Tuning relaxation and nonlinear upconversion of valley-exciton-polaritons in a monolayer semiconductor

Tuning relaxation and nonlinear upconversion of valley-exciton-polaritons in a monolayer semiconductor | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Tuning relaxation and nonlinear upconversion of valley-exciton-polaritons in a monolayer semiconductor Christian Schneider, Hangyong Shan, Jamie Fitzgerald, Roberto Rosati, and 8 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5318260/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 03 Nov, 2025 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Abstract Controlling exciton relaxation and energy conversion pathways via their coupling to photonic modes is a central task in cavity-mediated quantum materials research. In this context, the light-matter hybridization in optical cavities can lead to intriguing effects, such as modified carrier transport, enhancement of optical quantum yield, and control of chemical reaction pathways. Here, we investigate the impact of the strong light-matter coupling regime on energy conversion, both in relaxation and upconversion schemes, by utilizing a strongly charged MoSe 2 monolayer embedded in a spectrally tunable open-access cavity. We find that the charge carrier gas yields a significantly modified photoluminescence response of cavity exciton-polaritons, dominated by an intra-cavity like pump scheme. In addition, upconversion luminescence emerges from a population transfer from fermionic trions to bosonic exciton-polaritons. Due to the availability of multiple optical modes in the tunable open cavity, it seamlessly meets the cavity-enhanced double resonance condition required for an efficient upconversion. The latter can be actively tuned via the cavity length in-situ, displaying nonlinear scaling in intensity and fingerprints of the valley polarization. This suggests mechanisms that include both trion-trion Auger scattering and phonon absorption as its underlying microscopic origin. Physical sciences/Optics and photonics/Optical physics/Polaritons Physical sciences/Optics and photonics/Optical physics/Nonlinear optics Figures Figure 1 Figure 2 Figure 3 Figure 4 INTRODUCTION Atomically thin transition metal dichalcogenides (TMDCs) have emerged as a highly interesting class of materials for opto-electronic and nanophotonic applications 1-4 . Their spectral responses are dominated by correlated many-body excitations, even at elevated temperatures 5 , 6 . Furthermore, the enhanced stability of excitons paves the way to study the fundamentals of bosonic physics in the solid state and the interactions in Bose-Fermi mixtures 7-9 . TMDC monolayers have also evolved into one of the most versatile platforms to study the fundamentals of light-matter coupling 10-12 . This enables the emergence of exciton-polaritons supported by various conditions. Such studies include the formation of polaritonic condensates from cryogenic 13-15 to room temperature 16-18 , the emergence of moire exciton-polaritons and nonlinear dipolaritons in van der Waals heterostructures 19-21 , and even the formation of Fermi-polaron-polaritons in high doping conditions 22 . While many studies have addressed effects of free or charged electron gases on the polaritonic relaxation 22-26 , open questions regarding the interplay of excitons and trions in the strong coupling regime remain, for instance, the possibility of energy upconversion between trions and exciton-polaritons. Photon upconversion occurs when light emission has an energy greater than that of the absorbed photons. It has attracted tremendous interest in bioimaging and biophotodynamic therapy, attributed to the outstanding capability of near-infrared light in terms of deeper tissue penetration 27 . Furthermore, this anti-Stokes photoluminescence (PL) is one of the fundamental principles behind laser cooling in solids 28 , 29 , and it is of importance for improving solar energy harvesting in fields of photovoltaics and photocatalysis. Efficient upconversion PL requires a condition where both the excitation and the emission are resonant with electronic transitions 30 . TMDC monolayers are ideal for this requirement 31-33 , since they possess various bound excitations with an energy spacing fortuitously matched with typical phonon energies. In addition, TMDC monolayers are direct bandgap semiconductors, and this may overcome the limitation of the small absorption coefficient possessed by rare-earth doped glasses that have been extensively applied in photon upconversion 27 . The performance of upconversion can be further enhanced by photonic structures 34 , where the absorption and emission are separately mediated. It has been reported that upconversion efficiency can be modulated by plasmonic 35 , 36 , dielectric 37 and Tamm 38 cavities. However, passively tunable cavities, lacking flexible adjustment in resonance energy, are insufficient for practical opto-electronic applications; thus, the realization of actively tunable upconversion is desired. In this work, we scrutinize the impact of trions in a strongly charged MoSe 2 monolayer in a tunable optical cavity on energy relaxation and upconversion. We couple two cavity modes of the open cavity with electronic transitions of a MoSe 2 monolayer, observing a cavity-mediated double resonance condition for efficient upconversion: one mode weakly couples to trions, while the other is on resonance with excitons, yielding exciton-polaritons through strong coupling. Our results verify that the polariton luminescence is strongly dominated by the trionic state in the regular PL experiment. Furthermore, efficient and actively-tunable upconversion luminescence, emitted from exciton-polaritons, is observed. It demonstrates features of nonlinearity in intensity and valley-polarization with respect to the pump laser polarization, hinting at multiple mechanisms associated with trion Auger-like interaction and phonon absorption. RESULTS Figure 1a shows schematic diagrams of the sample structure. We use an optical open cavity, in which the cavity length can be precisely adjusted in-situ, to study interactions among photons, excitons, and trions in a charged MoSe 2 monolayer. The cavity length scanning is performed by tuning the piezo positioner that moves the bottom distributed Bragg reflectors (DBRs) in z-direction, allowing for a fine scanning of the air-gap over ~0.7 µm while maintaining nanometer resolution. The open cavity setup has a notable advantage to mediate a double resonance condition required for efficient upconversion: it has a series of longitudinal and transverse modes whose free spectral range can be tuned via the cavity length to match electronic transitions. Thus, the open cavity is a versatile platform for upconversion research. The bottom DBR is composed of 30 pairs of AlAs/AlGaAs layers, featuring a central Bragg wavelength of 750 nm. They are terminated by a 10 nm thick layer of GaInP, which facilitates doping the MoSe 2 monolayer with free charge carriers 39 . The MoSe 2 monolayer is transferred on the GaInP layer and covered by a hexagonal-boron nitride (hBN) layer. The top mirror of the open cavity consists of 5.5 pairs SiO 2 /TiO 2 DBRs. Harmonic in-plane mode confinement of the cavity is enabled by inclusion of a sphere cap-shaped lens 40 . The entire open cavity system is loaded into a liquid helium-free optical cryostat (3.5 K) with ultra-low vibration and long-term stability. More details of the setup can be found in our previous work 41 . PL of the MoSe 2 /GaInP/Bottom DBRs sample (without the top mirror) is plotted in Fig. 1b, together with the PL of a MoSe 2 monolayer on Si/SiO 2 substrate (grey curve) for comparison. The type II interface between MoSe 2 and GaInP, anticipated in a previous paper 39 , yields an efficient carrier transfer from the GaInP layer to the monolayer, hence flooding the MoSe 2 with free charges and dramatically tipping the balance between neutral excitons and trions: compared to the reference sample prepared on a Si/SiO 2 substrate, the PL of the MoSe 2 monolayer on GaInP is trion-dominated, accompanied by an extremely subdued emission from excitons. In contrast to previous reports on gated MoSe 2 monolayers 22 , in our sample, the oscillator strength transfer from the exciton to an attractive polaron has not been accomplished, despite the evident substantial charging. As a consequence, in optical reflection spectra (Fig. 1c), when scanning the cavity length through the two resonances of