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In this work we study a system of interacting fermions on a triangular lattice in the presence of an external magnetic field. We neglect spin and fix a density of one third, with one unit of magnetic flux per particle. The infinite density matrix renormalization group (iDMRG) algorithm is used to compute the ground state of this generalized Fermi-Hubbard model. Increasing the strength of the nearest-neighbor repulsion, we find a first order transition between an Integer Quantum Hall phase and a crystalline, generalized Wigner crystal state. The first-order nature of the phase transition is consistent with a Ginzburg-Landau argument. We expect our results to be relevant for moir\'e heterostructures of two-dimensional materials.

Moir\'e heterostructures consisting of transition metal dichalcogenide (TMD) hetero- and homobilayers have emerged as a promising material platform to study correlated electronic states. Optical signatures of strong correlations in the form of Mott-Wigner states and fractional Chern insulators have already been observed in TMD monolayers and their twisted bilayers. In this work, we use a moir\'e substrate containing a twisted hexagonal boron nitride (h-BN) interface to externally generate a superlattice potential for the TMD layer: the periodic structure of ferroelectric domains in h-BN effects a purely electrostatic potential for charge carriers. We find direct evidence for the induced moir\'e potential in the emergence of new excitonic resonances at integer fillings, and our observation of an enhancement of the trion binding energy by $\simeq$ 3 meV. A theoretical model for exciton-electron interactions allows us to directly determine the moir\'e potential modulation of 30$\pm$5 meV from the measured trion binding energy shift. We obtain direct evidence for charge order linked to electronic Mott-Wigner states at filling factors $\nu$ = 1/3 and $\nu$ = 2/3 through the associated exciton Umklapp resonances., Comment: 6 + 11 pages, 4 + 15 figures

Quantum dots are semiconductor nano-structures where particle motion is confined in all three spatial dimensions. Since their first experimental realization, nanocrystals confining the quanta of polarization waves, termed excitons, have found numerous applications in fields ranging from single photon sources for quantum information processing to commercial displays. A major limitation to further extending the range of potential applications has been the large inhomogeneity in, and lack-of tunability of, exciton energy that is generic to quantum dot materials. Here, we address this challenge by demonstrating electrically-defined quantum dots for excitons in monolayer semiconductors where the discrete exciton energies can be tuned using applied gate voltages. Resonance fluorescence measurements show strong spectral jumps and blinking of these resonances, verifying their zero-dimensional nature. Our work paves the way for realizing quantum confined bosonic modes where nonlinear response would arise exclusively from exciton--exciton interactions., Comment: updated version

We study a mechanism to induce superconductivity in atomically thin semiconductors where excitons mediate an effective attraction between electrons. Our model includes interaction effects beyond the paradigm of phonon-mediated superconductivity and connects to the well-established limits of Bose and Fermi polarons. By accounting for the strong-coupling physics of trions, we find that the effective electron-exciton interaction develops a strong frequency and momentum dependence accompanied by the system undergoing an emerging BCS-BEC crossover from weakly bound $s$-wave Cooper pairs to a superfluid of bipolarons. Even at strong-coupling the bipolarons remain relatively light, resulting in critical temperatures of up to 10\% of the Fermi temperature. This renders heterostructures of two-dimensional materials a promising candidate to realize superconductivity at high critical temperatures set by electron doping and trion binding energies., Comment: 9+9 pages, 4+5 figures

Heterostructures of two-dimensional transition metal dichalcogenides (TMDs) are emerging as a promising platform for investigating exotic correlated states of matter. Here, we propose to engineer Bose-Fermi mixtures in these systems by coupling inter-layer excitons to doped charges in a trilayer structure. Their interactions are determined by the inter-layer trion, whose spin-selective nature allows excitons to mediate an attractive interaction between charge carriers of only one spin species. Remarkably, we find that this causes the system to become unstable to topological p+ip superconductivity at low temperatures. We then demonstrate a general mechanism to develop and control this unconventional state by tuning the trion binding energy using a solid-state Feshbach resonance., Comment: 11 pages, 5 figures. Final version

Feshbach resonances play a vital role in the success of cold atoms investigating strongly-correlated physics. The recent observation of their solid-state analog in the scattering of holes and intralayer excitons in transition metal dichalcogenides [Schwartz et al., Science 374, 336 (2021)] holds compelling promise for bringing fully controllable interactions to the field of semiconductors. Here, we demonstrate how tunneling-induced layer hybridization can lead to the emergence of two distinct classes of Feshbach resonances in atomically thin semiconductors. Based on microscopic scattering theory we show that these two types of Feshbach resonances allow to tune interactions between electrons and both short-lived intralayer, as well as long-lived interlayer excitons. We predict the exciton-electron scattering phase shift from first principles and show that the exciton-electron coupling is fully tunable from strong to vanishing interactions. The tunability of interactions opens the avenue to explore Bose-Fermi mixtures in solid-state systems in regimes that were previously only accessible in cold atom experiments., Comment: 6+3 pages, 4+1 figures

