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David Schumacher Zeno nonlinear response ultrafast optical an of sensing force Nanoscale www.pnas.org/cgi/doi/10.1073/pnas.2003945117 microscopy force atomic at effects electrons or optical photons surface. emitted nonlinear the for from revisit need the to without means nanoscale, the powerful a electrostatic its is through force polarization nonlinear a capa- measure The to thus methods. bility is microscopy force and atomic cantilever resulting regular the by detectable force of frequency below The resonance components mechanical frequency sample. the has interaction the nonlinear second- in this a from interaction by fields. explained optical nonlinear qualitatively femtosecond be order can by forces driven polarization measured dielectric The microscopic, optical insulating nonlinear the an a resolving in from spatially is arising forces microscopy and electrostatic force temporally atomic of time-resolved capable that signal Here, decreases. demonstrate their volume probe however, we the limitation as scatterers; unfavorably this nanoscale scales strength circumvent local employing techniques by near-field Sev- via resolution. powerful spatial detected limiting eral fields. usually thus emission, light are light far-field strong polarizations their under probe microscopic sensitive dynamics induced a structural The is review and material for (received a electronic 2020 of 2, of July response Fisk optical Zachary nonlinear Member Board The Editorial by accepted and FL, Tallahassee, 2020) University, 2, State March Florida Cao, Jianming by Edited Germany nteodro e nanometers. few typically a system, of our order in spatial the in radius, on the tip change the AFM, the by In determined through (nc-AFM). is times resolution AFM delay noncontact using of by function sample with force the a pulses in as polarization measured electric two is in by change The induced width. polarization ∼100-fs gen- to electric niobate an lithium the erate of of advantage susceptibility take nonlinear We second-order (UHV). vacuum by ultrahigh tem- in niobate room at perature lithium (tr-AFM) AFM in time-resolved polarization using detection induced force optically the of sci- scale material physiological in in including grail environment, obtain semiconduc- any holy to solutions. in insulators, a used metals on and is be data tors, can fs) structural (AFM) resolved 100 and microscopy atomically to force (nanometer) fs Atomic length ence. (10 and relevant spatial scales the simultaneous time on Achieving femtosecond resolution fun- (1). the temporal many at scale trap observed among nanometer or be are and to defects behavior waiting of and processes effects motion damental the electron and on or solids, states sin- in conditions of reactions, dynamics processing motion chemical during electron the of changes defects level, conformation function fundamental molecules, of a gle more diversity a as On the material composition. of given appli- a relation characterization particular the in structure–property a is the challenge for experimental of material major the (or A of and cation. electricity lifetime viability the other to economic determine ultimately and thus light defects sites, These converting versa). recombination vice when traps, limitations charge efficiency to lead fections D eateto hsc,MGl nvriy otelQ 3 T,Cnd;and Canada; 2T8, H3A QC Montreal University, McGill Physics, of Department ee edmntaemaueet ntefmoeodtime femtosecond the on measurements demonstrate we Here, neape noteetoi aeil,srcua imper- structural materials, optoelectronic As in materials. example, real-world of an properties the determine efects a a,1,2 n ee Gr Peter and , | time-resolved aaRejali Rasa , | utter ¨ olna nonlinear a ahe Pachlatko Raphael , a,1 a nra Spielhofer Andreas , b doi:10.1073/pnas.2003945117/-/DCSupplemental at online information supporting contains article This 2 1 BY-NC-ND) (CC 4.0 NoDerivatives License distributed under is article access open This hsatcei NSDrc umsin ..i us dtrivtdb h Editorial the by invited editor guest a is J.C. Submission. Direct PNAS Board. a is article This interest.y competing no declare experimental authors the The improved paper.y the and wrote P.G. maintained and Y.M. D.G.C., MoSe and the A.S., fabricated R.P., P.N. and setup; R.R., A.S., ana- R.P., R.R. Z.S., and R.R., Z.S. data; Z.S., tools; lyzed reagents/analytic research; new designed contributed P.N. P.G. research; and performed Y.M. D.G.C., Z.S., contributions: Author pia olna susceptibility nonlinear second-order optical large a and structure, crystal noncentrosymmetric a the during fixed and remains aligned thereby simultane- is and beam stimulation tip, experiment. posi- laser the optical to fixed The relative images. the a focused AFM in to regular held response with variations is spatial ously tip sample the measure the the to setup, scanned of our is sample In the 1. and tion, Fig. the in inten- with shown light time, (∼ is delay the illumination in laser other, the oscillates, of each junction period two tip–sample to the the respect As at non- system. with sity UHV a delayed tip–sample a in are the in incorporated arranged onto pulses AFM focused be an and can of delay fashion junction trains temporal collinear pulse generate or well-defined The collinear a to two. with NIR), the trains, pro between pulse FemtoFiber wave- coherent (Toptica central laser two 780-nm mW fiber and femtosecond 200 rate mode-locked length, repetition a 80-MHz of at output operating the split We Results eateto hsc,Uiest fRgnbr,903Regensburg, 93053 Regensburg, of University Physics, of Department rsn drs:Dprmn fPyis T uih 03Zrc,Switzerland.y Zurich, 8093 Zurich, ETH Physics, of Department address: peter.Present or [email protected] Email: addressed. be [email protected]. may correspondence whom To aeil eevso hstcnqewl lo h correla- time-resolved the light-induced allow with kinetics. structure will any nanometer technique in of this tion nonlin- resolution envision spatial ultrafast We with observe material. Our interactions to sensor. interactions, light–matter possibility force tip–sample ear the nonlinear the advancing on of rely thus char- properties not pulse does the time light method 100-fs the by by and not set scale is acteristics, sub-15-nm resolution a time on The inter- the resolution. sample optical the in nonlinear in changes second-order actions observe from We originating microscopy. from measuredforce force be we originating can atomic dielectric Here, force using a fields. in electrostatic motion light electron the light-induced nanoscale ultrafast that by by governed demonstrate induced are motion materials charge of properties Optical Significance ihu ibt sa nuao ihabn a f37 V(2), eV 3.78 of gap band a with insulator an is niobate Lithium y y a hlp Nagler Philipp , 2 ape ..sprie h xeiet n .. R.R., Z.S., and experiment; the supervised P.G. sample; . y raieCmosAttribution-NonCommercial- Commons Creative χ (2) 2.6 . ngnrl h lcrcfield electric the general, In . y b ociMiyahara Yoichi , https://www.pnas.org/lookup/suppl/ s.Asec ftesystem the of sketch A fs). NSLts Articles Latest PNAS a , | f7 of 1

