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Interacting Polaron-Polaritons PHYSICAL REVIEW X 10, 021011 (2020) Featured in Physics Interacting Polaron-Polaritons Li Bing Tan,1,* Ovidiu Cotlet,1 Andrea Bergschneider ,1 Richard Schmidt ,2,3 Patrick Back,1 Yuya Shimazaki,1 † Martin Kroner,1 and Ataç İmamoğlu1, 1Institute for Quantum Electronics, ETH Zürich, CH-8093 Zürich, Switzerland 2Max Planck Institute of Quantum Optics, 85748 Garching, Germany 3Munich Center for Quantum Science and Technology, Schellingstrasse 4, 80799 Münich, Germany (Received 21 October 2019; revised manuscript received 19 January 2020; accepted 19 February 2020; published 15 April 2020) Two-dimensional semiconductors provide an ideal platform for exploration of linear exciton and polariton physics, primarily due to large exciton binding energy and strong light-matter coupling. These features, however, generically imply reduced exciton-exciton interactions, hindering the realization of active optical devices such as lasers or parametric oscillators. Here, we show that electrical injection of itinerant electrons into monolayer molybdenum diselenide allows us to overcome this limitation: dynamical screening of exciton-polaritons by electrons leads to the formation of new quasiparticles termed polaron-polaritons that exhibit unexpectedly strong interactions as well as optical amplification by Bose-enhanced polaron-electron scattering. To measure the nonlinear optical response, we carry out time- resolved pump-probe measurements and observe polaron-polariton interaction enhancement by a factor of 50 (0.5 μeV μm2) as compared to exciton-polaritons. Concurrently, we measure a spectrally integrated transmission gain of the probe field of ≳2 stemming from stimulated scattering of polaron-polaritons. We show theoretically that the nonequilibrium nature of optically excited quasiparticles favors a previously unexplored interaction mechanism stemming from a phase-space filling in the screening cloud, which provides an accurate explanation of the strong repulsive interactions observed experimentally. Our findings show that itinerant electron-exciton interactions provide an invaluable tool for electronic manipulation of optical properties, demonstrate a new mechanism for dramatically enhancing polariton-polariton interactions, and pave the way for realization of nonequilibrium polariton condensates. DOI: 10.1103/PhysRevX.10.021011 Subject Areas: Condensed Matter Physics, Quantum Physics, Semiconductor Physics I. INTRODUCTION or holes [6], and the realization of atomically thin mirrors [7,8]. However, nonlinear optical properties, crucial Monolayer transition metal dichalcogenides (TMDs) for the realization of novel photonic devices ranging from combine strong light-matter coupling and a large number parametric oscillators to exciton-polariton lasers, have been of degrees of freedom with which to manipulate photons. largely missing in the reported studies. This is at a first Because of the strong Coulomb interaction, excitons glance not surprising since nonlinearities typically scale as constitute the elementary optical excitation and dominate the exciton Bohr radius and hence are suppressed in TMD optical spectra in TMDs. Many novel features of linear monolayers where excitons are strongly bound [6,9,10],as optical properties of TMD excitons have been demon- compared to quasi-2D materials such as gallium arsenide strated, including the optical control of the valley degrees of (GaAs) quantum wells. Consequently, an outstanding freedom using the helicity of the excitation light [1,2] or challenge for the field is to find ways to enhance the external magnetic fields [3–5], electrical control of the exciton-exciton interaction strength, or more precisely, its optical spectrum through injection of itinerant electrons ratio to the exciton radiative decay rate. Theoretical proposals to date include the exploitation of large inter- actions between Rydberg excitons with three-level driving *[email protected] schemes [11] and the reduction of the exciton radiative † [email protected] decay rate by placing a monolayer in a high quality-factor (Q) cavity [12] or, more elegantly, by placing a monolayer Published by the American Physical Society under the terms of at λ=2 distance away from a mirror [13]. However, experi- the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to ments have so far only confirmed that exciton-exciton the author(s) and the published article’s title, journal citation, interactions in neutral TMD monolayers are more than an and DOI. order of magnitude weaker than those in GaAs [8,14]. 