Introduction

Atomically thin transition metal dichalcogenides (TMDCs) have emerged as a highly interesting class of materials for opto-electronic and nanophotonic applications1,2,3,4. Their spectral responses are dominated by correlated many-body excitations, even at elevated temperatures5,6. 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 mixtures7,8,9.

TMDC monolayers have also evolved into one of the most versatile platforms to study the fundamentals of light-matter coupling10,11,12. This enables the emergence of exciton-polaritons supported by various conditions. Such studies include the formation of polaritonic condensates from cryogenic13,14,15 to room temperature16,17,18, the emergence of moiré exciton-polaritons and nonlinear dipolaritons in van der Waals heterostructures19,20,21, and even the formation of Fermi-polaron-polaritons in high doping conditions22. While many studies have addressed effects of free or charged electron gases on the polaritonic relaxation22,23,24,25,26, 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 penetration27. Furthermore, this anti-Stokes photoluminescence (PL) is one of the fundamental principles behind laser cooling in solids28,29, 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 transitions30. TMDC monolayers are ideal for this requirement31,32,33, 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 upconversion27.

The performance of upconversion can be further enhanced by photonic structures34, where the absorption and emission are separately mediated. It has been reported that upconversion efficiency can be modulated by plasmonic35,36, dielectric37 and Tamm38 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 MoSe2 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 MoSe2 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

Sample structure and polariton relaxation

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 MoSe2 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.

Fig. 1: Sample sketch and strong coupling.
figure 1

a Schematic diagrams of the open cavity system and scanning electron microscope images of the top mirror. b PL of MoSe2 monolayer on the bottom DBRs with a GaInP cap layer (without the top mirror), and PL of MoSe2 on a conventional Si/SiO2 substrate, at temperature of 3.5 K. c 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 MoSe2 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.

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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 MoSe2 monolayer with free charge carriers39. The MoSe2 monolayer is transferred onto the GaInP layer and covered by a hexagonal-boron nitride (hBN) layer. The top mirror of the open cavity consists of 5.5 pairs of SiO2/TiO2. Harmonic in-plane mode confinement of the cavity is enabled by inclusion of a sphere cap-shaped lens40. 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 work41.

PL of the MoSe2/GaInP/Bottom DBRs sample (without the top mirror) is plotted in Fig. 1b, together with the PL of a MoSe2 monolayer on Si/SiO2 substrate (grey curve) for comparison. The type II interface between MoSe2 and GaInP, anticipated in a previous paper39, yields an efficient carrier transfer from the GaInP layer to the monolayer, hence flooding the MoSe2 with free charges and dramatically tipping the balance between neutral excitons and trions: compared to the reference sample prepared on a Si/SiO2 substrate, the PL of the MoSe2 monolayer on GaInP is trion-dominated, accompanied by an extremely subdued emission from excitons.

In contrast to previous reports on gated MoSe2 monolayers22, 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 MoSe2 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 cavity41,42,43, 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.

Fig. 2: Open cavity modulated PL.
figure 2

a 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. b Intensity profile of the PL as a function of energy. The profile path curve is indicated as the dashed line in a. c 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.

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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 distribution44 (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.

Actively tunable upconverted PL of exciton-polaritons

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 absorption30, which can yield effective laser cooling in solids28, and excitation pair scattering into higher energy bands45. Both processes are depicted in Fig. 3a.

Fig. 3: Actively tunable upconversion PL of exciton-polaritons under the double resonance condition.
figure 3

a Diagrams of upconversion processes: phonon absorption and Auger scattering of trions that are mediated by polaritons. b Upconversion PL plotted in false color scale as a function of piezo voltage (cavity length), with the excitation energy of 1.638 eV. c–e Visualization of the double resonance condition for efficient upconversion luminescence. c Polariton eigenmodes determined by white light reflection spectroscopy. Its color contrast is adapted to see clearly the set of transverse modes. d Emergent upconversion PL in the same axis range as c. The  vertical bright feature at 1.638 eV is the stray pump laser collected from environment. e Overlay of c and d. 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.

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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 MoSe2. 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. Figure 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 MoSe2 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 profile40.

Nonlinear upconverted valley-exciton-polaritons

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).

Fig. 4: Nonlinear upconverted PL of valley-exciton-polaritons.
figure 4

a Pump power dependent upconversion intensity at a fixed piezo voltage of 15.50 V, when the double resonance condition is met. b 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. c Circular polarization of upconversion emission with σ+ excitation, d with σ- excitation.

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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 PL45, 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 response30. 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 Fig. 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 WSe2 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 branches46, the valley depolarization observed in MoSe2 monolayers is much stronger than that in its MoS2 and WSe2 counterparts, leading to an intrinsic degree of circular polarization 10 times lower47.

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 K48. 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 MoSe231,49. 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 A1 optical phonon mode and the exciton-trion splitting leads to a doubly resonant Raman scattering49. 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 A1 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 action50 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 phonons51. 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 effect52: 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 meV49. 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 events51, 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 absorption53.

In summary, the utilization of a GaInP layer yields a substantial charge accumulation in MoSe2 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 GaInP layer. On top of the DBRs, we assemble a MoSe2 monolayer, capped with a multilayer hBN via the deterministic dry-transfer method. The top mirror of the open cavity is a SiO2 mesa coated with 5.5 pairs of SiO2/TiO2 (130.0 nm/81.9 nm) DBRs via sputter evaporation. The SiO2 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 work41.

Theoretical description

Using the Kubo-Martin-Schwinger relation44, 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 1 s 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.