Laser induced shift of atomic states due to the AC-Stark effect has played a central role in cold-atom physics and facilitated their emergence as analog quantum simulators. Here, we explore this phenomena in an atomically thin layer of semiconductor MoSe$_2$, which we embedded in a heterostructure enabling charge tunability. Shining an intense pump laser with a small detuning from the material resonances, we generate a large population of virtual collective excitations, and achieve a regime where interactions with this background population is the leading contribution to the AC-Stark shift. Using this technique we study how itinerant charges modify -- and dramatically enhance -- the interactions between optical excitations. In particular, our experiments show that the interaction between attractive polarons could be more than an order of magnitude stronger than those between bare excitons.

Magnetic properties of materials ranging from conventional ferromagnetic metals to strongly correlated materials such as cuprates originate from Coulomb exchange interactions. The existence of alternate mechanisms for magnetism that could naturally facilitate electrical control have been discussed theoretically but an experimental demonstration in an extended system has been missing. Here, we investigate MoSe$_2$/WS$_2$ van der Waals heterostructures in the vicinity of Mott insulator states of electrons forming a frustrated triangular lattice and observe direct evidence for magnetic correlations originating from a kinetic mechanism. By directly measuring electronic magnetization through the strength of the polarization-selective attractive polaron resonance, we find that when the Mott state is electron doped the system exhibits ferromagnetic correlations in agreement with the Nagaoka mechanism., Comment: 10 pages, 8 figures

Understanding the Hubbard model is crucial for investigating various quantum many-body states and its fermionic and bosonic versions have been largely realized separately. Recently, transition metal dichalcogenides heterobilayers have emerged as a promising platform for simulating the rich physics of the Hubbard model. In this work, we explore the interplay between fermionic and bosonic populations, using a $\rm{WS}_2$/$\rm{WSe}_2$ heterobilayer device that hosts this hybrid particle density. We independently tune the fermionic and bosonic populations by electronic doping and optical injection of electron-hole pairs, respectively. This enables us to form strongly interacting excitons that are manifested in a large energy gap in the photoluminescence spectrum. The incompressibility of excitons is further corroborated by measuring exciton diffusion, which remains constant upon increasing pumping intensity, as opposed to the expected behavior of a weakly interacting gas of bosons, suggesting the formation of a bosonic Mott insulator. We explain our observations using a two-band model including phase space filling. Our system provides a controllable approach to the exploration of quantum many-body effects in the generalized Bose-Fermi-Hubbard model., Comment: Main text: 7 pages, 5 figures. Supplementary Material: 10 pages, 7 figures

The ground-state properties and excitation energies of a quantum emitter can be modified in the ultrastrong coupling regime of cavity quantum electrodynamics (QED) where the light-matter interaction strength becomes comparable to the cavity resonance frequency. Recent studies have started to explore the possibility of controlling an electronic material by embedding it in a cavity that confines electromagnetic fields in deep subwavelength scales. Currently, there is a strong interest in realizing ultrastrong-coupling cavity QED in the terahertz (THz) part of the spectrum, since most of the elementary excitations of quantum materials are in this frequency range. We propose and discuss a promising platform to achieve this goal based on a two-dimensional electronic material encapsulated by a planar cavity consisting of ultrathin polar van der Waals crystals. As a concrete setup, we show that nanometer-thick hexagonal boron nitride layers should allow one to reach the ultrastrong coupling regime for single-electron cyclotron resonance in a bilayer graphene. The proposed cavity platform can be realized by a wide variety of thin dielectric materials with hyperbolic dispersions. Consequently, van der Waals heterostructures hold the promise of becoming a versatile playground for exploring the ultrastrong-coupling physics of cavity QED materials., Comment: 6+5 pages, 3+3 figures

The interaction between a mobile quantum impurity and a bosonic bath leads to the formation of quasiparticles, termed Bose polarons. The elementary properties of Bose polarons, such as their mutual interactions, can differ drastically from those of the bare impurities. Here, we explore Bose polaron physics in a two-dimensional nonequilibrium setting by injecting $\sigma^-$ polarised exciton-polariton impurities into a bath of coherent $\sigma^+$ polarised polaritons generated by resonant laser excitation of monolayer MoSe$_2$ embedded in an optical cavity. By exploiting a biexciton Feshbach resonance between the impurity and the bath polaritons, we tune the interacting system to the strong-coupling regime and demonstrate the coexistence of two new quasiparticle branches. Using time-resolved pump-probe measurements we observe how polaron dressing modifies the interaction between impurity polaritons. Remarkably, we find that the interactions between high-energy polaron quasiparticles, that are repulsive for small bath occupancy, can become attractive in the strong impurity-bath coupling regime. Our experiments provide the first direct measurement of Bose polaron-polaron interaction strength in any physical system and pave the way for exploration and control of many-body correlations in driven-dissipative settings., Comment: 7 pages, 5 figures