PHYSICS ABAFM Tip Stimulation AFM Detection Frequency shift recorded Laser Deflection PLL PID Z-Feedback Light Induced Photodiode p-Polarized Polarization Laser Diode Optical Cantilever Excitation E(t) Piezo Drive Fine Delay Lithium Δ 1 Niobate E(t+ ) Coarse U(x) Delay Line /2 Sample Δ 2 Focusing Lens P BBO Crystal Potential SP Filter Energy Optical Piezo Photodetector Photon Electron

CD Tip-sample interaction 12.5ns OR ~100 fs Cantilever resonance 80MHz & ~300kHz DFG Polarization 80 MHz Real time First radiating mode Tip-sample force measurement at each delay point Polarization ~1/100 fs 10 THz 2.6 fs (780nm)

0 Hz 80 MHz 384 THz (780nm) Spectral (2) χ nonlinear frequency Sample response Optical frequency Frequency shift optical interaction Delay time

Fig. 1. (A) Illustration of the experimental setup and beam alignment. An ultrafast laser is incorporated into an UHV-AFM. The laser beam is split, and one beam is time delayed, before both beams are recombined and focused into the UHV chamber. The beam impinges on the sample surface with an angle of ∼ 80◦ relative to the surface normal. (B) The ultrafast pulses, with τ denoting the relative temporal delay between the two, incident on the sample surface. The optical stimulation causes the electrons in the nonlinear medium to oscillate in the anharmonic potential of a noncentrosymmetric crystal (solid line), thereby generating a net static polarization. A purely parabolic potential (dashed line), characteristic of a linear medium, is shown for reference. (C) Spectral frequency sketch of the occurring signal. The χ(2) nonlinear interaction is converting the optical frequency down to a quasi-DC sample response (0 Hz), which, in turn, is detected by the AFM through the tip–sample interaction. (D) Time domain representation of the nonlinear polarization repeating at the repetition rate of the laser with a duration of the pulse overlap. The AFM measurement in delay time samples the nonzero averaged component (quasi-DC, 0 Hz) of this nonlinear polarization at each delay step, resulting in the sketched interference measurement.