the MoSe 2 monolayer, a strong coupling condition with a Rabi-splitting of 9 meV is notable only when the cavity approaches the exciton resonance. In contrast, when the cavity crosses the trion transition, it only exhibits weak coupling. The cavity mode that couples to the trion is a strongly detuned exciton-polariton resonance of primarily photonic character (~7% exciton fraction). Details of theoretical modelling based on the Hopfield approach can be found at Section 1 of the Supplementary Information (SI). Due to the three-dimensional confinement and the in-plane rotational symmetry of the hemispheric lens, in Fig. 1c we observe Laguerre-Gaussian-type transverse optical modes of the Fabry-Perot resonator in our open cavity 41-43 , i.e., various transverse modes (labelled II, III, IV, etc.) associated to one ground longitudinal mode I. Carrier relaxation in our system is studied via non-resonant injection (532 nm, CW pump) of electron-holes pairs, and detection of the steady state PL. In Fig. 2a, as a notable result, we only detect significant PL from the lower polariton branch (LPB) as its energy approaches the trion resonance. No PL is observed from exciton-polaritons around 1.666 eV. The left y-axis of the figure indicates the voltage supplied to the piezo positioner, while the right y-axis presents corresponding cavity lengths estimated via the free spectral range between two adjacent longitudinal modes. The spectral tuning curve along one longitudinal mode (dashed line in Fig. 2a) is plotted in Fig. 2b, where the intensity of the detuned polaritonic mode is displayed as a function of energy. This tuning curve qualitatively reproduces the PL spectrum of trions at low temperature (Fig. 1b), and suggests a direct energy conversion from trions to strongly detuned exciton-polaritons. We model the emission of the coupled system via first calculating the absorption by using the transfer-matrix method. The PL can then be determined using the Kubo-Martin-Schwinger relation, which states that at thermodynamic equilibrium, the PL is proportional to the absorption scaled by the Boltzmann distribution 44 (details can be found in the Methods). Translational invariance is assumed in the in-plane direction, so transverse optical modes are neglected. The result of the model is shown in Fig. 2c and shows excellent agreement with the experiment. In addition to the investigation of carrier relaxation from respect of regular PL experiment, the versatility of our open cavity setup allows us to study energy conversion pathways in more complex settings. Upconversion luminescence is an anti-Stokes process, in which the detected emission signal occurs at a higher energy than the optical pump. This process can arise from multiple microscopic origins, such as phonon absorption 30 , which can yield effective laser cooling in solids 28 , and excitation pair scattering into higher energy bands 45 . Both processes are depicted in Fig. 3a. In our study, we use energy-tunable cavity polariton modes to actively tune the upconversion process. We use 2 ps long excitation pulses with a central energy of 1.638 eV, i.e. spectrally resonant with the trion transition of MoSe 2 . In Fig. 3b, as the cavity length is scanned, the emergence of upconversion luminescence occurs periodically whenever a resonance condition between the laser frequency/trion and the LPB is established. We see two groups of significant upconversion PL features, with the most intense emission at applied piezo voltages of 15.50 V and 51.25 V, respectively, featuring a double peak at energies of 1.659 eV and 1.665 eV. We note that the left edge of the lower energy peak with a maximum at 1.659 eV is partially cut by spectral filters that are used to separate the pump laser from upconversion signals. The in-situ active tunability demonstrated by Fig. 3b is of significance for the opto-electronic and biomedical applications upon upconversion. It implies the possibility of an efficient switch for practical upconversion devices: regarding the case of bright emission as ‘on’, and the case under non-resonance condition as ‘off’. A precise control of the tunability via the cavity length is feasible in this open cavity system and is present in Fig. S2. Our findings verify that resonance conditions are essential to observe strong upconversion PL. In addition, measurements with different excitation energies can be found in Fig. S3, which further verify that the laser spectral matching with the trion transition is also essential for a strong upconverted signal. The required double resonance conditions for efficient upconversion are visualized in Fig 3c-e, where the mutual y-axis represents the cavity length as our tuning knob. In Fig. 3c, we plot the reflectivity spectrum with a largely adapted color contrast, zoomed into the relevant energy range, where the spectral crossing of the polariton modes with the trion, and the anticrossing with the exciton at an energy of 1.666 eV are prominently visible. Fig. 3d represents the outcome of the upconversion experiment upon scanning our cavity in the same experimental spectral tuning range. The narrowband signal at an energy of 1.638 eV is stray light from the pump laser, which is energy-matched to the MoSe 2 trion. Upconversion emission occurs at energies that are exactly corresponding with the polaritonic energies arising from higher order transverse modes. The latter is best seen in the overlay representation of the two experiments in Fig. 3e. For an applied tuning voltage of 15.50 V, corresponding to a cavity length of 8.76 µm, the Gaussian mode I matches the laser (and trion) energy, and efficient upconversion PL arises from polaritons, which consist of excitons strongly coupled to the transverse mode III. As the voltage is changed to 10.25 V, the pump is on resonance with the transverse mode II, and we observe upconverted polariton emission of slightly reduced intensity, originating from a strong coupling between excitons and transverse mode IV. The larger upconversion intensity for the applied tuning voltage of 15.50 V arises, since the ground mode I matches the Gaussian profile of the pump laser, whereas the transverse mode II, being on resonance with the pump laser at 10.25 V features minimum intensity at its center of mode profile 40 . Information about the microscopic origin of the upconversion luminescence is revealed by its power-dependence at various cavity-laser detunings. In Fig. 4a, we exemplarily focus on the resonance occurring at 15.50 V. We show power-dependent upconversion PL, where the intensities of both peaks feature a nonlinear scaling with the pump power (see Fig. 4b). It is remarkable to note an unconventional emission feature: the upper polariton branch (UPB) is distinctly bright in upconverted PL spectra, while it usually is strongly quenched due to the efficient population relaxation from UPB to LPB. As the pump power increases, the intensity of the lower energy peak gradually exceeds the high energy peak. This phenomenon is attributed to a polariton bottleneck effect which is important at low densities, but can be overcome at higher densities (see further details in the Discussion). The power-dependent integrated intensity of the 1.665 eV peak, recorded at various piezo voltages, is shown in Fig. 4b. It reveals a nonlinear dependence of upconverted signal on pump power for different voltages. To extract the characteristic power-law coefficient, the log-log plot of the data from Fig. 4b is shown in Fig. S4. At 15.50 V and 10.25 V, power-law coefficients of 1.4 are extracted for both voltages. At the voltage 13.00 V, where the cavity-like LPB mode is detuned from the pump laser, we observe a reduced upconversion signal with a slightly smaller power law coefficient of 1.3 (Fig. S4). It is insightful to compare the power-law coefficients of regular and upconversion PL. As shown in Fig. S1, we see a linear increase of luminescence intensity in regular PL, i.e., with a coefficient of 1, which contrasts with the coefficient of 1.4 for the upconversion PL. If upconverted luminescence solely originates from Auger-type scattering, the power-law coefficient can be expected to be approximately twice as large as that of regular PL 45 , however, this condition does not fit our results. In contrast, phonon-assisted upconversion, where a trion absorbs one or multiple phonon(s) and dissociates into an exciton and free electron/hole, gives rise to a linear response 30 . Therefore, the intermediate power-law coefficients suggest the upconversion process involves both Auger-type scattering and direct phonon absorption. A further fingerprint of the phonon-assisted upconversion process is revealed by polarization-resolved studies. In Figs. 4c,d, we show circular-polarization dependent upconversion PL. We find that upconverted exciton-polaritons retain part of the pump laser polarization. In Ref. 30 , phonon-assisted upconversion of exciton emission in WSe 2 monolayers was reported to partially preserve the valley polarization. In contrast, in the case of Auger scattering, strong valley depolarization is expected to occur during the relaxation from high energy states. Due to Rashba-induced coupling of the dark and bright exciton branches 46 , the valley depolarization observed in MoSe 2 monolayers is much stronger than that in its MoS 2 and WSe 2 counterparts, leading to an intrinsic degree of circular polarization 10 times lower 47 . DISCUSSION At first sight, phonon absorption seems an unlikely mechanism for the observed upconverted PL in our system since there will be a vanishingly small phonon population at the experimental temperature of 3 . 