We develop a comprehensive theoretical model for the interaction strength between a pair of exciton-polaritons in microcavity devices. Ab initio numerical calculations for dipolar polaritons in one dimension are used as a starting point to build a Born-Oppenheimer theory that generally applies to generic -- dipolar or non-dipolar polaritons -- in both one and two dimensions. This theory anticipates that the strong coupling to the cavity mode leads to a drastic enhancement of the polariton interactions as compared to bare excitons, and predicts unexpected scaling laws in the interaction strength as a function of system parameters. Comparisons with available experimental data are drawn, and specific suggestions to validate it with new experiments are made. Promising strategies towards the observation of a strong polariton blockade regime are finally sketched., Comment: Main manuscript: 18 pages, 6 figures. Appendix: 2 pages, 2 figures

We study induced pairing between two identical fermions mediated by an attractively interacting quantum impurity in two-dimensional systems. Based on a Stochastic Variational Method (SVM), we investigate the influence of confinement and finite interaction range effects on the mass ratio beyond which the ground state of the quantum three-body problem undergoes a transition from a composite bosonic trimer to an unbound dimer-fermion state. We find that confinement as well as a finite interaction range can greatly enhance trimer stability, bringing it within reach of experimental implementations such as found in ultracold atom systems. In the context of solid-state physics, our solution of the confined three-body problem shows that exciton-mediated interactions can become so dominant that they can even overcome detrimental Coulomb repulsion between electrons in atomically-thin semiconductors. Our work thus paves the way towards a universal understanding of boson-induced pairing across various fermionic systems at finite density, and opens perspectives towards realizing novel forms of electron pairing beyond the conventional paradigm of Cooper pair formation., Comment: 21 pages, 15 figures

Recent advances in fabrication of two dimensional materials and their moir\'e heterostructures have opened up new avenues for realization of ground-state excitonic insulators, where the structure spontaneously develops a finite interlayer electronic polarization. We propose and analyze a scheme where an optically generated intralayer exciton is screened by excitations out of the excitonic insulator to form interlayer polarons. Using Quantum Monte-Carlo calculations we first determine the binding energy of the biexciton state composed of inter- and intralayer excitons, which plays a central role in understanding polaron formation. We describe the excitations out of the ground-state condensate using BCS theory and use a single interacting-quasiparticle-pair excitation Ansatz to describe dynamical screening of optical excitations. Our predictions carry the hallmarks of the excitonic insulator excitation spectrum and show how changing the interlayer exciton binding energy by increasing the layer separation modifies the optical spectra.

We propose multi-layer moire structures in strong external magnetic fields as a novel platform for realizing highly-tunable, frustrated Hubbard physics with topological order. Identifying the layer degree of freedom as a pseudo spin, allows us to retain SU(2) symmetry while controlling ring-exchange processes and concurrently quenching the kinetic energy by large external magnetic fields. This way, a broad class of interacting Hubbard-Hofstadter states and their transitions can be studied. Remarkably, in the limit of strong interactions the system becomes Mott insulating and we find chiral pseudo spin liquid phases which are induced by the magnetic field. We find that this topologically ordered state remains exceptionally stable towards relevant perturbations. We discuss how layer pseudo-spin can be probed in near-term experiments. As the magnetic flux can be easily tuned in moire systems, our approach provides a promising route towards the experimental realization and control of topologically ordered phases of matter., Comment: 12+3 pages, 8+5 figures