of an impinging laser pulse causes electrons in the medium to well-known nonlinear effects, such as optical rectification (OR), oscillate around the potential minimum. However, in a nonlin- sum frequency generation (SFG), difference frequency genera- ear material, such as lithium niobate, this potential is no longer tion (DFG), and second harmonic generation (SHG) follow (see purely parabolic, due to the higher-order perturbations, and the Materials and Methods for details). resultant motion of the electrons in the potential well leads to Second-order interactions between pulses with the same cen- a net quasi-DC electric polarization, known as optical rectifica- ter frequency lead to quasi-DC polarizations. Here we separate tion, as shown in Fig. 1 (3). Optical rectification does not carry these polarizations into two parts: those arising from interactions any information about the phase of the optical carrier wave, but (2) of a pulse with itself POR(t) and between two separate and time instead gives rise to a polarization that follows the envelope of (2) the laser pulse. delayed pulses POR(t, τ). The resulting polarization from this (2) More generally, when two nonresonant intense electric fields POR(t, τ) term are incident on a material with a nonzero second-order sus- ceptibility, the resultant nonlinear polarization is described (2) (2) ? −iωτ P (t, τ) = 0χ E(t)E (t + τ)e [2] by (4) OR (2) (2) 2 P (t) = 0χ [E˜ (t) + E˜ (t + τ)] , [1] oscillates with respect to the delay time, τ, with a period of 2π/ω, and follows the envelope E(t) in real time t. This quasi-DC where E˜ (t) = E(t)e−iωt + E ?(t)eiωt , with the pulse envelope polarization retains the information about the phase differ- E(t) and ω denoting the carrier frequency. From Eq. 1, the ence between the two pulses. Even though this term has no

2 of 7 | www.pnas.org/cgi/doi/10.1073/pnas.2003945117 Schumacher et al. Downloaded by guest on September 30, 2021 Downloaded by guest on September 30, 2021 cuahre al. et Schumacher as written be can AFM the present, by 6) be and probed (5 will force time, electrostatic (see delay background The with constant a oscillating in not resulting is which term, iei hwn h tt h nest uoorlto,in autocorrelation, intensity the to fit filtering. low-pass the showing pro- is Gaussian 106.5 a line of Using width chamber. pulse UHV a the file, before retrieved placed recorded Concurrently photodiode traces, a envelope. autocorrelation using intensity (red) (D) upper and and interferometric optical (yellow) (B) lower the 108.6 of of fit width pulse A other. each to LiNbO in change tion (C 2. Fig. the to Additionally, due volume. errors delay in probe matching change phase nanometer-sized a without the from beams arising two field the electric between the in changes any from 1 originating (Fig. field electric MHz quasi-static 80 of rate time etition real in field oscillating lcrn.Ti niae htol h pia us duration, pulse optical the the of (λ/c only response that expected instantaneous indicates and as nonresonant This measured the electrons. 2.6 is to (period overlap due response delayed fs) oscillating pulse are An during beams other. two fs) each the to while respect 2A shift with Fig. frequency normal. recorded induced surface conjunction the strongest the the in along for niobate, occurring allows lithium polarization light, of incident crystal p-polarized thus can- z-cut with are the The of forces shift (7). frequency tip–sample tilever brought resonance sample; the is recording the by frequency to measured resonance proximity its close at into amplitude) optical (6-nm lating nonresonant for benchmark its good with a and, optics is nonlinearities. nonlinear gap, in band used large extensively is Niobate. crystal Lithium bulk on Measurements tr-AFM terms polarization two-beam and by denoted is material the in ization sample the and distance tip the between ence capacitance tip–sample the with C A oclierlsrcngrto;tesga sgnrtdb h polariza- the by generated is signal the configuration; laser noncollinear ) Norm. frequency shift oscil- cantilever a (FM-AFM), AFM modulation frequency In

0.98 0.99 1.01 1.02 Frequency shift [Hz] -17 -16 -15 -14 -13 1 olna and collinear (A) with measurement FM-AFM the of shift Frequency oc eeto opticaldetection force detection z h oeta rsn u otelgtidcdpolar- light-induced the to due arising potential The . 100100 0 -100 100 0 -100 Delay time[fs] Delay time[fs] F elec 3 = hl h w ae em r eae ihrespect with delayed are beams laser two the while 1 2 dC ± dz si esrdi ohcss h e solid red The cases. both in measured is fs 0.2  V t cpd ti tl usda h ae rep- laser the at pulsed still is it ± C C − si eoee,ilsrtdb the by illustrated recovered, is fs 3.8 P and h otc oeta differ- potential contact the , OR (2) V φ D Intensity [a.u.] B pol 0.2 0.4 0.6 0.8 dc