2160-3308=20=10(2)=021011(17) 021011-1 Published by the American Physical Society LI BING TAN et al. PHYS. REV. X 10, 021011 (2020) In this work, we demonstrate that the presence of itinerant the polaron-LP state, this scattering process is Bose electrons dramatically enhances nonlinear optical properties enhanced [34,35], leading to the observed gain. of TMD monolayers. In an earlier work, we investigated the After describing the experimental setup and reviewing linear optics of doped monolayer MoSe2 and identified the linear optical properties in the presence of nonpertur- exciton-polarons as the relevant quasiparticles [15–17].In bative coupling between excitons and the cavity mode as TMD monolayers, the exciton has an ultralarge binding well as excitons and electrons in Sec. II, we present energy that dominates over the electron plasma frequency the experimental signatures unveiled in nonlinear spectros- and Fermi energy. In consequence, the exciton can be copy, namely the enhancement of nonlinearities (Sec. III) considered as a robust quantum impurity interacting with and polariton amplification in the presence of itinerant a fermionic bath. The itinerant electrons dynamically screen electrons as compared to the charge neutral regime the exciton to form new quasiparticle branches—the attrac- (Sec. IV). We then present the theoretical model and tive and repulsive polaron—each with a renormalized mass calculations of the scattering rates due to residual inter- and energy [15,16]. A simple description of the polaron as a actions in Sec. V. Finally, in Sec. VI, we discuss avenues for superposition of a bare exciton and an exciton dressed with a further work. single electron-hole pair [18] was sufficient to accurately predict the resonances observed in linear spectroscopy. We II. ELEMENTARY OPTICAL EXCITATIONS OF remark that optical excitations in the presence of a 2DEG MoSe AN ELECTRON-DOPED MONOLAYER 2 were previously analyzed both theoretically and experimen- EMBEDDED IN A MICROCAVITY tally, where the attractive polaron resonance was termed a tetron [19] or a trion-hole pair [20,21]. Our experiments are based on a van der Waals hetero- Here, we use nonlinear spectroscopy to investigate the structure consisting of a MoSe2 monolayer semiconductor residual quasiparticle interactions in the strong cavity- embedded between 2 hexagonal boron nitride (h-BN) coupling regime [22–26] where elementary optical excita- flakes. A top graphene layer allows us to control the tions are polaron-polaritons [15]. We find their effective electron density [Fig. 1(a)]. We place the heterostructure in polariton-polariton interaction strength to exceed that of a tunable zero-dimensional open cavity [36] consisting of a their undressed counterparts by up to a factor of ∼50, and flat distributed-Bragg-reflector- (DBR) coated transparent we demonstrate an unexpected but unequivocal amplifica- substrate and a concave DBR-coated fiber facet [Fig. 1(b)] tion of polaron-polaritons accompanying the interaction- (Q ≃ 1800). All experiments are carried out at liquid induced blueshifts, with gain factors ≳2. helium temperature (see the Appendix A). The enhanced nonlinearities can be attributed to residual Figures 1(c) and 1(d) show the white light transmission interactions between the polaron quasiparticles. Using a spectrum measured for vanishing electron density ¼ −30 ¼ 5 wave function technique, we show how the measured (Vg V) and finite electron density (Vg V), repulsive interaction shift in the presence of itinerant respectively, in the strong-coupling regime as a function electrons can be understood in terms of a phase-space of the cavity length. In both cases, the measured spectra filling (PSF) effect. Here, the strong correlations between exhibit avoided crossings associated with the formation of pump-generated polaritons and electrons, that are associ- half-light, half-matter quasiparticles termed polaritons ¼ −30 ated with the formation of a polaron dressing cloud, lead to [15,37]. In the charge neutral regime at Vg V, an effective depletion of the electronic medium. Thus, we observe an exciton-polariton normal mode splitting additional polaritons created by the probe cannot be of 14 meV. When the monolayer is electron doped ¼ 5 screened with maximal efficiency, resulting in an increase (Vg V), dynamical screening of the excitons by elec- of their energy. Already at the lowest order, our approach trons dramatically alters the nature of elementary optical leads to a remarkable agreement between theory and excitations, leading to the appearance of attractive and experiment: we attribute this in part to the zero-dimensional repulsive exciton-polaron resonances. nature of the cavity mode which ensures that the lowest- To analyze how the exciton-electron interaction modifies energy optically excited state of the coupled system— the ground state of the cavity-coupled system, we start from ¼ þ the lower-polaron-polariton
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