5 K 48 . Remarkably though, the observed polarization-retention and power law strongly suggest an important contribution of phonon-assisted upconversion, which is in agreement with prior cavity-free studies of MoSe 2 31 , 49 . Thus, we propose a combination of physical mechanisms that lead to a significant phonon-driven upconverted signal from the polariton states. First, the coincidental energy matching between the A 1 optical phonon mode and the exciton-trion splitting leads to a doubly resonant Raman scattering 49 . The small Rabi splitting of 9 meV preserves this near coincidence in energy between the trion and exciton-polaritons (denoted as δ in Fig. 3e). Furthermore, the small number of phonons available for absorption can be partially compensated by a large trion population. Under the resonance excitation condition, efficient absorption of the A 1 phonon will take place and lead to a transient over-population of the exciton-polariton states, i.e., a much larger occupation than predicted by the Boltzmann ratio. It is also important to consider the formation mechanism of the trion. At higher pump powers, the law of mass action 50 predicts a depletion of free electron population, which favours the formation of exciton-polaritons, resulting in a stronger upconversion signal at steady state. For further details, see Section 2 of the SI. Furthermore, Auger scattering between trions leads to the decay of one trion and the excitation of a higher energetic state. This state will then relax toward the ground state by emitting a cascade of optical phonons 51 . This generation of hot phonons, which is dictated by the ratio of the trion energy to the phonon energies, heats the system and acts as a source for phonon-assisted upconversion. This is supported by the measured pump-power dependent relative peak intensity of the upconverted signal in Fig. 4a. In the case of a thermalized system, we would expect the lower-energy peak to dominate in intensity, but this is only observed at high pump power. We attribute this to a polariton bottleneck effect 52 : excited hot excitons get trapped in the high-energy (and momenta) exciton state and cannot relax efficiently because the energy jump between the states is small compared to a typical phonon energy of ~30 meV 49 . The phonon absorption mechanism injects population directly from trions to UPB/LPB, while the relaxation from UPB to LPB is expected to be inefficient because their energy difference is smaller than the phonon energy. At higher pump power, the Auger mechanism yields transient excitation of very high-energy states, which would thermalize via multiple scattering events 51 , hence increasing the opportunity to bypass the bottleneck. Additionally, a greater effective temperature of the system due to a hot phonon population could further reduce the bottleneck effect via increased phonon absorption 53 . In summary, the utilization of a GaInP layer yields a substantial charge accumulation in MoSe 2 monolayers, resulting in trion-dominated PL, both in the cavity-free case as well as at the strong coupling regime. Efficient upconversion luminescence from exciton-polaritons can be observed, consistent with the condition that one detuned polariton mode is on resonance with the pump laser. The upconverted PL intensity exhibits a nonlinear dependence on pump power, with a power-law suggesting contributions from both trion-trion Auger scattering and phonon absorption. The preservation of valley polarization further confirms the role of phonon absorption, and provides an additional tuning knob for optoelectronic applications based on upconversion. Our demonstration of upconversion from an intrinsic material-based resonance (trions) to hybrid quasi-particles (exciton-polaritons) outlines novel schemes for injection of bosonic polaritons from Fermi reservoirs. The nonlinear behaviour reveals that upconversion can become an efficient injection method of polariton populations, and provides new insights into investigations of bosonic condensation and many-body correlation physics of Bose-Fermi mixtures. METHODS Sample fabrication The bottom DBRs are grown by molecular beam epitaxy, and consist of 30 pairs of AlAs/AlGaAs layers (61.5 nm/56.5 nm), and has a central wavelength of 750 nm. It is terminated by a 10 nm GaInPlayer. On top of the DBRs, we assemble a MoSe 2 monolayer, capped with a multilayer hBN via the deterministic dry-transfer method. The top mirror of the open cavity is a SiO 2 mesa coated with 5.5 pairs of SiO 2 /TiO 2 (130.0 nm/81.9 nm) DBRs via sputter evaporation. The SiO 2 mesa has a size of 100 µm x 100 µm, where sphere cap-shaped lenses with various diameters are milled with focused ion beam lithography. The utilized lens has a diameter of 6 µm and a depth of ~330 nm. Experimental setup In regular PL measurements, the sample is excited with a 532 nm CW laser, while a pulsed laser (Coherent Mira Optima 900-F mode-locked Ti:Sapphire laser) with 2 ps pulse duration is used for upconversion PL experiments. To filter out the excitation laser, we use 600 nm long-pass filter for regular PL, and 750 nm short-pass filters for upconversion measurements, respectively. In circular polarization measurements, the polarization control at the excitation and detection is calibrated with a polarization analyser (Schäfter+Kirchhoff SK010PA). In white-light reflection experiments, a 200 µm pinhole is mounted at the focal plane in real space to realize spatial filtering. All spectra are recorded using a spectrometer (Andor Shamrock SR-500i) attached with a CCD camera (Andor iKon-M934 Series). The open cavity is placed in a liquid helium-free optical cryostat (Attodry 1000), which features an ultra-low vibration, long-term stable measurement system. The whole setup was introduced in detail in our previous work 41 . Theoretical description Using the Kubo-Martin-Schwinger relation 44 , the PL is obtained using a transfer-matrix calculation of the absorption, which is then scaled by the Boltzmann distribution evaluated at the experimental temperature of 3.5 K. Both the 1s exciton and trion energy are set to the experimental values. The exciton oscillator strength is chosen to match the experimental Rabi splitting of 9 meV. The oscillator strength and linewidth of the trion are extracted from measurements of a bare flake on the bottom DBRs. The ratio of the exciton and trion radiative decay rates is found to be ~130. We include a Gaussian broadening of 4 meV to mimic inhomogeneous broadening, and assume translational invariance in the in-plane direction, so transverse optical modes are neglected. Declarations DATA AVAILABILITY The data that support the findings of this study are available from the corresponding authors upon reasonable request. Acknowledgement The authors acknowledge support by the German research foundation (DFG) via the project SCHN1376 14-2, funded within the priority program 2244. Financial support by the Niedersächsisches Ministerium für Wissenschaft und Kultur (“DyNano”) is gratefully acknowledged. The Marburg group acknowledges funding from the DFG via SFB 1083 and the regular project 524612380. S.T. acknowledges support from U.S department of Energy DE-SC0020653. K.W. and T.T. acknowledge support from the JSPS KAKENHI (Grant Numbers 21H05233 and 23H02052) and World Premier International Research Center Initiative (WPI), MEXT, Japan. We thank Raül Perea-Causín (Stockholm University) for valuable discussions. COMPETING INTERESTS The authors declare no competing interests. References Wang, G. , et al. Colloquium: Excitons in atomically thin transition metal dichalcogenides. Rev. Mod. Phys. 90 , 021001 (2018). Mak, K. F., Shan, J. Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides. Nat. Photonics 10 , 216-226 (2016). Xia, F., Wang, H., Xiao, D., Dubey, M., Ramasubramaniam, A. Two-dimensional material nanophotonics. Nat. Photonics 8 , 899-907 (2014). Mueller, T., Malic, E. Exciton physics and device application of two-dimensional transition metal dichalcogenide semiconductors. npj 2D Mater. Appl. 2 , 29 (2018). Chernikov, A. , et al. Exciton Binding Energy and Nonhydrogenic Rydberg Series in Monolayer WS 2 . Phys. 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Nano Lett. 19 , 7317-7323 (2019). Fitzgerald, J. M., Rosati, R., Ferreira, B., Shan, H., Schneider, C., Malic, E. Circumventing the polariton bottleneck via dark excitons in 2D semiconductors. Optica 11 , 1346 (2024). Thompson, J. J. P. , et al. Phonon-Bottleneck Enhanced Exciton Emission in 2D Perovskites. Adv. Energy Mater. 14 , 2304343 (2024). Additional Declarations There is NO Competing Interest. Supplementary Files PolaritonupconversionSupplement20250623.docx Supplementary and Additional Material (Seen by all) # 1 Cite Share Download PDF Status: Published Journal Publication published 03 Nov, 2025 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5318260","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":515327755,"identity":"3cc19ebc-6c92-455e-ba18-f9fe218052b4","order_by":0,"name":"Christian Schneider","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABYElEQVRIie2Sv0vDQBTHXzi4LJdmvVIh/8KVQlqxWv+USCGOUjIKNVBIp+4W8X9ItrilHJglf0Chgi2FbkKlS8RBX+OvVNvBTSQfSCDv+Nz3vbsAFBT8RThAlL0Rgg/DT2WaVVQQoLjZivihWJsKEVmd7FYALPhU1jvQjx22KvrVYDZ6ShtGHdTZqhM290rxYHGuhQ3QCQnmnVCeGcckmOZC7mIhmcWrNy6rVYaJzcpJbE60hEO5R53aMJH7QUSdXIzgNkicRfEjRonmSSbGNp1oHr/wJTMrWBFVl5l8UxmlFm/5kbpA5YWJ+wV1UAFMrz+/K/V0U4mwsRM/AhOVCFPoOi5T1hUpDGBm/sDG2BizeRvbqGEbbZzFJuVr722WipacCkGok2tMv7TJY9rsHvpxf7bSvKNWKb5Vlg9eF3S1F6y08EAY/V6w/P4LfF3KNoTcubQLw/21UlBQUPCveAWAZHOKCkbwTAAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-2268-471X","institution":"Carl von Ossietzky University Oldenburg","correspondingAuthor":true,"prefix":"","firstName":"Christian","middleName":"","lastName":"Schneider","suffix":""},{"id":515327756,"identity":"10ff9337-bdc3-4cf0-b142-b0f4f2a663cf","order_by":1,"name":"Hangyong Shan","email":"","orcid":"https://orcid.org/0000-0003-3988-4870","institution":"Universität Oldenburg","correspondingAuthor":false,"prefix":"","firstName":"Hangyong","middleName":"","lastName":"Shan","suffix":""},{"id":515327757,"identity":"21cdb831-4ef9-4264-99bb-e815d420ee0b","order_by":2,"name":"Jamie Fitzgerald","email":"","orcid":"https://orcid.org/0000-0003-3652-0676","institution":"Philipps-Universität Marburg","correspondingAuthor":false,"prefix":"","firstName":"Jamie","middleName":"","lastName":"Fitzgerald","suffix":""},{"id":515327758,"identity":"6eb7f38e-1983-43c2-8eb5-02ed72412c1a","order_by":3,"name":"Roberto Rosati","email":"","orcid":"","institution":"Department of Physics, Philipps-Universität Marburg","correspondingAuthor":false,"prefix":"","firstName":"Roberto","middleName":"","lastName":"Rosati","suffix":""},{"id":515327759,"identity":"453c1534-3905-40c4-b456-4bf16f901603","order_by":4,"name":"Gilbert 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Science","correspondingAuthor":false,"prefix":"","firstName":"Takashi","middleName":"","lastName":"Taniguchi","suffix":""},{"id":515327762,"identity":"6c087103-b482-44ce-87a6-54d08338a95b","order_by":7,"name":"Seth Tongay","email":"","orcid":"https://orcid.org/0000-0001-8294-984X","institution":"Arizona State University","correspondingAuthor":false,"prefix":"","firstName":"Seth","middleName":"","lastName":"Tongay","suffix":""},{"id":515327763,"identity":"32cb93b2-0aa5-4b84-a163-46cf8d855677","order_by":8,"name":"Falk Eilenberger","email":"","orcid":"https://orcid.org/0000-0002-4646-2484","institution":"Friedrich-Schiller-Universität, Jena","correspondingAuthor":false,"prefix":"","firstName":"Falk","middleName":"","lastName":"Eilenberger","suffix":""},{"id":515327764,"identity":"67c14ae3-4328-4a56-bf07-3ad3ae72dc70","order_by":9,"name":"Martin Esmann","email":"","orcid":"https://orcid.org/0000-0002-2329-9696","institution":"Carl von Ossietzky Universität Oldenburg","correspondingAuthor":false,"prefix":"","firstName":"Martin","middleName":"","lastName":"Esmann","suffix":""},{"id":515327765,"identity":"60d90b2e-c579-4213-adbe-89c8dc00704b","order_by":10,"name":"Sven Höfling","email":"","orcid":"https://orcid.org/0000-0003-0034-4682","institution":"Universität Würzburg","correspondingAuthor":false,"prefix":"","firstName":"Sven","middleName":"","lastName":"Höfling","suffix":""},{"id":515327766,"identity":"10eeaf22-e138-4c1f-bfb5-065976d1d22e","order_by":11,"name":"Ermin Malic","email":"","orcid":"https://orcid.org/0000-0003-1434-9003","institution":"Philipps-Universität Marburg","correspondingAuthor":false,"prefix":"","firstName":"Ermin","middleName":"","lastName":"Malic","suffix":""}],"badges":[],"createdAt":"2024-10-23 10:47:38","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5318260/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5318260/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41467-025-65737-5","type":"published","date":"2025-11-03T05:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":91396516,"identity":"43fbabac-d50d-4a5e-89c7-0aa77a21fd9f","added_by":"auto","created_at":"2025-09-16 06:07:13","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":646555,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSample sketch and strong coupling a\u003c/strong\u003e Schematic diagrams of the open cavity system and scanning electron microscope images of the top mirror. \u003cstrong\u003eb\u003c/strong\u003e PL of MoSe\u003csub\u003e2\u003c/sub\u003e monolayer on the bottom DBRs with a GaInP cap layer (without the top mirror), and PL of MoSe\u003csub\u003e2\u003c/sub\u003e on a conventional Si/SiO\u003csub\u003e2\u003c/sub\u003e substrate, at temperature of 3.5 K. \u003cstrong\u003ec\u003c/strong\u003e Reflection spectra recorded at different detuning. We observe the ground longitudinal cavity mode I, and a number of higher order transverse modes (II, III, IV). The anticrossing with MoSe\u003csub\u003e2\u003c/sub\u003e excitons (X) occurs at 1.666 eV, whereas the trions (T) only weakly perturb the optical resonance. Solid lines: fitting of a two-oscillator model between excitons and the ground longitudinal cavity mode I.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5318260/v1/82ec72c4207d16d83365130f.png"},{"id":91397316,"identity":"b84722e5-b7a5-473b-aec9-3fd9de122e63","added_by":"auto","created_at":"2025-09-16 06:15:13","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":206572,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eOpen cavity modulated PL a\u003c/strong\u003e Experimentally measured PL of the sample with excitation of 532 nm laser. The emission is almost exclusively occurring as the detuned LPB (predominately photon-like) crosses the trion resonance. The right y-axis shows estimated cavity length at corresponding voltages. \u003cstrong\u003eb\u003c/strong\u003e Intensity profile of the PL as a function of energy. The profile path curve is indicated as the dashed line in panel \u003cstrong\u003ea\u003c/strong\u003e. \u003cstrong\u003ec\u003c/strong\u003e Theoretical model of PL intensity based on a single mode cavity (without the consideration of transverse modes), showing the weak coupling between the trion resonance and the strongly detuned LPB branch.