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Hyojin Choi, [Jinjae Kim](https://orcid.org/0009-0003-9517-2824), Jiwon Park, Jekwan Lee, Wonhyeok Heo, Jaehyeon Kwon, Suk-Ho Lee, Faisal Ahmed, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Zhipei Sun](https://orcid.org/0000-0002-9771-5293), [Moon-Ho Jo](https://orcid.org/0000-0002-3160-358X), [Hyunyong Choi](https://orcid.org/0000-0003-3295-1049)

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[Ultrafast Floquet engineering of Fermi-polaron resonances in charge-tunable monolayer WSe2 devices](https://mdr.nims.go.jp/datasets/d03538df-88a9-43c0-b5f3-2ed74ffbebeb)

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Ultrafast Floquet engineering of Fermi-polaron resonances in charge-tunable monolayer WSe2 devicesArticle https://doi.org/10.1038/s41467-024-55138-5Ultrafast Floquet engineering of Fermi-polaron resonances in charge-tunablemonolayer WSe2 devicesHyojin Choi1,2,8, Jinjae Kim 1,2,8, Jiwon Park1,2, Jekwan Lee1,2, Wonhyeok Heo3,Jaehyeon Kwon3, Suk-Ho Lee4,5, Faisal Ahmed6, Kenji Watanabe 7,Takashi Taniguchi 7, Zhipei Sun 6,Moon-Ho Jo 4,5 &HyunyongChoi 1,2Fermi polarons are emerging quasiparticles when a bosonic impurityimmersed in a fermionic bath. Depending on the boson-fermion interactionstrength, the Fermi-polaron resonances exhibit either attractive or repulsiveinteractions, which impose further experimental challenges on understandingthe subtle light-driven dynamics. Here, we report the light-driven dynamics ofattractive and repulsive Fermi polarons in monolayer WSe2 devices. Time-resolved polaron resonances are probed using femtosecond below-gap Flo-quet engineering with tunable exciton-Fermi sea interactions. While conven-tional optical Stark shifts are observed in the weak interaction regime, theresonance shift of attractive polarons increases, but that of repulsive polaronsdecreases with increasing the Fermi-sea density. A model Hamiltonian usingChevy ansatz suggests the off-resonant pump excitation influences the freecarriers that interact with excitons in an opposite valley, thereby reducing thebinding energy of attractive polarons. Our findings may enable coherent Flo-quet engineering of Bose-Fermi mixtures in ultrafast time scales.As initially described by Landau1 and Pekar2, when electrons move in adielectric medium, fermionic particles are dressed by lattice distortion,resulting in Bose-polaron quasiparticles3. After elaboration byFröhlich4,5 and Feynman6,7, the polaron idea has successfully explainedmany-body exotic phenomena, for instance helium-3 in helium-4bosonic bath8, formation of bipolarons9, and Rydberg polarons inultracold quantum gases10–12. A similar counterpart is a Fermi polaron, abosonic impurity in a dressed fermionic bath. In the context of ultra-cold atoms, the large ratio of atomic transition energy to the fermionicparticle density can be straightforwardly controlled, enabling a strongcoupling regime of Bose-Fermi mixtures13. For solid state systems,although the significance of Fermi-polaron problems has beenexemplified in studying phase transition dynamics14–23, experimentalstudies on the transient Fermi-polaron problems have been barelyconducted. This may be partly because of the limited availability ofrigid bosonic candidates in fermion-rich solids; even when a well-characterized solid is prepared, probing the light-driven fine structuresof the Fermi-polaron branches is experimentally challenging.Atomically thin transition metal dichalcogenides (TMDs) exhibitstrong exciton binding energy ΔEX of around hundreds of meV due toboth the reduced Coulomb screening and the large effective mass ofelectrons and holes. Along with the atom-like bosonic impurity ofexcitons, the ability to electrostatically tune the Fermi energy EF offersa way to reach a strongly interacting regime of single mobile bosonReceived: 31 July 2024Accepted: 28 November 2024Check for updates1Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea. 2Institute of Applied Physics, Seoul National University, Seoul 08826,Korea. 