We study kinetic magnetism for the Fermi-Hubbard models in triangular type lattices, including a zigzag ladder, four- and six-legged triangular cylinders and a full two-dimensional triangular lattice. We focus on the regime of strong interactions, $U\gg t$ and filling factors around one electron per site. For temperatures well above the hopping strength, the Curie-Weiss form of the magnetic susceptibility suggests effective antiferromagnetic correlations for systems that are hole doped with respect to $\nu=1$, and ferromagnetic correlations for systems with electron dopings. We show that these correlations arise from magnetic polaron dressing of charge carrier propagating in a spin incoherent Mott insulator. Effective interactions corresponding to these correlations can strongly exceed the magnetic super-exchange energy. In the case of hole doping, antiferromagnetic polarons originate from kinetic frustration of individual holes in a triangular lattice. In the case of electron doping, Nagaoka type ferromagnetic correlations are induced by propagating doublons. These results provide a theoretical explanation of recent experimental results in moire TMDC materials. To understand many-body states arising from antiferromagentic polarons at low temperatures, we study hole doped systems in finite magnetic fields. At low dopings and intermediate magnetic fields we find a magnetic polaron phase, separated from the fully polarized state by a metamagnetic transition. With decreasing magnetic field the system shows a tendency to phase separate, with hole rich regions forming antiferromagnetic spinbags. We demonstrate that direct observations of magnetic polarons in triangular lattices can be achieved in experiments with ultracold atoms, which allow measurements of three point hole-spin-spin correlations., Comment: 6 pages, 5 figures + 3 pages, 3 figures

Detecting magnetic order at the nanoscale is of central interest for the study of quantum magnetism in general, and the emerging field of moir\'e magnets in particular. Here, we analyze the exciton band structure that arises from a periodic modulation of the valley Zeeman effect. Despite long-range electron-hole exchange interactions, we find a sizable splitting in the energy of the bright circularly-polarized exciton Umklapp resonances, which serves as a direct optical probe of magnetic order. We first analyze quantum moir\'e magnets realized by periodic ordering of electron spins in Mott-Wigner states of transition metal dichalcogenide (TMD) monolayers or twisted bilayers: we show that spin-valley dependent exciton-electron interactions allow for probing the spin-valley order of electrons and demonstrate that it is possible to observe unique signatures of ferromagnetic order in a triangular lattice and both ferromagnetic and N\'eel order in a honeycomb lattice. We then focus on semiclassical moir\'e magnets realized in twisted bilayers of ferromagnetic materials: we propose a detection scheme for moir\'e magnetism which is based on inter-layer exchange coupling between spins in a moir\'e magnet and excitons in a TMD monolayer., Comment: 6+5 pages, 4+3 figures, 1 table

Quantum transduction between the microwave and optical domains is an outstanding challenge for long-distance quantum networks based on superconducting qubits. For all transducers realized to date, the generally weak light-matter coupling does not allow high transduction efficiency, large bandwidth, and low noise simultaneously. Here we show that a large electric dipole moment of an exciton in an optically active self-assembled quantum dot molecule (QDM) efficiently couples to a microwave resonator field at a single-photon level. This allows for transduction between microwave and optical photons without coherent optical pump fields to enhance the interaction. With an on-chip device, we demonstrate a sizeable single-photon coupling strength of 16 MHz. Thanks to the fast exciton decay rate in the QDM, the transduction bandwidth between an optical and microwave resonator photon reaches several 100s of MHz., Comment: 30 pages, 12 figures

The quest to improve transparent conductors balances two key goals: increasing electrical conductivity and increasing optical transparency. To improve both simultaneously is hindered by the physical limitation that good metals with high electrical conductivity have large carrier densities that push the plasma edge into the ultra-violet range. Transparent conductors are compromises between electrical conductivity, requiring mobile electrons, and optical transparency based on immobile charges to avoid screening of visible light. Technological solutions reflect this trade-off, achieving the desired transparencies by reducing the conductor thickness or carrier density at the expense of a lower conductance. Here we demonstrate that highly anisotropic crystalline conductors offer an alternative solution, avoiding this compromise by separating the directions of conduction and transmission. Materials with a quasi-two-dimensional electronic structure have a plasma edge well below the range of visible light while maintaining excellent in-plane conductivity. We demonstrate that slabs of the layered oxides Sr$_2$RuO$_4$ and Tl$_2$Ba$_2$CuO$_{6+\delta}$ are optically transparent even at macroscopic thicknesses >2$\mu$m for c-axis polarized light. Underlying this observation is the fabrication of out-of-plane slabs by focused ion beam milling. This work provides a glimpse into future technologies, such as highly polarized and addressable optical screens, that advancements in a-axis thin film growth will enable.