Intensity [a.u.] (t V 0 2 4 6 8 1 .AMcnpoethe probe can AFM D). hc otisteone- the contains which , − ) aeil n Methods). and Materials cpd 20-0 0 200 100 0 -100 -200 200 100 0 -100 -200 and P ihu ibt sa as niobate Lithium φ n h tip–sample the and , OR (2) e pol P (t  Delay time[fs] Delay time[fs] OR (2) , 2 τ , (t n resolve and ), xrce by extracted B, , τ ). P shows OR (2) 2 = [3] (t .6 ) ufc oml h aemaueet eepromdusing performed the were along measurements tip–sample decays same signal different The tr-AFM at normal. the surface recorded how is determine signal to distances the tip– of and amplitude First, the performed. polarization-, are power-, measurements distance-dependent optical sample various Measure- origin, tr-AFM induced Distance-Dependent and ments. Polarization-, by not Power-, and probe and pump the of detector. length AFM experiments AFM pulse the delay our the the in the by resolution of to limited time stability is that due frequency conclude or as thus We sensitivity 25 itself. the is not setup. time and delay delay setup time minimum measurable double-wedge the minimal our by The with separated ms. achievable points 2 step for data averaged delay data two each Two distinguish with swept. step, can delay is We height each trains at constant pulse taken two a are the points at between shift delay frequency 3E the Fig. while cantilever change. the shift of that frequency step surement resolvable delay achievable a minimal in the results determine to used be can sub-15-nm a on setup. response our to sample in used the the scale be of can 3C), 40%. variations signal Fig. of spatial tr-AFM drop in probe the another that scan by demonstrates line followed clearly 30%, (see This by each drops con- nm signal two scans 12.25 tr-AFM Within delay 3D. of full Fig. in steps the plotted nanometers, secutive are positions of two tens the at few taken ultra- a the within of signal drop the significant fast during the power illustrate laser To in signal inten- time. fluctuation tr-AFM autocorrelation measurement small any The measured for account reached. optically to is the sity when PPLN by recovered two the normalized is between of is and boundary terrace 3C), the upper due (Fig. the at likely regions situated is polarized adsorbent which oppositely the attenuation, surface of strong a amplitude loca- a The to the scan. shows on delay signal depending each tr-AFM of nm, location 400 the to in indicates profile nm height 200 (see of tion extent over lateral gradually changes a height The (8). directions poling different sample a an see creates (PPLN) of image, 3A niobate mode large-scale Fig. FM-AFM lithium surface. (for in poled sample recorded periodically the image on HF-etched the topography point pump– a each Thus, the at shows repeating resolution. scan by mapped delay spatial spatially probe microscopy be nanometer the can signal thereby intrinsic tr-AFM and its AFM, the retains on modifications sitate the of scale the the to of fringes. compared interference two interference volume optical smaller the the much a between detects from averaging measurement pulses spatial no AFM the the has to pulses, autocorrelation due noncollinear macro- sensitivity a as traditional phase collinear of a in While measurement signal arrangement. scopic oscillating noncollinear fast a a as shows measurement, well hand, AFM other of recorded the overlap concurrently on noncollinear The intensity the pulses. the two traces while the simply 2B), autocorrela- 2D) (Fig. (Fig. optical oscillations satisfied autocorrelation interferometric always fast the is exhibits expected, matching volume tion phase As probing that 2). small ensures (Fig. the tip AFM addition, the in of resolution; spatial high signal. S4 and h esrdsga a ulttvl emdldb Eq. by modeled technique. be excita- this qualitatively the of can in resolution (see signal cycles temporal measured the field The limits optical pulses, of tion number the specifically, ent httefs siltososre nteAMscan AFM the in observed oscillations fast the that note We neces- not does source laser ultrafast the of incorporation The us grants only not detector force our as tip AFM an Using aeil n Methods and Materials ofrhrcaatrz h rAMsga n t light- its and signal tr-AFM the characterize further To hw oprsno h acltdadmeasured and calculated the of comparison a shows 2-mhih ifrnebtentergoswith regions the between difference height ∼120-nm .Tedte line dotted The S5). Fig. Appendix, SI .Teetching The S5). Fig. Appendix, SI o details). for NSLts Articles Latest PNAS is S2 Figs. Appendix, SI samea- a is | f7 of 3 9