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5318260/v1/d87ad86bbfc56155ad679428.png"},{"id":91397318,"identity":"d588f51a-07c1-4c00-9ea2-68598f16404a","added_by":"auto","created_at":"2025-09-16 06:15:13","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":561400,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eActively tunable upconversion PL of exciton-polaritons under the double resonance condition\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e Diagrams of upconversion processes: phonon absorption and Auger scattering of trions that are mediated by polaritons. \u003cstrong\u003eb\u003c/strong\u003e Upconversion PL plotted in false color scale as a function of piezo voltage (cavity length), with the excitation energy of 1.638 eV. \u003cstrong\u003ec-e: \u003c/strong\u003eVisualization of the double resonance condition for efficient upconversion luminescence. \u003cstrong\u003ec\u003c/strong\u003e Polariton eigenmodes determined by white light reflection spectroscopy. Its color contrast is adapted to see clearly the set of transverse modes. \u003cstrong\u003ed\u003c/strong\u003e Emergent upconversion PL in the same axis range as panel \u003cstrong\u003ec\u003c/strong\u003e. The straight bright feature at 1.638 eV is the stray pump laser collected from environment. \u003cstrong\u003ee \u003c/strong\u003eOverlay of panels \u003cstrong\u003ec\u003c/strong\u003e and \u003cstrong\u003ed\u003c/strong\u003e. Upconversion PL only occurs from polaritonic doublets (transverse modes III or IV), while the pump laser is on resonant with the ground mode I or transverse mode II. δ is the upconverted energy from trions to exciton-polaritons.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5318260/v1/74078a58fb1d6f910e004355.png"},{"id":91396517,"identity":"de15cde8-1d45-4528-9e26-2b38c83b5086","added_by":"auto","created_at":"2025-09-16 06:07:13","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":306225,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eNonlinear upconverted PL of valley-exciton-polaritons\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e Pump power dependent upconversion intensity at a fixed piezo voltage of 15.50 V, when the double resonance condition is met. \u003cstrong\u003eb\u003c/strong\u003e Integrated upconversion intensity as a function of pump power. The higher energy mode at 1.665 eV is analyzed. At 15.50 V and 10.25 V, intensive upconversion emission is observed, with a nonlinear increase versus pump power (nonlinear power law coefficient ~1.4). At 13.00 V, inefficient upconversion occurs due to being off-resonance. \u003cstrong\u003ec\u003c/strong\u003e Circular polarization of upconversion emission with σ\u003csup\u003e+\u003c/sup\u003e excitation, \u003cstrong\u003ed\u003c/strong\u003e with σ\u003csup\u003e-\u003c/sup\u003e excitation.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5318260/v1/427f734028815a2b05f9469e.png"},{"id":95090387,"identity":"96d3005c-04cb-42b0-aa77-c2d8bce98ccc","added_by":"auto","created_at":"2025-11-04 08:09:10","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2460622,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5318260/v1/a85afd82-d85a-49f7-b1b8-48e81d7e90b0.pdf"},{"id":91396524,"identity":"6c964ad3-39b3-4251-85ce-0d9c6c6495bd","added_by":"auto","created_at":"2025-09-16 06:07:13","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":515879,"visible":true,"origin":"","legend":"Supplementary and Additional Material (Seen by all) # 1","description":"","filename":"PolaritonupconversionSupplement20250623.docx","url":"https://assets-eu.researchsquare.com/files/rs-5318260/v1/b692b5f5afbd2fb28cc94476.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Tuning relaxation and nonlinear upconversion of valley-exciton-polaritons in a monolayer semiconductor","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eAtomically thin transition metal dichalcogenides (TMDCs) have emerged as a highly interesting class of materials for opto-electronic and nanophotonic applications\u003csup\u003e1-4\u003c/sup\u003e. Their spectral responses are dominated by correlated many-body excitations, even at elevated temperatures\u003csup\u003e5\u003c/sup\u003e\u003csup\u003e, \u003c/sup\u003e\u003csup\u003e6\u003c/sup\u003e. Furthermore, the enhanced stability of excitons paves the way to study the fundamentals of bosonic physics in the solid state and the interactions in Bose-Fermi mixtures\u003csup\u003e7-9\u003c/sup\u003e. \u003c/p\u003e\n\u003cp\u003eTMDC monolayers have also evolved into one of the most versatile platforms to study the fundamentals of light-matter coupling\u003csup\u003e10-12\u003c/sup\u003e. This enables the emergence of exciton-polaritons supported by various conditions. Such studies include the formation of polaritonic condensates from cryogenic\u003csup\u003e13-15\u003c/sup\u003e to room temperature\u003csup\u003e16-18\u003c/sup\u003e, the emergence of moire exciton-polaritons and nonlinear dipolaritons in van der Waals heterostructures\u003csup\u003e19-21\u003c/sup\u003e, and even the formation of Fermi-polaron-polaritons in high doping conditions\u003csup\u003e22\u003c/sup\u003e. While many studies have addressed effects of free or charged electron gases on the polaritonic relaxation\u003csup\u003e22-26\u003c/sup\u003e, open questions regarding the interplay of excitons and trions in the strong coupling regime remain, for instance, the possibility of energy upconversion between trions and exciton-polaritons. \u003c/p\u003e\n\u003cp\u003ePhoton upconversion occurs when light emission has an energy greater than that of the absorbed photons. It has attracted tremendous interest in bioimaging and biophotodynamic therapy, attributed to the outstanding capability of near-infrared light in terms of deeper tissue penetration\u003csup\u003e27\u003c/sup\u003e. Furthermore, this anti-Stokes photoluminescence (PL) is one of the fundamental principles behind laser cooling in solids\u003csup\u003e28\u003c/sup\u003e\u003csup\u003e, \u003c/sup\u003e\u003csup\u003e29\u003c/sup\u003e, and it is of importance for improving solar energy harvesting in fields of photovoltaics and photocatalysis. Efficient upconversion PL requires a condition where both the excitation and the emission are resonant with electronic transitions\u003csup\u003e30\u003c/sup\u003e. TMDC monolayers are ideal for this requirement\u003csup\u003e31-33\u003c/sup\u003e, since they possess various bound excitations with an energy spacing fortuitously matched with typical phonon energies. In addition, TMDC monolayers are direct bandgap semiconductors, and this may overcome the limitation of the small absorption coefficient possessed by rare-earth doped glasses that have been extensively applied in photon upconversion\u003csup\u003e27\u003c/sup\u003e. \u003c/p\u003e\n\u003cp\u003eThe performance of upconversion can be further enhanced by photonic structures\u003csup\u003e34\u003c/sup\u003e, where the absorption and emission are separately mediated. It has been reported that upconversion efficiency can be modulated by plasmonic\u003csup\u003e35\u003c/sup\u003e\u003csup\u003e, \u003c/sup\u003e\u003csup\u003e36\u003c/sup\u003e, dielectric\u003csup\u003e37\u003c/sup\u003e and Tamm\u003csup\u003e38\u003c/sup\u003e cavities. However, passively tunable cavities, lacking flexible adjustment in resonance energy, are insufficient for practical opto-electronic applications; thus, the realization of actively tunable upconversion is desired. \u003c/p\u003e\n\u003cp\u003eIn this work, we scrutinize the impact of trions in a strongly charged MoSe\u003csub\u003e2\u003c/sub\u003e monolayer in a tunable optical cavity on energy relaxation and upconversion. We couple two cavity modes of the open cavity with electronic transitions of a MoSe\u003csub\u003e2\u003c/sub\u003e monolayer, observing a cavity-mediated double resonance condition for efficient upconversion: one mode weakly couples to trions, while the other is on resonance with excitons, yielding exciton-polaritons through strong coupling. Our results verify that the polariton luminescence is strongly dominated by the trionic state in the regular PL experiment. Furthermore, efficient and actively-tunable upconversion luminescence, emitted from exciton-polaritons, is observed. It demonstrates features of nonlinearity in intensity and valley-polarization with respect to the pump laser polarization, hinting at multiple mechanisms associated with trion Auger-like interaction and phonon absorption. \u003c/p\u003e"},{"header":"RESULTS","content":"\u003cp\u003eFigure 1a shows schematic diagrams of the sample structure. We use an optical open cavity, in which the cavity length can be precisely adjusted in-situ, to study interactions among photons, excitons, and trions in a charged MoSe\u003csub\u003e2\u003c/sub\u003e monolayer. The cavity length scanning is performed by tuning the piezo positioner that moves the bottom distributed Bragg reflectors (DBRs) in z-direction, allowing for a fine scanning of the air-gap over ~0.7 \u0026micro;m while maintaining nanometer resolution. The open cavity setup has a notable advantage to mediate a double resonance condition required for efficient upconversion: it has a series of longitudinal and transverse modes whose free spectral range can be tuned via the cavity length to match electronic transitions. Thus, the open cavity is a versatile platform for upconversion research.