3Semiconductor R&D Center, Samsung Electronics, Suwon 18848, Korea. 4Department of Materials Science and Engineering, Pohang University ofScience and Technology, Pohang 37673, Korea. 5Center for van der Waals Quantum Solids, Institute for Basic Science (IBS), Pohang 37673, Korea.6Department of Electronics and Nanoengineering and QTF Centre of Excellence, Aalto University, Espoo 02150, Finland. 7Advanced Materials Laboratory,National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 8These authors contributed equally: Hyojin Choi, Jinjae Kim.e-mail: mhjo@postech.ac.kr; hy.choi@snu.ac.krNature Communications |        (2024) 15:10852 11234567890():,;1234567890():,;http://orcid.org/0009-0003-9517-2824http://orcid.org/0009-0003-9517-2824http://orcid.org/0009-0003-9517-2824http://orcid.org/0009-0003-9517-2824http://orcid.org/0009-0003-9517-2824http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-9771-5293http://orcid.org/0000-0002-9771-5293http://orcid.org/0000-0002-9771-5293http://orcid.org/0000-0002-9771-5293http://orcid.org/0000-0002-9771-5293http://orcid.org/0000-0002-3160-358Xhttp://orcid.org/0000-0002-3160-358Xhttp://orcid.org/0000-0002-3160-358Xhttp://orcid.org/0000-0002-3160-358Xhttp://orcid.org/0000-0002-3160-358Xhttp://orcid.org/0000-0003-3295-1049http://orcid.org/0000-0003-3295-1049http://orcid.org/0000-0003-3295-1049http://orcid.org/0000-0003-3295-1049http://orcid.org/0000-0003-3295-1049http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-55138-5&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-55138-5&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-55138-5&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-55138-5&domain=pdfmailto:mhjo@postech.ac.krmailto:hy.choi@snu.ac.krwww.nature.com/naturecommunicationswith a fluctuating Fermi sea. Indeed, steady-state optical spectroscopyhas revealed that the light-generated excitons are dressed by intra-band particle-hole excitations in a two-dimensional Fermi sea, result-ing in the renormalized exciton spectra in the forms of attractive andrepulsive Fermi polarons24. Investigation of scattering channels hasfurther revealed the electrically tunable Feshbach resonances25,strongly coupled Fermi-polaron polaritons24, and nonlinear polaroninteractions26,27. In principle, such strong light-matter interactions candramatically turn the equilibrium properties into dynamical ones.However, because the energy scale of the two Fermi-polaron branchesis typically of around tens of meV in monolayer TMDs, the Fermi-polaron problems using conventional above-gap optical-field drivinggenerally involves hot-carriers mediated heat dissipation, hinderingexperimental observation of intrinsic Fermi-polaron spectraldynamics28.When below-gap light excitation takes place, new hybridized states(Floquet quasistates) emerge. Because the Floquet-interaction strengthscales inversely with an energy detuning, the light-induced heat dis-sipation can be significantly suppressed, which can realize coherentphoton-quasiparticle interactions such as optical Stark effects29. Whileprevious efforts have discovered various phenomena, such as ac Starkshift of n= 1 exciton in GaAs30–34, dynamic valley-degeneracy lifting inmonolayer TMD35–37, bandgap renormalization in black phosphorus38,and ultrafast switching of optical nonlinearity in manganese phos-phorus trisulfide39, these studies have focused on the “isolated” exci-tons, and yet it is only very recent to apply the Floquet engineering intothe “interacting” exciton-Fermi sea using a charge-tunable TMDs40.Here, we employ the ultrafast Floquet engineering into the gate-tunable monolayer WSe2 to investigate the light-driven Fermi-polaronproblems in