PHYSICS A 300 nm 150 nm

100

50

0 B D 150 -14 100 -15 50

Height [nm] -16

0 Frequency shift [Hz] 0 200 400 600 -100 0 100 CEDelay time [fs] 8 -398

6 -400 -402 4

tr-AFM [a.u.] -404

2 Frequency shift [Hz] 0 200 400 600 0123 Relative position [nm] Delay time [fs]

Fig. 3. Spatially resolved measurement of the ultrafast light-induced AFM signal. (A) The topography is shown, indicating the position of the line scan. At each point (separated by 12.25 nm), a full delay scan is performed. (C) The oscillation amplitude is plotted at each point, with (B) the extracted topography. The vertical lines indicate the extent of the surface adsorbent. (D) Raw data from the tr-AFM scans are shown, corresponding to the red and blue markers in the line scan (A and C), respectively. (E) Constant height nc-AFM measurement with minimal achievable delay. The full oscillation can be clearly resolved with a minimum resolvable step size of about ∼ 25 as.

s and p polarization. When p polarization is used (Fig. 4B), the nc-AFM distance-dependent spectra are fit to the electrostatic tip–sample force extends over a range of 700 nm, while, with s force from Eq. 4 with a tip–sample capacitance according to polarization, it decays toward 0 frequency shift within 200 nm. ref. 10 (see Materials and Methods for details). The distance- This can be explained by the surface or bulk response when using dependent results in Fig. 4A show that the photoinduced signal s or p polarization, respectively. Lithium niobate exhibits a sur- is present at both small and large gap spacings, and thus can- face nonlinear response resulting in a p polarization when driven not be due to a thermal expansion effect of the tip or sample. with s polarization (9). This surface response is observed to be Additional evidence of the electrostatic nature of the signal is weaker in amplitude, as seen with s polarization in our measure- given by a measurement on an island of MoSe2 shown in SI ment (Fig. 4). In Fig. 4A, the normal FM-AFM frequency shift Appendix, Fig. S1C. The symmetry breaking of odd-layer MoSe2 signal follows the same trend. Both the tr-AFM and the regular is expected to yield a χ(2) response and an enhanced SHG for

AC0 0.25 -50

-100 0.2

-150

Frequency shift [Hz] 0.15 -200

100 200 300 400 500 600 700 800 900 1000 1100 1200 B 0.25 0.1

0.2 tr-AFM amplitude

0.15

0.1 0.05

tr-AFM amplitude Data 0.05 s-pol. p-pol. Fit 0 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 0 5 10 15 20 25 30 Piezo position [nm] Average power [mW]

Fig. 4. (A and B) Frequency shift and tr-AFM signal amplitude vs. z-piezo position for two different optical polarizations. S polarization corresponds to the most optimal excitation along the z direction of the PPLN crystal, resulting in a stronger light-induced polarization. All measurements are fitted (solid line) to an electrostatic model. (C) Power-dependent measurement of the tr-AFM signal. A second-order polynomial is fitted to the data according to Eqs. 2 and 3.

