQC)[117,122, 69], it has been demonstrated, that this can be employed for phase-modulation experiments using light generated in higher harmonic generation (HHG)processes [119]. In a recent approach, we successfully performed an extension of thiswork at the seeded Free-Electron Laser (FEL) FERMI, where by means of phasemodulation of the UV seed laser, attosecond wave packet interferometry at XUVphoton energies (28 eV) was done [177]. Control of femtosecond pulse timing andCEP at higher harmonics in the XUV has been demonstrated, only acting on thefundamental UV laser pulses. In view of the rich options based on HHG XUVlight sources covering pulse durations down to the attosecond range, the prospectiveextension of multidimensional coherent methods at high photon energies would opena new field including inner shell processes, site specifity in molecular complexes, andattosecond time resolution.Of course, many specific aspects realizing these kind of new experiments are stillto be worked out and will remain challenging. However, the recent steps in 2DES areencouraging for many more exciting experiments that are underway.
Acknowledgments
Funding by the European Research Council within the Advanced Grant ”COCONIS”(694965), by the Bundesministerium f¨ur Bildung und Forschung (05K16VFB) and bythe Deutsche Forschungsgemeinschaft (IRTG 2079) are acknowledged.
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