presence of a fluctuating Fermi sea. In the polaronicphase, an exciton, regarded as a mobile impurity, experiences attrac-tive (repulsive) interactions with the surrounding Fermi sea. Theseinteractions produce the attractive (repulsive) polarons, as illustratedin the left of Fig. 1a. With below-gap pump excitation, a reducedinteraction in Fermi polarons (right in Fig. 1a) leads to a larger reso-nance shift in the attractive polarons. We have developed an inter-acting Hamiltonian based on a contact exciton-Fermi sea interaction.Our model demonstrates that the circularly polarized below-gapoptical pump results in a reduced binding energy of the attractivepolarons, rendering a stronger resonance shift with increasing EFcompared to the repulsive polarons.ResultsSteady-state optical spectroscopy of Fermi polaronsOur experiments are performed on bottom-gated monolayer WSe2devices (Fig. 1b). The results from device #1 are discussed in the maintext, while those from device #2 and #3 are presented in the Supple-mentaryNote. Figure 1c shows the EF, h-dependent reflectance contrast(RC) spectra. We focus on the hole doped regime, i.e., increasing EF, hindicatesmore hole doping (see Supplementary Note 1 for the detaileddiscussion about the Fermi polarons in the electron-doped regime).Near the charge neutrality (EF, h ffi 0meV), the RC spectra show asingle exciton peak EX near 1.72 eV. With increasing the hole dopingdensity (EF, h above −2.8meV), the spectral resonance is shifted to theblue. Concurrently, a new resonance emerges near 1.7 eV, which isslightly redshifted compared to the exciton. The energy differencebetween these two resonances varies in the range of 21.7–30.6meV atnonzero EF, h, which is larger than the trion binding energy ΔETacRepulsivepolaronAttractivepolarondAttractivepolaron RepulsivepolaronAttractive polaron Repulsive polaron Attractive polaron Repulsive polaronb20 μmGraphite contacthBNVGhBNWSe2hBNAuMonolayer WSe2Bo�om gateVGFig. 1 | Exciton-polaron interactions and optical properties inmonolayerWSe2.a Schematic illustration of Fermi-polaron dynamics before the below-gap pumpexcitation (left) and after the excitation (right). The attractive interaction betweenexcitons and holes is weakened whereas the repulsive interaction is less affectedunder the off-resonant pump.bAnopticalmicroscopic imageof hBN-encapsulatedWSe2 device (Inset: a schematic of the device structure). c Reflectance contrastspectra as a function of the probe photon energy (bottom axis) and Fermi energyEF, h (left axis). Here, RC= ðR�R0Þ=R0, where R is reflection signal from the WSe2monolayer sample andR0 is reference spectrum from the background (hBN) nearbythe sample. The dashed line (EF, h = 0meV) is the regime where an excitonic Starkeffect is measured (Fig. 2a, c). The dotted line is for the hole density (EF, h =−12.4meV). Figure 2b, d are the measured data at this hole-doped density. d Theoscillator strength parameters of attractive and repulsive polarons calculated from(c). Vertical error bars are obtained from the fits.Article https://doi.org/10.1038/s41467-024-55138-5Nature Communications |        (2024) 15:10852 2www.nature.com/naturecommunications(20.9meV). These polaronic features originate from the interactionsbetween the excitons and the Fermi sea24,41–44 (see SupplementaryNote 2 for more detailed analysis of the spectra). The EF, h-dependenttransfer of oscillator strength from repulsive polarons to attractivepolarons is summarized in Fig. 1d. The attractive polarons show red-shifted resonanceswith an increasedoscillator strength,whichemergefrom the increased binding energy between the excitons and the Fermisea. Conversely, the repulsive polarons display a blueshifted featurewith a reduced oscillator strength. The carrier-induced screening andPauli blocking effects are the main contributors to the characteristicsof the