Understanding physical properties of quantum emitters strongly interacting with quantized electromagnetic modes is one of the primary goals in the emergent field of waveguide quantum electrodynamics (QED). When the light-matter coupling strength is comparable to or even exceeds energies of elementary excitations, conventional approaches based on perturbative treatment of light-matter interactions, two-level description of matter excitations, and photon-number truncation are no longer sufficient. Here we study in and out of equilibrium properties of waveguide QED in such nonperturbative regimes on the basis of a comprehensive and rigorous theoretical approach using an asymptotic decoupling unitary transformation. We uncover several surprising features ranging from symmetry-protected many-body bound states in the continuum to strong renormalization of the effective mass and potential; the latter may explain recent experiments demonstrating cavity-induced changes in chemical reactivity as well as enhancements of ferromagnetism or superconductivity. To illustrate our general results with concrete examples, we use our formalism to study a model of coupled cavity arrays, which is relevant to experiments in superconducting qubits interacting with microwave resonators or atoms coupled to photonic crystals. We examine the relation between our results and delocalization-localization transition in the spin-boson model; notably, we point out that a reentrant transition can occur in the regimes where the coupling strength becomes the dominant energy scale. We also discuss applications of our results to other problems in different fields, including quantum optics, condensed matter physics, and quantum chemistry., Comment: 27 pages, 10 figures

Moire superlattices in twisted transition metal dichalcogenide bilayers have emerged as a rich platform for exploring strong correlations using optical spectroscopy. Despite observation of rich Mott-Wigner physics stemming from an interplay between the periodic potential and Coulomb interactions, the absence of tunnel coupling induced hybridization of electronic states ensured a classical layer degree of freedom in these experiments. Here, we investigate a MoSe$_2$ homobilayer structure where inter-layer coherent tunnelling and layer-selective optical transitions allow for electric field controlled manipulation and measurement of the layer-pseudospin of the ground-state holes. A striking example of qualitatively new phenomena in this system is our observation of an electrically tunable 2D Feshbach resonance in exciton-hole scattering, which allows us to control the strength of interactions between excitons and holes located in different layers. Our findings enable hitherto unexplored possibilities for optical investigation of many-body physics, as well as realization of degenerate Bose-Fermi mixtures with tunable interactions, without directly exposing the itinerant fermions to light fields., Comment: Main text: 9 pages, 4 figures; Supplementary Material: 9 pages, 7 figures

Feshbach resonances are an invaluable tool in atomic physics, enabling precise control of interactions and the preparation of complex quantum phases of matter. Here, we theoretically analyze a solid-state analogue of a Feshbach resonance in two dimensional semiconductor heterostructures. In the presence of inter-layer electron tunneling, the scattering of excitons and electrons occupying different layers can be resonantly enhanced by tuning an applied electric field. The emergence of an inter-layer Feshbach molecule modifies the optical excitation spectrum, and can be understood in terms of Fermi polaron formation. We discuss potential implications for the realization of correlated Bose-Fermi mixtures in bilayer semiconductors., Comment: 6+2 pages, 4 figures

Quantum confinement is the discretization of energy when motion of particles is restricted to length scales smaller than their de Broglie wavelength. The experimental realization of this effect has had wide ranging impact in diverse fields of physics and facilitated the development of new technologies. In semiconductor physics, quantum confinement of optically excited quasiparticles, such as excitons or trions, is typically achieved by modulation of material properties - an approach crucially limited by the lack of insitu tunability and scalability of confining potentials. Achieving fully tunable quantum confinement of optical excitations has therefore been an outstanding goal in quantum photonics. Here, we demonstrate electrically controlled quantum confinement of neutral excitons in a gate-defined monolayer p-i-n diode. A combination of dc Stark shift induced by large in-plane fields and a previously unknown confining mechanism based on repulsive interaction between excitons and free charges ensures tight exciton confinement in the narrow neutral region. Quantization of exciton motion manifests in multiple discrete, spectrally narrow, voltage-dependent optical resonances that emerge below the free exciton resonance. Our measurements reveal several unique physical features of these quantum confined excitons, including an in-plane dipolar character, one-dimensional center-of-mass confinement, and strikingly enhanced exciton size in the presence of magnetic fields. Our method provides an experimental route towards creating scalable arrays of identical single photon sources, which will constitute building blocks of strongly correlated photonic systems.

Quantum light-matter systems at strong coupling are notoriously challenging to analyze due to the need to include states with many excitations in every coupled mode. We propose a nonperturbative approach to analyze light-matter correlations at all interaction strengths. The key element of our approach is a unitary transformation that achieves asymptotic decoupling of light and matter degrees of freedom in the limit where light-matter interaction becomes the dominant energy scale. In the transformed frame, truncation of the matter/photon Hilbert space is increasingly well-justified at larger coupling, enabling one to systematically derive low-energy effective models, such as tight-binding Hamiltonians. We demonstrate the versatility of our approach by applying it to concrete models relevant to electrons in crystal potential and electric dipoles interacting with a cavity mode. A generalization to the case of spatially varying electromagnetic modes is also discussed., Comment: 7+6 pages, 3+2 figures, to appear in PRL