4 of 7 | www.pnas.org/cgi/doi/10.1073/pnas.2003945117 Schumacher et al. Downloaded by guest on September 30, 2021 Downloaded by guest on September 30, 2021 cuahre al. et Schumacher ifrn olna fet n hi otiuint h overall between the distinguish to to contribution force. able their measured and are control- effects we nonlinear By polarization, different variations. light separation induced the tip–sample optically ling or as thermal such exclude artifacts can and response, sample the On (11). pumping resonant on absorption two-photon 92) rAMfrsraevlaemaueet 2–4,to (22–24), measurements voltage surface for force AFM (14, microscopy or THz photoinduced optical 19–21), as near-field (12–15), scanning such (16–18), microscopy microscopy techniques, com- tunneling probe responses scanning scanning optical nonlinear emerging conditions, of plements detection matching pre- The tr-AFM phase challenging. sented less to experiments optical insensitive nonlinear making is in scale without magnitude nanometer modeling of initio orders ab many over of interpolation space-time. validation for the need resolu- the allow as real-space nanometer of will such with Experiments wide- tion materials, dynamics electronics. or study electron optoelectronic PHz films, ultrafast detailed for in thin semiconductors the organic defects bandgap dichalcogenides, allow of charge metal particular, ultrafast role transition on in the effect will, of dis- their on and This spatial defects scale and the dynamics. length inhomogeneities studying nanometer of for a tr-AFM correlations method by and powerful detection tribution a force the localized become that by will predict limited we resolution methods, nanome- temporal pump–probe with well-established Using and measurement characteristics. injection processes, pump–probe resolution force or mixing a spatial shift via four-wave ter as measurable and electric be such averaged semiconductors should frequency, nonzero in zero a currents AFM. essentially in a with at results to field resolved which limited spatially change not induced be is can this However, materials nonlinear of of of distance layers few a a over of SiO response crystal the of imaging PPLN change By a large nm. 15 of a observed response have polarization the sam- we the the particular, by of the variation In not spatial Scanning response. the and ple of frequency. mapping length, allows then resonance pulse tip AFM mea- cantilever laser force the AFM this by 300-kHz of limited in resolution is time response to surement the polarization used Surprisingly, pulse-induced be material. can laser a measurements 100-fs force the that detect show we summary, In Discussion tr-AFM ultrafast electro- to measured this responses polarization of illumination. the nonlinear origin sample-specific The that is field nature. static conclude in electrostatic we is interaction 4, Fig. in in beams. term input additional φ (Eq. an the potential to of tip–sample leads intensity the polarization the second-order on behavior This linearly observed The Eqs. depends 4C. by ization Fig. fit in be shown can as power, laser input effects from these moving as when tip, the vanish substrate. of not expansion dis- an would tip–sample or light-induced that modulation, a indicates substrate from tance silicon originate the cannot on signal signal the a of the lack by The determined signal. mea- reference the envelope a car- on while an overlap, pump with surement pulse the the fs at at duration 2.6 pulse oscillating pump of signal period strong wave a rier observe we island, pol rmoreprmns ecnld htthe that conclude we experiments, our From oc rbn ftennierotclrsos tthe at response optical nonlinear the of probing Force the of function a as measured also was signal tr-AFM The /e 2 usrt,w eosrt htt-F esrstelocal the measures tr-AFM that demonstrate we substrate, ) 2 and φ pol ∝ SiO 2 P OR and (2) 2 usrt osntso n resolvable any show not does substrate (t oeta h eododrpolar- second-order the that Note 3. , τ ) ∝ ,whereby 3), (E ) 2 χ rmtedt presented data the From . 