\u003c/p\u003e\n\u003cp\u003eThe bottom DBR is composed of 30 pairs of AlAs/AlGaAs layers, featuring a central Bragg wavelength of 750 nm. They are terminated by a 10 nm thick layer of GaInP, which facilitates doping the MoSe\u003csub\u003e2\u003c/sub\u003e monolayer with free charge carriers\u003csup\u003e39\u003c/sup\u003e. The MoSe\u003csub\u003e2\u003c/sub\u003e monolayer is transferred on the GaInP layer and covered by a hexagonal-boron nitride (hBN) layer. The top mirror of the open cavity consists of 5.5 pairs SiO\u003csub\u003e2\u003c/sub\u003e/TiO\u003csub\u003e2\u003c/sub\u003e DBRs. Harmonic in-plane mode confinement of the cavity is enabled by inclusion of a sphere cap-shaped lens\u003csup\u003e40\u003c/sup\u003e. The entire open cavity system is loaded into a liquid helium-free optical cryostat (3.5 K) with ultra-low vibration and long-term stability. More details of the setup can be found in our previous work\u003csup\u003e41\u003c/sup\u003e. \u003c/p\u003e\n\u003cp\u003ePL of the MoSe\u003csub\u003e2\u003c/sub\u003e/GaInP/Bottom DBRs sample (without the top mirror) is plotted in Fig. 1b, together with the PL of a MoSe\u003csub\u003e2\u003c/sub\u003e monolayer on Si/SiO\u003csub\u003e2\u003c/sub\u003e substrate (grey curve) for comparison. The type II interface between MoSe\u003csub\u003e2\u003c/sub\u003e and GaInP, anticipated in a previous paper\u003csup\u003e39\u003c/sup\u003e, yields an efficient carrier transfer from the GaInP layer to the monolayer, hence flooding the MoSe\u003csub\u003e2\u003c/sub\u003e with free charges and dramatically tipping the balance between neutral excitons and trions: compared to the reference sample prepared on a Si/SiO\u003csub\u003e2\u003c/sub\u003e substrate, the PL of the MoSe\u003csub\u003e2 \u003c/sub\u003emonolayer on GaInP is trion-dominated, accompanied by an extremely subdued emission from excitons. \u003c/p\u003e\n\u003cp\u003eIn contrast to previous reports on gated MoSe\u003csub\u003e2\u003c/sub\u003e monolayers\u003csup\u003e22\u003c/sup\u003e, in our sample, the oscillator strength transfer from the exciton to an attractive polaron has not been accomplished, despite the evident substantial charging. As a consequence, in optical reflection spectra (Fig. 1c), when scanning the cavity length through the two resonances of the MoSe\u003csub\u003e2\u003c/sub\u003e monolayer, a strong coupling condition with a Rabi-splitting of 9 meV is notable only when the cavity approaches the exciton resonance. In contrast, when the cavity crosses the trion transition, it only exhibits weak coupling. The cavity mode that couples to the trion is a strongly detuned exciton-polariton resonance of primarily photonic character (~7% exciton fraction). Details of theoretical modelling based on the Hopfield approach can be found at Section 1 of the Supplementary Information (SI).\u003c/p\u003e\n\u003cp\u003eDue to the three-dimensional confinement and the in-plane rotational symmetry of the hemispheric lens, in Fig. 1c we observe Laguerre-Gaussian-type transverse optical modes of the Fabry-Perot resonator in our open cavity\u003csup\u003e41-43\u003c/sup\u003e, i.e., various transverse modes (labelled II, III, IV, etc.) associated to one ground longitudinal mode I.\u003c/p\u003e\n\u003cp\u003eCarrier relaxation in our system is studied via non-resonant injection (532 nm, CW pump) of electron-holes pairs, and detection of the steady state PL. In Fig. 2a, as a notable result, we only detect significant PL from the lower polariton branch (LPB) as its energy approaches the trion resonance. No PL is observed from exciton-polaritons around 1.666 eV. The left y-axis of the figure indicates the voltage supplied to the piezo positioner, while the right y-axis presents corresponding cavity lengths estimated via the free spectral range between two adjacent longitudinal modes. The spectral tuning curve along one longitudinal mode (dashed line in Fig. 2a) is plotted in Fig. 2b, where the intensity of the detuned polaritonic mode is displayed as a function of energy. This tuning curve qualitatively reproduces the PL spectrum of trions at low temperature (Fig. 1b), and suggests a direct energy conversion from trions to strongly detuned exciton-polaritons. \u003c/p\u003e\n\u003cp\u003eWe model the emission of the coupled system via first calculating the absorption by using the transfer-matrix method. The PL can then be determined using the Kubo-Martin-Schwinger relation, which states that at thermodynamic equilibrium, the PL is proportional to the absorption scaled by the Boltzmann distribution\u003csup\u003e44\u003c/sup\u003e (details can be found in the Methods). Translational invariance is assumed in the in-plane direction, so transverse optical modes are neglected. The result of the model is shown in Fig. 2c and shows excellent agreement with the experiment.\u003c/p\u003e\n\u003cp\u003eIn addition to the investigation of carrier relaxation from respect of regular PL experiment, the versatility of our open cavity setup allows us to study energy conversion pathways in more complex settings. Upconversion luminescence is an anti-Stokes process, in which the detected emission signal occurs at a higher energy than the optical pump. This process can arise from multiple microscopic origins, such as phonon absorption\u003csup\u003e30\u003c/sup\u003e, which can yield effective laser cooling in solids\u003csup\u003e28\u003c/sup\u003e, and excitation pair scattering into higher energy bands\u003csup\u003e45\u003c/sup\u003e. Both processes are depicted in Fig. 3a.\u003c/p\u003e\n\u003cp\u003eIn our study, we use energy-tunable cavity polariton modes to actively tune the upconversion process. We use 2 ps long excitation pulses with a central energy of 1.638 eV, i.e. spectrally resonant with the trion transition of MoSe\u003csub\u003e2\u003c/sub\u003e. In Fig. 3b, as the cavity length is scanned, the emergence of upconversion luminescence occurs periodically whenever a resonance condition between the laser frequency/trion and the LPB is established. We see two groups of significant upconversion PL features, with the most intense emission at applied piezo voltages of 15.50 V and 51.25 V, respectively, featuring a double peak at energies of 1.659 eV and 1.665 eV. We note that the left edge of the lower energy peak with a maximum at 1.659 eV is partially cut by spectral filters that are used to separate the pump laser from upconversion signals. \u003c/p\u003e\n\u003cp\u003eThe in-situ active tunability demonstrated by Fig. 3b is of significance for the opto-electronic and biomedical applications upon upconversion. It implies the possibility of an efficient switch for practical upconversion devices: regarding the case of bright emission as \u0026lsquo;on\u0026rsquo;, and the case under non-resonance condition as \u0026lsquo;off\u0026rsquo;. A precise control of the tunability via the cavity length is feasible in this open cavity system and is present in Fig. S2. Our findings verify that resonance conditions are essential to observe strong upconversion PL. In addition, measurements with different excitation energies can be found in Fig. S3, which further verify that the laser spectral matching with the trion transition is also essential for a strong upconverted signal. \u003c/p\u003e\n\u003cp\u003eThe required double resonance conditions for efficient upconversion are visualized in Fig 3c-e, where the mutual y-axis represents the cavity length as our tuning knob. In Fig. 3c, we plot the reflectivity spectrum with a largely adapted color contrast, zoomed into the relevant energy range, where the spectral crossing of the polariton modes with the trion, and the anticrossing with the exciton at an energy of 1.666 eV are prominently visible. Fig. 3d represents the outcome of the upconversion experiment upon scanning our cavity in the same experimental spectral tuning range. The narrowband signal at an energy of 1.638 eV is stray light from the pump laser, which is energy-matched to the MoSe\u003csub\u003e2\u003c/sub\u003e trion. Upconversion emission occurs at energies that are exactly corresponding with the polaritonic energies arising from higher order transverse modes. The latter is best seen in the overlay representation of the two experiments in Fig. 3e.