The elementary optical excitations in two dimensional semiconductors hosting itinerant electrons are attractive and repulsive polarons -- excitons that are dynamically screened by electrons. Exciton-polarons have hitherto been studied in translationally invariant degenerate Fermi systems. Here, we show that electronic charge order breaks the excitonic translational invariance and leads to a direct optical signature in the exciton-polaron spectrum. Specifically, we demonstrate that new optical resonances appear due to spatially modulated interaction between excitons and electrons in an incompressible Mott state. Our observations demonstrate that resonant optical spectroscopy provides an invaluable tool for studying strongly correlated states, such as Wigner crystals and density waves, where exciton-electron interactions are modified by the emergence of new electronic charge or spin order., Comment: Main text: 9 pages, 5 figures; Supplemental Material: 9 pages, 5 figures

The elementary optical excitations of a two-dimensional electron or hole system have been identified as exciton-Fermi-polarons. Nevertheless, the connection between the bound state of an exciton and an electron, termed trion, and exciton-polarons is subject of ongoing debate. Here, we use an analogy to the Tavis-Cummings model of quantum optics to show that an exciton-polaron can be understood as a hybrid quasiparticle -- a coherent superposition of a bare exciton in an unperturbed Fermi sea and a bright collective excitation of many trions. The analogy is valid to the extent that the Chevy Ansatz provides a good description of dynamical screening of excitons and provided the Fermi energy is much smaller than the trion binding energy. We anticipate our results to bring new insight that could help to explain the striking differences between absorption and emission spectra of two-dimensional semiconductors., Comment: 5 pages

Spin and photonic systems are at the heart of modern information devices and emerging quantum technologies. An interplay between electron-hole pairs (excitons) in semiconductors and collective spin excitations (magnons) in magnetic crystals would bridge these heterogeneous systems, leveraging their individual assets in novel interconnected devices. Here, we report the magnon-exciton coupling at the interface between a magnetic thin film and an atomically-thin semiconductor. Our approach allies the long-lived magnons hosted in a film of yttrium iron garnet (YIG) to strongly-bound excitons in a flake of a transition metal dichalcogenide, MoSe$_2$. The magnons induce on the excitons a dynamical valley Zeeman effect ruled by interfacial exchange interactions. This nascent class of hybrid system suggests new opportunities for information transduction between microwave and optical regions., Comment: 23 pages with 14 figures

We experimentally demonstrate a dipolar polariton based electric field sensor. We tune and optimize the sensitivity of the sensor by varying the dipole moment of polaritons. We show polariton interactions play an important role in determining the conditions for optimal electric field sensing, and achieve a sensitivity of 0.12 V-m$^{-1}$-Hz$^{-0.5}$. Finally we apply the sensor to illustrate that excitation of polaritons modify the electric field in a spatial region much larger than the optical excitation spot.

The light-matter interaction can be utilized to qualitatively alter physical properties of materials. Recent theoretical and experimental studies have explored this possibility of controlling matter by light based on driving many-body systems via strong classical electromagnetic radiation, leading to a time-dependent Hamiltonian for electronic or lattice degrees of freedom. To avoid inevitable heating, pump-probe setups with ultrashort laser pulses have so far been used to study transient light-induced modifications in materials. Here, we pursue yet another direction of controlling quantum matter by modifying quantum fluctuations of its electromagnetic environment. In contrast to earlier proposals on light-enhanced electron-electron interactions, we consider a dipolar quantum many-body system embedded in a cavity composed of metal mirrors, and formulate a theoretical framework to manipulate its equilibrium properties on the basis of quantum light-matter interaction. We analyze hybridization of different types of the fundamental excitations, including dipolar phonons, cavity photons, and plasmons in metal mirrors, arising from the cavity confinement in the regime of strong light-matter interaction. This hybridization qualitatively alters the nature of the collective excitations and can be used to selectively control energy-level structures in a wide range of platforms. Most notably, in quantum paraelectrics, we show that the cavity-induced softening of infrared optical phonons enhances the ferroelectric phase in comparison with the bulk materials. Our findings suggest an intriguing possibility of inducing a superradiant-type transition via the light-matter coupling without external pumping. We also discuss possible applications of the cavity-induced modifications in collective excitations to molecular materials and excitonic devices., Comment: 30 pages, 14 figures, to appear in PRX

Van der Waals heterostructures combining two-dimensional magnetic and semiconducting layers constitute a promising platform for interfacing magnetism, electronics, and optics. Here, we use resonant optical reflection spectroscopy to the observe magnetic proximity effect in a gate-tunable MoSe$_2$/CrBr$_3$ heterostructure. High quality of the interface leads to a giant zero-field splitting of the K and K' valley excitons in MoSe$_2$, equivalent to an external magnetic field of 12 T, with a weak but distinct electric field dependence that hints at potential for electrical control of magnetization. The magnetic proximity effect allows us to use resonant optical spectroscopy to fully characterize the CrBr$_3$ magnet, determining the easy-axis coercive field, the magnetic anisotropy energy, and critical exponents associated with spin susceptibility and magnetization.