repulsivepolarons. Similar features have also been confirmedbyalternative devices (Supplementary Note 2) as well as prior reportedstudies24,43,45.Off-resonant optical dynamics of exciton-polaronsFigure 2a, b displays the two-dimensional plots corresponding to thedifferential reflectance spectra ΔR=R0 measured using σ + (right-cir-cularly)-polarized probe upon excitation with σ + -polarized pumppulses. The pump-photon energy _ωpump is set below the 1s exciton toprevent any band-to-band population (a typical detuning energyδX = EX � _ωpump is 171meV) as well as below the attractive-polaronresonance.We show the two representative data: Fig. 2a ismeasured atEF, h =0meV, i.e., charge neutral regime (see dashed line in Fig. 1c) andFig. 2b at EF, h = −12.4meV, i.e., hole-doped regime (see dotted line inFig. 1c), respectively. The positive (negative) ΔR=R0 implies a decrease(increase) in absorption. Whereas a single sign flip of ΔR=R0 is seen inFig. 2a, two clear sign flips are observed in Fig. 2b. Both ΔR=R0 spectraexhibit significant spectral changes near the zero pump-probe timedelay, Δt ffi 0ps. Such instantaneous responses indicate that ΔR=R0cannotbe explainedby the band-to-bandpopulation changes, becausesuch signals are measured to be lasting for many picoseconds (Sup-plementary Note 3 presents the data under above-gap pumpexcitation).Figure 2c, d are the line cuts of ΔR=R0 at Δt = 0 ps using co-circular polarization (σ + -pump and σ + -probe, red circles) and cross-circular polarization (σ�-pump and σ + -probe, black circles),respectively. The red solid line corresponds to the fit using one(Fig. 2c) and two Gaussian oscillators (Fig. 2d), respectively (Sup-plementary Note 4). The polarization-dependent ΔR=R0 suggeststhat both signals closely resemble the valley-contrasting optical Starkeffects. It is straightforward to fit using absorption derivative orintegral of the change of absorption for the case of exciton-dominantΔR=R0 regime, i.e., EF, h ffi 0meV (Fig. 2c). Experiments probingexcitonic and biexcitonic Stark effects also fall into this category35,46.When EF, h is nonzero (Fig. 2d), a significant transient reshapingoccurs. Clearly, the dynamics does not follow a single oscillator shift,a= −12.4 meV, bdc= 0 meV, Fig. 2 | Valley-selective resonance shifts of excitons and Fermi-polarons. a Atwo-dimensional plot ΔR=R0 when EF, h is 0 meV, i.e., the dashed line in Fig. 1c. Theσ+-polarized pump (photon energy of 1.55 eV) is incident onto the sample and thepump-induced ΔR=R0 changes are measured using with σ+-polarized white-lightpulses. The data correspond to the conventional optical Stark effects of non-interacting excitons. b The pump-induced ΔR=R0 spectra when EF, h is −12.4meV.See the dotted line in Fig. 1c. In contrast to a, two oscillatory signals are visible at1.6981 eV and 1.7303 eV, implying the existence of two oscillator shifts. The former(latter) is attributed to the resonance blueshift due to the attractive (repulsive)Fermi polarons.Data of c andd are the spectrally-resolvedΔR=R0 at zero time-delaybetween the pump and probe pulses. The pump and probe pulses are co-circularlypolarized (open red circles). No significant ΔR=R0 spectrum are observed for thecross-circularly polarized pump-probe case, i.e., σ�-polarized pump andσ + -polarized probe (open black circles). Solid red curves are the fit using shiftedGaussian oscillators. We have used a single Gaussian for (c) and two Gaussianoscillators model for (d). For more details on the fits, refer to the Note 4 in theSupplementary Information.Article https://doi.org/10.1038/s41467-024-55138-5Nature Communications |        (2024) 15:10852 3www.nature.com/naturecommunicationsrepresenting a strong deviation from the few-body exciton regime.This dynamics, therefore, does not represent a simple Floquet-driven“isolated” exciton picture. Based on the above aspects, one