\u003c/p\u003e\n\u003cp\u003eFor an applied tuning voltage of 15.50 V, corresponding to a cavity length of 8.76 \u0026micro;m, the Gaussian mode I matches the laser (and trion) energy, and efficient upconversion PL arises from polaritons, which consist of excitons strongly coupled to the transverse mode III. As the voltage is changed to 10.25 V, the pump is on resonance with the transverse mode II, and we observe upconverted polariton emission of slightly reduced intensity, originating from a strong coupling between excitons and transverse mode IV. The larger upconversion intensity for the applied tuning voltage of 15.50 V arises, since the ground mode I matches the Gaussian profile of the pump laser, whereas the transverse mode II, being on resonance with the pump laser at 10.25 V features minimum intensity at its center of mode profile\u003csup\u003e40\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eInformation about the microscopic origin of the upconversion luminescence is revealed by its power-dependence at various cavity-laser detunings. In Fig. 4a, we exemplarily focus on the resonance occurring at 15.50 V. We show power-dependent upconversion PL, where the intensities of both peaks feature a nonlinear scaling with the pump power (see Fig. 4b). It is remarkable to note an unconventional emission feature: the upper polariton branch (UPB) is distinctly bright in upconverted PL spectra, while it usually is strongly quenched due to the efficient population relaxation from UPB to LPB. As the pump power increases, the intensity of the lower energy peak gradually exceeds the high energy peak. This phenomenon is attributed to a polariton bottleneck effect which is important at low densities, but can be overcome at higher densities (see further details in the Discussion). \u003c/p\u003e\n\u003cp\u003eThe power-dependent integrated intensity of the 1.665 eV peak, recorded at various piezo voltages, is shown in Fig. 4b. It reveals a nonlinear dependence of upconverted signal on pump power for different voltages. To extract the characteristic power-law coefficient, the log-log plot of the data from Fig. 4b is shown in Fig. S4. At 15.50 V and 10.25 V, power-law coefficients of 1.4 are extracted for both voltages. At the voltage 13.00 V, where the cavity-like LPB mode is detuned from the pump laser, we observe a reduced upconversion signal with a slightly smaller power law coefficient of 1.3 (Fig. S4). \u003c/p\u003e\n\u003cp\u003eIt is insightful to compare the power-law coefficients of regular and upconversion PL. As shown in Fig. S1, we see a linear increase of luminescence intensity in regular PL, i.e., with a coefficient of 1, which contrasts with the coefficient of 1.4 for the upconversion PL. If upconverted luminescence solely originates from Auger-type scattering, the power-law coefficient can be expected to be approximately twice as large as that of regular PL\u003csup\u003e45\u003c/sup\u003e, however, this condition does not fit our results. In contrast, phonon-assisted upconversion, where a trion absorbs one or multiple phonon(s) and dissociates into an exciton and free electron/hole, gives rise to a linear response\u003csup\u003e30\u003c/sup\u003e. Therefore, the intermediate power-law coefficients suggest the upconversion process involves both Auger-type scattering and direct phonon absorption.\u003c/p\u003e\n\u003cp\u003eA further fingerprint of the phonon-assisted upconversion process is revealed by polarization-resolved studies. In Figs. 4c,d, we show circular-polarization dependent upconversion PL. We find that upconverted exciton-polaritons retain part of the pump laser polarization. In Ref.\u003csup\u003e30\u003c/sup\u003e, phonon-assisted upconversion of exciton emission in WSe\u003csub\u003e2\u003c/sub\u003e monolayers was reported to partially preserve the valley polarization. In contrast, in the case of Auger scattering, strong valley depolarization is expected to occur during the relaxation from high energy states. Due to Rashba-induced coupling of the dark and bright exciton branches\u003csup\u003e46\u003c/sup\u003e, the valley depolarization observed in MoSe\u003csub\u003e2\u003c/sub\u003e monolayers is much stronger than that in its MoS\u003csub\u003e2\u003c/sub\u003e and WSe\u003csub\u003e2\u003c/sub\u003e counterparts, leading to an intrinsic degree of circular polarization 10 times lower\u003csup\u003e47\u003c/sup\u003e.\u003c/p\u003e"},{"header":"DISCUSSION","content":"\u003cp\u003eAt first sight, phonon absorption seems an unlikely mechanism for the observed upconverted PL in our system since there will be a vanishingly small phonon population at the experimental temperature of 3\u003cem\u003e.\u003c/em\u003e5 K\u003csup\u003e48\u003c/sup\u003e. Remarkably though, the observed polarization-retention and power law strongly suggest an important contribution of phonon-assisted upconversion, which is in agreement with prior cavity-free studies of MoSe\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e31\u003c/sup\u003e\u003csup\u003e, \u003c/sup\u003e\u003csup\u003e49\u003c/sup\u003e. Thus, we propose a combination of physical mechanisms that lead to a significant phonon-driven upconverted signal from the polariton states.\u003c/p\u003e\n\u003cp\u003eFirst, the coincidental energy matching between the \u003cem\u003eA\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e optical phonon mode and the exciton-trion splitting leads to a doubly resonant Raman scattering\u003csup\u003e49\u003c/sup\u003e. The small Rabi splitting of 9 meV preserves this near coincidence in energy between the trion and exciton-polaritons (denoted as δ in Fig. 3e). Furthermore, the small number of phonons available for absorption can be partially compensated by a large trion population. Under the resonance excitation condition, efficient absorption of the \u003cem\u003eA\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e phonon will take place and lead to a transient over-population of the exciton-polariton states, i.e., a much larger occupation than predicted by the Boltzmann ratio.\u003c/p\u003e\n\u003cp\u003eIt is also important to consider the formation mechanism of the trion. At higher pump powers, the law of mass action\u003csup\u003e50\u003c/sup\u003e predicts a depletion of free electron population, which favours the formation of exciton-polaritons, resulting in a stronger upconversion signal at steady state. For further details, see Section 2 of the SI.\u003c/p\u003e\n\u003cp\u003eFurthermore, Auger scattering between trions leads to the decay of one trion and the excitation of a higher energetic state. This state will then relax toward the ground state by emitting a cascade of optical phonons\u003csup\u003e51\u003c/sup\u003e. This generation of hot phonons, which is dictated by the ratio of the trion energy to the phonon energies, heats the system and acts as a source for phonon-assisted upconversion. \u003c/p\u003e\n\u003cp\u003eThis is supported by the measured pump-power dependent relative peak intensity of the upconverted signal in Fig. 4a. In the case of a thermalized system, we would expect the lower-energy peak to dominate in intensity, but this is only observed at high pump power. We attribute this to a polariton bottleneck effect\u003csup\u003e52\u003c/sup\u003e: excited hot excitons get trapped in the high-energy (and momenta) exciton state and cannot relax efficiently because the energy jump between the states is small compared to a typical phonon energy of ~30 meV\u003csup\u003e49\u003c/sup\u003e. The phonon absorption mechanism injects population directly from trions to UPB/LPB, while the relaxation from UPB to LPB is expected to be inefficient because their energy difference is smaller than the phonon energy. At higher pump power, the Auger mechanism yields transient excitation of very high-energy states, which would thermalize via multiple scattering events\u003csup\u003e51\u003c/sup\u003e, hence increasing the opportunity to bypass the bottleneck. Additionally, a greater effective temperature of the system due to a hot phonon population could further reduce the bottleneck effect via increased phonon absorption\u003csup\u003e53\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eIn summary, the utilization of a GaInP layer yields a substantial charge accumulation in MoSe\u003csub\u003e2\u003c/sub\u003e monolayers, resulting in trion-dominated PL, both in the cavity-free case as well as at the strong coupling regime. Efficient upconversion luminescence from exciton-polaritons can be observed, consistent with the condition that one detuned polariton mode is on resonance with the pump laser. The upconverted PL intensity exhibits a nonlinear dependence on pump power, with a power-law suggesting contributions from both trion-trion Auger scattering and phonon absorption. The preservation of valley polarization further confirms the role of phonon absorption, and provides an additional tuning knob for optoelectronic applications based on upconversion. \u003c/p\u003e\n\u003cp\u003eOur demonstration of upconversion from an intrinsic material-based resonance (trions) to hybrid quasi-particles (exciton-polaritons) outlines novel schemes for injection of bosonic polaritons from Fermi reservoirs. The nonlinear behaviour reveals that upconversion can become an efficient injection method of polariton populations, and provides new insights into investigations of bosonic condensation and many-body correlation physics of Bose-Fermi mixtures.