2 epne n optically Any response. MoSe ∆f 2 ∝ MoSe otesilicon the to (V χ cpd 2 2 response − n the and MoSe V dc − 2 in eut nteepeso o utpennierpoess hycnbe can They processes. nonlinear multiple as for written expression the Shift. in results Frequency tion, Measured the the in to mentioned As Polarization Second-Order of Contribution rmec emwl edt akrudwihcnb enb h DC the by seen be can which background a to lead The right. will the beam to labeled each are from term each for processes respective The function fitting a in resulting shift, frequency the describe to mW, 22.8 (z and mW 22.3 at constant power the keep respectively. to tip–sample plate absolute wave the 90 and reflect by izer not rotated does was this polarization that The a note set distance. should approach as is One closest drift position the nm. z long-term with 0 average distance, to for The tip–sample correct recorded. the is determining just overlap for feedback to pulsed used z full loop the the with feedback over performed scan slow is delay scan very delay a The with Hz. –2 on to rang- Hz points –222 set from shift frequency ing different to approaching by performed were attoseconds. Measurement. of Distance-Dependent the tens in few delay a overall of an size while generate step fixed to minimal is path a wedge achieve beam with One the To beam used: into ODL220). moved are the (Thorlabs is wedges between second quartz stage the two delay delay fs, temporal linear 0.6 The below a delays occurs. by delay, from piezo controlled the of nm is the sweep 0.5 pulses full of the by drift during that, lifted significant verified while was no was position It piezo tip swept. constant was a The delay at off. held the and turned point set was shift frequency feedback –400-Hz z the while Measurement. Single-Cycle to size step steps 1.2-fs missed/double stage. randomly to delay to size the due fs. step of response 0.6 0.6-fs frequency of false from stage any downsampled delay prevent linear scan are the delay data of The raw resolution extracted, laser. The highest is incident the THz the delay with 384 of performed versus around wavelength is amplitude the shift peak to frequency Extraction. the corresponds the FFT, which Amplitude the on From performed tr-AFM data. is time for (FFT) Analysis transform Fourier ms, Fast 10 in circle) 10-nm-diameter used. power a average be the to on (assumed depending sur- area sample probe sphere the per on a photons size on 900 spot approximately laser is The a face motors. of piezo consisting stick–slip home- AFM. by system, a controlled the steering via of chamber beam control UHV in-vacuum the for into built used coupled the is is with laser system interfering femtosecond-pulsed OC4 The laser Nanonis femtosecond sys- A the deflection measurement. from the AFM light of stray filter photodiode prevent band-pass four-quadrant to the A tem study. of this front in in mounted used is is configuration AFM deflection beam Setup. AFM Methods and Material high with nanoscale resolution. the temporal on interactions light–matter investigate (z o tigteeetottcmdl eue(10) use we model, electrostatic the fitting For P + (2) R))]V (t ) 2 +2E + + = 0 2 2E  χ omrilJO SM40AUVsse ihacantilever a with system UHV JSPM-4500A JEOL commercial A nfis prxmto,w s h rtdrvtv fteforce the of derivative first the use we approximation, first In . 0 (t (2) χ (t )E (2) )E [E (t (t (t h E + )E + (t Eq. Results, (t τ ) ω 2 ) ) ? e ? )e ∆f −2i e + −i −i y200 by µm E h igeccemaueetwsperformed was measurement single-cycle The ω ∝ (ω (ω (t t t t π +ω + −ω + 0 E o h eododrnnierpolariza- nonlinear second-order the for 1, τ (t (t (t " +τ )E +τ h itnedpnetmeasurements distance-dependent The R + z (t 2 2 )) ,wt netmtd200t 9,000 to 2,000 estimated an with µm, )) (z (R τ + + ) 2 + + τ e c ) −2i .c R) 2z ? ◦ ] . 2 i ) ω splrzto)uigapolar- a using polarization) (s # (t Ro P or (OR NSLts Articles Latest PNAS V +τ F rP or (DFG 2 . ) (SFG) (SHG) OR (2) OR (2) (t F )) (t z (z , τ ) )). = OR π | fast A f7 of 5 0 term [ R [7] [6] [5] [4] [8] 2 /