cananticipate ΔR=R0 dynamics to exhibit a strong dependence of theFermi energy.If the exciton resonance shift scales inversely with δ2X, it can beaccounted for by the Coulomb repulsion between virtual excitons47,48,which are known to be dominant when δX ≪ΔEX49. Figure 3a is theextracted exciton-resonance shiftΔX from the co-circular pump-probespectroscopy with _ωpump from 1.53 eV to 1.59 eV. Here, we vary thepump fluence F from 120 μJcm�2 to 360 μJcm�2. The gray line corre-sponds to a fit assuming that ΔX is linearly dependent of F=δX. Nohigher-order quadratic dependence is found in our case. Because ourδX is in the range of 131–191meV, which is substantially larger than therecent study (δX �10–50meV)40, our experiment is different from therecent investigation of ac-Stark shifts of attractive polarons40 (seeSupplementary Note 5 for the detailed discussion about pumpdetuning dependence for Fermi polarons).Gate- and pump fluence-dependent dynamics of Fermi polaronsHaving confirmed that the Coulomb repulsion between the virtualexcitons is excluded, we show in Fig. 3b the resonance shiftsΔP of bothattractive polarons and repulsive polarons as a function of pump flu-ence F . Both resonance shifts exhibit a linear dependence on F, whichis similar to the conventional excitonic Stark shifts35,50. We find, how-ever, that ΔP for the attractive polarons is almost twice larger than therepulsive polarons. This is contradictory to the conventional atom-photon two-level model, where the resonance shift is directly pro-portional to the oscillator strength f osc of the involved resonance, i.e.,ΔX / F � f osc� �=δX. Because f osc of the attractive polarons is smallerthan that of repulsive polarons (Fig. 1d), one expects a smaller reso-nance shift ΔP for the attractive polarons under the same F and δX. Infact, we find the standard atom-photon Floquet picture, cannotreproduce our data of Fig. 3b (see SupplementaryNote 6 for details onsuch conventional dressed atom models). Thus, our case is differentcompared to the excitonic Stark effect with no Fermi-sea interactions.A central concern of our study is the ΔP changes for attractive andrepulsive polarons as a function of EF, h (Fig. 3c). For the repulsivepolarons, theΔP characteristics closely follow the excitonic properties.Thus, increasing the Fermi energy leads to amonotonically decreasingΔP feature. On the other hand, the increased ΔP in the attractivepolarons means that the binding energy of the attractive polarons isweakened. Thebelow-gapopticalpumpgenerates “hot”holes fromthetop to the deep valence band, thereby extra holes are released fromaAttractivepolaronRepulsivepolaronAttractivepolaronRepulsivepolaroncbF,h = 0 meV, + +F,h = −12.4 meV, + +ExcitonFig. 3 | Detuning, fluence, and Fermi energy dependence of Fermi-polaronresonance shifts. a The optical Stark shiftΔX of excitons (black squares)measuredat EF, h = 0 meV is shown as a function of F=δX. Gray line represents F=δX depen-dence of ΔX. Because our measurement is by far off-resonant, higher-order cor-rection including interactions between virtual excitons or polaron-polaroninteractions is negligible. bThe pump-fluence F dependence of resonance shiftsΔPfor attractive polarons (red circles) and repulsivepolarons (black squares) is shown.The linear dependence is clearly seen for both polarons. The data have been takenat EF, h of −12.4meV (dotted line in Fig. 1c) with _ωpump of 1.55 eV. At the same F(120–360 μJ cm�2), ΔP for the attractive polarons is much larger than that of therepulsive polarons. Due to the released holes from attractive interactions withexcitons due to the pump excitation, the additional blueshift occurs in the attrac-tive polarons. c Resonance shifts of attractive polarons (red circles) and repulsivepolarons (black squares) at F is 240μJ cm�2 and δX is around 171meV are plotted asa function of the