\u003c/p\u003e"},{"header":"METHODS","content":"\u003cp\u003e\u003cstrong\u003eSample fabrication \u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe bottom DBRs are grown by molecular beam epitaxy, and consist of 30 pairs of AlAs/AlGaAs layers (61.5 nm/56.5 nm), and has a central wavelength of 750 nm. It is terminated by a 10 nm GaInPlayer. On top of the DBRs, we assemble a MoSe\u003csub\u003e2 \u003c/sub\u003emonolayer, capped with a multilayer hBN via the deterministic dry-transfer method. The top mirror of the open cavity is a SiO\u003csub\u003e2\u003c/sub\u003e mesa coated with 5.5 pairs of SiO\u003csub\u003e2\u003c/sub\u003e/TiO\u003csub\u003e2\u003c/sub\u003e (130.0 nm/81.9 nm) DBRs via sputter evaporation. The SiO\u003csub\u003e2\u003c/sub\u003e mesa has a size of 100 µm x 100 µm, where sphere cap-shaped lenses with various diameters are milled with focused ion beam lithography. The utilized lens has a diameter of 6 µm and a depth of ~330 nm. \u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eExperimental setup \u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn regular PL measurements, the sample is excited with a 532 nm CW laser, while a pulsed laser (Coherent Mira Optima 900-F mode-locked Ti:Sapphire laser) with 2 ps pulse duration is used for upconversion PL experiments. To filter out the excitation laser, we use 600 nm long-pass filter for regular PL, and 750 nm short-pass filters for upconversion measurements, respectively. In circular polarization measurements, the polarization control at the excitation and detection is calibrated with a polarization analyser (Schäfter+Kirchhoff SK010PA). In white-light reflection experiments, a 200 µm pinhole is mounted at the focal plane in real space to realize spatial filtering. All spectra are recorded using a spectrometer (Andor Shamrock SR-500i) attached with a CCD camera (Andor iKon-M934 Series). The open cavity is placed in a liquid helium-free optical cryostat (Attodry 1000), which features an ultra-low vibration, long-term stable measurement system. The whole setup was introduced in detail in our previous work\u003csup\u003e41\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTheoretical description\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eUsing the Kubo-Martin-Schwinger relation\u003csup\u003e44\u003c/sup\u003e, the PL is obtained using a transfer-matrix calculation of the absorption, which is then scaled by the Boltzmann distribution evaluated at the experimental temperature of 3.5 K. Both the 1s exciton and trion energy are set to the experimental values. The exciton oscillator strength is chosen to match the experimental Rabi splitting of 9 meV. The oscillator strength and linewidth of the trion are extracted from measurements of a bare flake on the bottom DBRs. The ratio of the exciton and trion radiative decay rates is found to be ~130. We include a Gaussian broadening of 4 meV to mimic inhomogeneous broadening, and assume translational invariance in the in-plane direction, so transverse optical modes are neglected.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eDATA AVAILABILITY\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data that support the findings of this study are available from the corresponding authors upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors acknowledge support by the German research foundation (DFG) via the project SCHN1376 14-2, funded within the priority program 2244. Financial support by the Niedersächsisches Ministerium für Wissenschaft und Kultur (“DyNano”) is gratefully acknowledged. The Marburg group acknowledges funding from the DFG via SFB 1083 and the regular project 524612380. S.T. acknowledges support from U.S department of Energy DE-SC0020653. K.W. and T.T. acknowledge support from the JSPS KAKENHI (Grant Numbers 21H05233 and 23H02052) and World Premier International Research Center Initiative (WPI), MEXT, Japan. We thank Raül Perea-Causín (Stockholm University) for valuable discussions.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCOMPETING INTERESTS\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eWang, G.\u003cem\u003e, et al.\u003c/em\u003e Colloquium: Excitons in atomically thin transition metal dichalcogenides. \u003cem\u003eRev. Mod. 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Energy Mater.\u003c/em\u003e \u003cstrong\u003e14\u003c/strong\u003e, 2304343 (2024).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-5318260/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5318260/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eControlling exciton relaxation and energy conversion pathways via their coupling to photonic modes is a central task in cavity-mediated quantum materials research. In this context, the light-matter hybridization in optical cavities can lead to intriguing effects, such as modified carrier transport, enhancement of optical quantum yield, and control of chemical reaction pathways. Here, we investigate the impact of the strong light-matter coupling regime on energy conversion, both in relaxation and upconversion schemes, by utilizing a strongly charged MoSe\u003csub\u003e2\u003c/sub\u003e monolayer embedded in a spectrally tunable open-access cavity. We find that the charge carrier gas yields a significantly modified photoluminescence response of cavity exciton-polaritons, dominated by an intra-cavity like pump scheme. In addition, upconversion luminescence emerges from a population transfer from fermionic trions to bosonic exciton-polaritons. Due to the availability of multiple optical modes in the tunable open cavity, it seamlessly meets the cavity-enhanced double resonance condition required for an efficient upconversion. The latter can be actively tuned via the cavity length in-situ, displaying nonlinear scaling in intensity and fingerprints of the valley polarization. This suggests mechanisms that include both trion-trion Auger scattering and phonon absorption as its underlying microscopic origin.\u003c/p\u003e","manuscriptTitle":"Tuning relaxation and nonlinear upconversion of valley-exciton-polaritons in a monolayer semiconductor","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-16 05:59:08","doi":"10.21203/rs.3.rs-5318260/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-communications","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"NCOMMS","sideBox":"Learn more about [Nature Communications](http://www.nature.com/ncomms/)","snPcode":"","submissionUrl":"https://mts-ncomms.nature.com/","title":"Nature Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Communications","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"ee6157a7-4547-4c6f-b2dd-04fe90e6f028","owner":[],"postedDate":"September 16th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":54739170,"name":"Physical sciences/Optics and photonics/Optical physics/Polaritons"},{"id":54739171,"name":"Physical sciences/Optics and photonics/Optical physics/Nonlinear optics"}],"tags":[],"updatedAt":"2025-11-04T08:08:45+00:00","versionOfRecord":{"articleIdentity":"rs-5318260","link":"https://doi.org/10.1038/s41467-025-65737-5","journal":{"identity":"nature-communications","isVorOnly":false,"title":"Nature Communications"},"publishedOn":"2025-11-03 05:00:00","publishedOnDateReadable":"November 3rd, 2025"},"versionCreatedAt":"2025-09-16 05:59:08","video":"","vorDoi":"10.1038/s41467-025-65737-5","vorDoiUrl":"https://doi.org/10.1038/s41467-025-65737-5","workflowStages":[]},"version":"v1","identity":"rs-5318260","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5318260","identity":"rs-5318260","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}