PHYSICS filter signal in SI Appendix, Figs. S2 and S4. The SHG and SFG terms both AFM Autocorrelation. In our experiment, a metal-coated silicon tip oscillate in time, but do not lead to a DC offset measured by our setup. (Nanosensors, PPP-NCHPt, f0 = 297.6 kHz, Q = 12,524) is approached to the Due to the zero frequency difference between the two laser pulses, the DFG sample surface. A measured normalized frequency shift (∆f/mean(∆f)) is term is not oscillating in real time. However, it is oscillating in delay time as shown in Fig. 2C. The tr-AFM signal can be recorded in multiple modes, (2) (2) shown in Eq. 2. The OR (POR(t)) and DFG (POR(t, τ)) terms are therefore the like any other spectroscopy technique in AFM. The measurement shown in two processes we measure in our setup. Fig. 2A is recorded with a very slow z feedback to correct for slow drift, but the feedback is not fast enough to compensate for the frequency shift   2 1 dC φOR(t) φOR(t, τ) change due to the pulse overlap. For the measurement in Fig. 2C, the AFM F = V − V − + . [9] elec 2 dz cpd dc e e tip is held at a constant height above the sample, while the beam delay is swept. The tip is occasionally approached to the surface to correct for any The polarization term φOR(t, τ) leads to an oscillation in delay time (Eq. 8), drift in the tip–sample distance. Fig. 2D shows an optical intensity autocorre- while the φOR(t) term leads to a DC offset with no modulation in delay time lation trace recorded simultaneously outside of the UHV chamber (Fig. 1A). (Eq. 5). This allows us to distinguish these two different terms in the AFM The envelopes of both curves are fit to a Gaussian profile, and this yields measurement and treat φOR(t) as a simple electrostatic background together a pulse width of 106.5 ± 0.2 fs for the optical intensity autocorrelation. with Vcpd as VBG. The envelope measured by FM-AFM shows a pulse width of 108.6 ± 3.8 fs. Due to the quadratic contribution to the force, φOR(t, τ) will also con- The observed pulse broadening can be accounted for by the dispersion that 2 tribute with a quadratic component φOR(t, τ) and a φOR(t, τ)*VBG compo- arises from the UHV window and the lens used to focus the beam into the nent. The φ (t, τ)2 term will exhibit a nonsymmetric shape in frequency OR UHV chamber. LiNbO3 as a sample can therefore be used to characterize the shift and have a component at zero frequency with a modulation fol- pulse shape at the tip apex. lowing the pulse envelope (SI Appendix, Fig. S4). The relative strength between the φOR(t, τ) and VBG components can alter the final signal toward Optical Autocorrelation. A β-barium borate crystal is used for optical auto- a symmetric or nonsymmetric shape, depending on the strength of the correlation measurements through SHG for both intensity (noncollinear) electrostatic background, including the one-beam φOR(t) term. A strong and interferometric (collinear) autocorrelation as shown in Fig. 1. A pho- VBG, as observed in the lithium niobate sample by the large frequency todiode is used for detection of the second harmonic signal, with either a shift and long approach curves, will lead to a stronger φOR(t, τ)*VBG over 2 spatial or low-pass filter to separate the signal from the fundamental. A the φOR(t, τ) contribution, resulting in the observed symmetric signal in Gaussian pulse is fitted to extract the pulse duration. An FFT with a low- lithium niobate. Comparable strength between the background and two- pass filter is applied to the interferometric autocorrelation to extract the beam polarization φOR(t, τ) term leads to an asymmetric signal in frequency intensity autocorrelation contribution. Built-in envelope extraction is used shift with a DC component following the pulse envelope, like observed in MATLAB to extract the envelope of the AFM autocorrelation signal. The in MoSe2. same fitting procedure used for the optical autocorrelation is applied to the Based on Eqs. 1 and 3, we can qualitatively model the response expected (2) (2) (2) extracted envelope to retrieve the pulse width. from POR(t) and POR(t, τ). Note that the polarization term POR(t, τ) leads to an oscillation in delay time with the period corresponding to the light fre- Chopper Measurements. The measurements on MoSe are performed with quency (Eq. 7), while the P(2) (t) term leads to a DC offset with no modulation 2 OR a chopper wheel in one arm of the interferometer. The use of the chopper in delay time (Eq. 4). The two contributions are thus present at different wheel results in the modulation of the AFM frequency shift at the chop- frequencies in delay time, and a Fourier analysis can be used to distin- per frequency. This modulation is detected with a Zurich Instruments lock-in guish and quantify their respective contributions. SI Appendix, Fig. S2 shows amplifier (UHF). The lock-in signal is directly proportional to the effects due the Fourier-filtered signal for the lithium niobate (SI Appendix, Fig. S2E), to illumination without any artifacts due to drift of the AFM tip during tip and the MoSe sample (SI Appendix, Fig. S2G). The measured results can 2 lift measurements (25). qualitatively be reproduced by our model including a strong electrostatic background. As mentioned above, a strong electrostatic background (SI Appendix, Fig. S2B) leads to a symmetrical response in frequency shift; the Lithium Niobate. The z cut of the crystal, in conjunction with p-polarized DC Fourier component at pulse overlap is strongly damped (SI Appendix, incident light, allows for the strongest induced polarization occurring along Fig. S2F). Assuming a weak electrostatic background (SI Appendix, Fig. S2D) the surface normal. results in an asymmetric shape in frequency shift and a noticeable signal in the DC component at pulse overlap. This qualitatively matches the measure- MoSe2 Sample Fabrication. The monolayer MoSe2 was obtained by using an all-dry polydimethylsiloxane (PDMS) transfer technique. For this, bulk ment on MoSe2 (SI Appendix, Fig. S2C). The strong electrostatic background in the lithium niobate manifests itself by the long approach curves and MoSe2 (HQ Graphene) was first mechanically exfoliated onto a PDMS sub- high-frequency shift set point needed to reach imaging condition close to strate and subsequently transferred on a silicon substrate with a 285-nm the surface. SiO2 capping layer. The thickness of the flake was determined by optical contrast. Spatially Resolved Measurement. The AFM tip is held at constant frequency shift with a slow z feedback to correct for long-term drift during the delay Data Availability. All relevant data supporting the findings of this study are scan at each point. From each delay scan, the tr-AFM signal amplitude is available at Figshare (https://doi.org/10.6084/m9.figshare.12478334). extracted according to the FFT analysis explained above. The extracted tr- ACKNOWLEDGMENTS. We acknowledge Christopher Phillips for provid- AFM amplitude is normalized by the optical autocorrelation intensity to ing the PPLN sample. This work was supported by Natural Sciences and account for any small fluctuation in laser power (average 7.29 mW) during Engineering Research Council of Canada, Fonds de recherche du Quebec´ – the measurement time. Nature et technologies, and Canada Foundation for Innovation.

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