Fermi energy: −14.3 < EF, h <−3.8meV. The error bars are obtainedfrom the fits. The red and black dashed lines are theoretical calculations of thespectral function obtained from the interacting Hamiltonian using Chevy ansatz(see themain text andSupplementaryNote 7 formoredetails). Vertical error bars ina–c are obtained from the fits.Article https://doi.org/10.1038/s41467-024-55138-5Nature Communications |        (2024) 15:10852 4www.nature.com/naturecommunicationsthe attractive interactions with the excitons51. Such kinetics result inthe reduced Coulomb binding of holes in the attractive polarons, sothat ΔP is blueshifted.DiscussionQuasiparticle interactions between an exciton and the Fermi sea inFermi polarons can be theoretically described by the Hamiltonianconsisted of a bare exciton and the exciton dressed by the intrabandparticle-hole excitation in an opposite valley24:H =XωX kð Þx +k xk +Xð_k2=2mhÞh+k hk+XVq x +k +qh+k0�qhk0xk +h:c:� �,ð1Þwhere ωX kð Þ is the exciton dispersion described as ωX kð Þ=ΔEX +δ EF� �+ _k2=2mexc, in which offset δ EF� �is βEF with fitting parameter βfor band gap renormalization. xk (x +k ) and hk (h+k ) represent the anni-hilation (creation) operator for the exciton and the hole, respectively,andmexc andmh denote the effectivemasses of the exciton and the hole.The first and second terms describe the energies of excitons and theFermi sea, and the third term indicates the interaction of the Fermi seawith the excitons. We also include the bandgap renormalization52, forwhich δ EF� �=0:68 EF is introduced for the best fit of the RC measure-ments (Supplementary Note 7 for details on the polaron theory). In thepresence of the finite Fermi-sea density, such interactions can be derivedfrom the self-energy Σ Eð Þ using Chevy Ansatz:Σ Eð Þ=Xq1V�XΩk = kF1E + i0+ � ωX q� kð Þ+ ϵ kð Þ � ϵ qð Þ� ��1, ð2Þwhere 1V =PkFk =01ΔEP�ωX 0ð Þ+ωX kð Þ+ ϵ kð Þ and 0+ is the small positive ima-ginary for the causality of retarded Green’s function53. Ω denotes anultra-violet cutoff, while ϵ kð Þ represents the dispersion relationfor holes.We compare the data of Fig. 3c with the theoretically derivedspectrum using Eq. (2). We find that the agreement is excellent whenΔEP = 23meV+ 1:3EF (Fig. 4a). Supposing that the below-gap excitationmainly affects ΔEP of the attractive polarons, we introduce a fractionalfactor η to consider the reduced ΔEP. The spectral function iscomputed with η in the expression ΔEP, pump = 23meV+ 1:3EF 1� ηð Þ,where η is bounded between 0 and 1. Figure 4b–d are the calculatedspectral functions at η=0.3, 0.5, and 0.7, respectively. An increased(decreased) blueshift of the attractive (repulsive) polarons is clearwithincreasing η. After running multiple simulations, we have found that ηof 0.3 faithfully corresponds to the experimental data of Fig. 3c withinthe EF, h range of −3.8 to −14.3meV. It means that the photoexcitedholes are released from their attractive interactions with a constantfraction η of the hole density. This 30% reduction in the Fermi-polaronbinding energy cannot be associated with the fluctuating thermalenergy� 4kBT = 1.38meV at 4 K, which remains far below the broadenlinewidths of ~59.8meV and ~9.4meV for the repulsive and attractivepolarons, respectively. Further theoretical investigations areneeded toaccurately determine the fractional factor η.In summary, we have investigated the light-driven Fermi-polarondynamics when a bosonic impurity strongly interacts with the residentFermi sea. Below-gap photoexcitation is employed in the gate-tunablemonolayer WSe2. Both attractive and repulsive Fermi polarons showthe valley-selective resonance shifts with a linear correlation with F .While the dynamical shift of the repulsive polarons exhibits adecreasing feature, that of the attractive polarons is strongly enhancedwith increasing the Fermi-sea density. Such dynamics are found