Optically generated electron-hole pairs can probe strongly correlated electronic matter, or, by forming exciton-polaritons within an optical cavity, give rise to photonic nonlinearities. The present paper theoretically studies the properties of electron-hole pairs in a two-dimensional electron liquid in the fractional quantum Hall regime. In particular, we quantify the effective interactions between optical excitations by numerically evaluating the system's energy spectrum under the assumption of full spin and Landau level polarization. Optically most active are those pair excitations which do not modify the correlations of the electron liquid, also known as multiplicative states. In the case of spatial separation of electrons and holes, these excitations interact repulsively with each other. However, when the electron liquid is compressible, other non-multiplicative configurations occur at lower energies. The interactions of such dark excitations strongly depend on the liquid, and can also become attractive. For the case of a single excitation, we also study the effect of Landau level mixing in the valence band which can dramatically change the effective mass of an exciton., Comment: 8 + 4 pages, 3 figures

The realization of mixtures of excitons and charge carriers in van-der-Waals materials presents a new frontier for the study of the many-body physics of strongly interacting Bose-Fermi mixtures. In order to derive an effective low-energy model for such systems, we develop an exact diagonalization approach based on a discrete variable representation that predicts the scattering and bound state properties of three charges in two-dimensional transition metal dichalcogenides. From the solution of the quantum mechanical three-body problem we thus obtain the bound state energies of excitons and trions within an effective mass model which are in excellent agreement with Quantum Monte Carlo predictions. The diagonalization approach also gives access to excited states of the three-body system. This allows us to predict the scattering phase shifts of electrons and excitons that serve as input for a low-energy theory of interacting mixtures of excitons and charge carriers at finite density. To this end we derive an effective exciton-electron scattering potential that is directly applicable for Quantum Monte-Carlo or diagrammatic many-body techniques. As an example, we demonstrate the approach by studying the many-body physics of exciton Fermi polarons in transition-metal dichalcogenides, and we show that finite-range corrections have a substantial impact on the optical absorption spectrum. Our approach can be applied to a plethora of many-body phenomena realizable in atomically thin semiconductors ranging from exciton localization to induced superconductivity.

It is widely assumed that photons cannot be manipulated using electric or magnetic fields. Even though hybridization of photons with electronic polarization to form exciton-polaritons has paved the way to a number of ground-breaking experiments in semiconductor microcavities, the neutral bosonic nature of these quasiparticles has severely limited their response to external gauge fields. Here, we demonstrate polariton acceleration by external electric and magnetic fields in the presence of nonperturbative coupling between polaritons and itinerant electrons, leading to formation of new quasiparticles termed polaron-polaritons. We identify the generation of electron density gradients by the applied fields to be primarily responsible for inducing a gradient in polariton energy, which in turn leads to acceleration along a direction determined by the applied fields. Remarkably, we also observe that different polarization components of the polaritons can be accelerated in opposite directions when the electrons are in $\nu = 1$ integer quantum Hall state., Comment: 10 pages, 9 figures

Two dimensional materials and their heterostructures constitute a promising platform to study correlated electronic states as well as many body physics of excitons. Here, we present experiments that unite these hitherto separate efforts and show how excitons that are dynamically screened by itinerant electrons to form exciton-polarons, can be used as a spectroscopic tool to study interaction-induced incompressible states of electrons. The MoSe$_2$/hBN/MoSe$_2$ heterostructure that we study exhibits a long-period Moir\'e superlattice as evidenced by coherent-hole tunneling mediated avoided crossings between the intra-layer exciton with three inter-layer exciton resonances separated by $\sim$ 3meV. For electron densities corresponding to half-filling of the lowest Moir\'e subband, we observe strong layer-paramagnetism demonstrated by an abrupt transfer of all $\sim$ 1500 electrons from one MoSe$_2$ layer to the other upon application of a small perpendicular electric field. Remarkably, the electronic state at half-filling of each MoSe$_2$ layer is resilient towards charge redistribution by the applied electric field, demonstrating an incompressible Mott-like state of electrons. Our experiments demonstrate that optical spectroscopy provides a powerful tool for investigating strongly correlated electron physics in the bulk and pave the way for investigating Bose-Fermi mixtures of degenerate electrons and dipolar excitons., Comment: Main text: 12 pages, 5 figures; Supplemental Material: 12 pages, 6 figures