not tobe explained by the conventional dressed atom-photon picture. Toaccommodate these features, we present a simple interacting Hamil-tonian using Chevy ansatz, and have found that the below-gap exci-tation invokes a substantial reduction of the binding energy of theattractive polarons.MethodsSample fabricationFor the fabrication of gate-tunable monolayerWSe2 devices, we followthe procedures established in previous studies54–57, which are based onthe mechanical exfoliation of the monolayer WSe2. Thin hexagonalboron nitride (hBN) layer (~15 nm) are transferred onto a 300 nm SiO2/Si substrate and another hBN layer (~30 nm) is used to encapsulate thewhole device (top layer). The monolayer WSe2 and the thin-film hBNare obtained by exfoliating them from a bulk crystal of WSe2 (HQgraphene) and the high-quality hBN (National Institute for MaterialsScience, Japan), respectively. As depicted in Fig. 1b, the WSe2 layer isFig. 4 | Spectral functionsofFermi-polaronresonances. aThe calculated spectralfunction as a function of Fermi energy EF, h is overlapped with the experimentallymeasured reflectance contrast without the pump excitation. The open red circlesare for the attractive polarons, and the open black squares represent the repulsivepolarons. Both are extracted from Fig. 1c. b–d Calculated spectral functions whendifferent fractional factor η is used for the polaron binding energyΔEP, pump = 23meV+ 1:3EF, h 1� ηð Þ; b–d are the plots when η is 0.3, 0.5, and 0.7,respectively. With varying η, the spectral functions show different slopes for theattractive and repulsive polaron branches as a function of EF, h. When a specificvalley is excitedwith thebelow-gappump, thebinding energy between the excitonsand the surrounding Fermi sea in an opposite valley becomes smaller than the casewithout the pump.Article https://doi.org/10.1038/s41467-024-55138-5Nature Communications |        (2024) 15:10852 5www.nature.com/naturecommunicationsgrounded by a few-layer graphene electrodes. The bottom gate ispatterned using a standard e-beam lithography. Ti/Au with a thicknessof 5/45 nm is deposited using a thermal evaporator. The hBN/WSe2/graphite(electrodes)/hBN layers are picked up in series using a PDMSfilm covered with a polycarbonate (PC) film, and they are released on apre-patterned bottom gate. Instead of the conventional dual-gateconfiguration, our bottom-gate VG geometry enables to exclude anypossible transient pump-probe artifacts from the top gate.Steady-state and pump-probe spectroscopyFor the reflectance contrast (RC) measurement, we have used a halo-gen lamp (Thorlabs OSL2) as a source. The laser is focused at thesample with 1 μm beam size using a × 50 long working distanceobjective (Mitutoyo Plan Apo SL, NA =0.42). A grating mono-chromator (Dongwoo optron MonoRa 512i) equipped with a CCD(OxfordNewton970 EMCCD) camera is used to gather and analyze thereflection signal R from the WSe2 monolayer sample. The referencespectrum R0 is obtained from the background with hBN right next tothe WSe2 area. The corresponding normalized difference signal ðR0 �RÞ=R0 is plotted in Fig. 1c.For the ultrafast spectroscopy, the femtosecond pulses at1.55 eV are generated by a 250 kHz Ti:sapphire regenerative amplifier(Coherent RegA 9040). The femtosecond pulses, with a pulse dura-tion of around 40 fs, are divided into two parts: 75% of the totalpower of 1.3W is utilized as pump pulses, while the remaining 25% isfocused into a 0.5-mm-thick sapphire disk. The generated white lightcovers a probe photon energy from 1.65 eV to 1.8 eV. A pair of prisms(Thorlabs SF10) are inserted into both pump and probe paths tocompensate the dispersion caused by the presence of dispersiveoptical elements. The overall temporal resolution of the measure-ment is around 300 fs. A dual-slotted chopper (Stanford ResearchSystems SR 540) is used to measure the reflectance without thepump (R0) and the differential reflectance (ΔR) with the pump.Frequency-synchronized signals are simultaneously collected using adual lock-in detection technique (Stanford Research Systems SR830). The spot sizes of the pump and the probe on the sample are 2.5μm and 1μm, respectively. The probe light is detected using anavalanche photodiode (Thorlabs APD410A) after the wavelengthselection through a monochromator. The pump-probe time delay iscontrolled using a motorized delay stage. Time zero refers to thetime delay where the correlation between the pump pulses and theprobe pulses is maximum. The polarization of the pump and probepulses is controlled by utilizing a set of waveplates (AQWP05M,AHWP05M-580, 10RP52-2) and a linear polarizer (GL10-A, GL10-B,10GT04). Both RC and the pump-probe experiment are conducted ina closed-cycle Montana cryostat (Cryostation s50), with a constantbase temperature of 4 K.Data availabilityThe data that support the finding of this study are available from thecorresponding author upon request. The full set of pump-probe datagenerated in this study are provided in the Supplementary Informa-tion file.References1. Landau, L. D. Electron motion in crystal lattices. Phys. Z. Sowjetu-nion 3, 664 (1933).2. Pekar, S. I. Research in the electron theory of crystals. J. Phys. USSR10, 341 (1946).3. Franchini, C., Reticcioli, M., Setvin, M. & Diebold, U. Polarons inmaterials. Nat. Rev. Mater. 6, 560 (2021).4. Fröhlich, H., Pelzer, H. & Zienau, S. Properties of slow electrons inpolar materials. Philos. Mag. 41, 221 (1950).5. Adlong, H. S. et al. 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Lett.105, 013101 (2014).AcknowledgementsThis research was supported by the National Research Foundation ofKorea (NRF) through the government of Korea (Grant No. 2021R1A2C3005905, RS-2024-00413957, RS-2024-00466612), Scalable QuantumComputer Technology Platform Center (Grant No. 2019R1A5A1027055),the Institute for Basic Science (IBS) in Korea (Grant No. IBS-R034-D1),Global Research Development Center (GRDC) Cooperative Hub Pro-gram through the National Research Foundation of Korea (NRF) fundedby the Ministry of Science and ICT (MSIT) (Grant No. RS-2023-00258359), and the core center program (2021R1A6C101B418) by theMinistry of Education.Author contributionsHyojin Choi, J.Kim, and J.P. fabricated samples. J.L., W.H., J.Kwon, andS.-H.L. performed the device characteristics examination. K.W. and T.T.provided high-quality hBN crystal. Hyojin Choi and J.Kim performed themeasurements. Hyojin Choi, J.Kim, A.F., Z.S., M.-H.J., and HyunyongChoi performed data analysis and discussed the results. HyunyongChoi andM.-H.J. supervised the project. Hyojin Choi and J.Kimwrote themanuscript with input from all co-authors.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-024-55138-5.Correspondence and requests for materials should be addressed toMoon-Ho Jo or Hyunyong Choi.Peer review information Nature Communications thanks ZhenshengTao and the other, anonymous, reviewer(s) for their contribution to thepeer review of this work. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.© The Author(s) 2024Article https://doi.org/10.1038/s41467-024-55138-5Nature Communications |        (2024) 15:10852 7https://doi.org/10.1038/s41467-024-55138-5http://www.nature.com/reprintshttp://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/www.nature.com/naturecommunications Ultrafast Floquet engineering of Fermi-polaron resonances in charge-tunable monolayer WSe2 devices Results Steady-state optical spectroscopy of Fermi polarons Off-resonant optical dynamics of exciton-polarons Gate- and pump fluence-dependent dynamics of Fermi polarons Discussion Methods Sample fabrication Steady-state and pump-probe spectroscopy Data availability References Acknowledgements Author contributions Competing interests Additional information