The second-order correlation function of light $g^{(2)}(\tau)$ constitutes a pivotal tool to quantify the quantum behavior of an emitter and in turn its potential for quantum information applications. The experimentally accessible time resolution of $g^{(2)}(\tau)$ is usually limited by the jitter of available single photon detectors. Here, we present a versatile technique allowing to measure $g^{(2)}(\tau)$ from a large variety of light signals with a time resolution given by the pulse length of a mode-locked laser. The technique is based on frequency upconversion in a nonlinear waveguide, and we analyze its properties and limitations by modeling the pulse propagation and the frequency conversion process .We measure $g^{(2)}(\tau)$ from various signals including light from a quantum emitter - a confined exciton-polariton structure - revealing its quantum signatures at a scale of a few picoseconds and demonstrating the capability of the technique.

Engineering strong interactions between optical photons is a great challenge for quantum science. Envisioned applications range from the realization of photonic gates for quantum information processing to synthesis of photonic quantum materials for investigation of strongly-correlated driven-dissipative systems. Polaritonics, based on the strong coupling of photons to atomic or electronic excitations in an optical resonator, has emerged as a promising approach to implement those tasks. Recent experiments demonstrated the onset of quantum correlations in the exciton-polariton system, showing that strong polariton blockade could be achieved if interactions were an order of magnitude stronger. Here, we report time resolved four-wave mixing experiments on a two-dimensional electron system embedded in an optical cavity, demonstrating that polariton-polariton interactions are strongly enhanced when the electrons are initially in a fractional quantum Hall state. Our experiments indicate that in addition to strong correlations in the electronic ground state, exciton-electron interactions leading to the formation of polaron polaritons play a key role in enhancing the nonlinear optical response. Besides potential applications in realization of strongly interacting photonic systems, our findings suggest that nonlinear optical measurements could provide information about fractional quantum Hall states that is not accessible in linear optical response.

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 realisation 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 quasi-particles 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 ($0.5 \mu$eV $\mu$m$^2$) as compared to exciton-polaritons. Concurrently, we measure a spectrally integrated transmission gain of the probe field of $\gtrsim 2$ stemming from stimulated scattering of polaron-polaritons. We show theoretically that the non-equilibrium nature of optically excited quasiparticles favours 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 realisation of nonequilibrium polariton condensates.

Optically generated excitons dictate the absorption and emission spectrum of doped semiconductor transition metal dichalcogenide monolayers. We show that upon increasing the electron density, the elementary optical excitations develop a roton-like dispersion, evidenced by a shift of the lowest energy state to a finite momentum on the order of the Fermi momentum. This effect emerges due to Pauli exclusion between excitons and the electron Fermi sea, but the robustness of the roton minimum in these systems is a direct consequence of the long-range nature of the Coulomb interaction and the nonlocal dielectric screening characteristic of monolayers. Finally, we show that the emergence of rotons could be related to hitherto unexplained aspects of photoluminescence spectra in doped transition metal dichalcogenide monolayers., Comment: Supplemental material available as ancillary file

The non-trivial geometry encoded in the Quantum Mechanical wavefunctions has important consequences for its single-particle as well as many-body dynamics. Yet, our understanding of how the geometry of the single-particle eigenstates are manifest in the characteristics of a many-particle system is still incomplete. Here, we demonstrate how the single-particle Berry curvature modifies the fluxoid quantization of a two dimensional Bardeen-Cooper-Schrieffer (BCS) superconductor, and discuss the experimental scenarios where this anomalous quantization is expected to be realized., Comment: 5 pages, 2 figures, Comments welcome

The strong spin-orbit coupling and the broken inversion symmetry in monolayer transition metal dichalcogenides (TMDs) results in spin-valley coupled band structures. Such a band structure leads to novel applications in the fields of electronics and optoelectronics. Density functional theory calculations as well as optical experiments have focused on spin-valley coupling in the valence band. Here we present magnetotransport experiments on high-quality n-type monolayer molybdenum disulphide (MoS$_{2}$) samples, displaying highly resolved Shubnikov-de Haas oscillations at magnetic fields as low as $2~T$. We find the effective mass $0.7~m_{e}$, about twice as large as theoretically predicted and almost independent of magnetic field and carrier density. We further detect the occupation of the second spin-orbit split band at an energy of about $15~meV$, i.e. about a factor $5$ larger than predicted. In addition, we demonstrate an intricate Landau level spectrum arising from a complex interplay between a density-dependent Zeeman splitting and spin and valley-split Landau levels. These observations, enabled by the high electronic quality of our samples, testify to the importance of interaction effects in the conduction band of monolayer MoS$_{2}$., Comment: Phys.Rev.Lett. (2018)

Cavity-polaritons in semiconductor microstructures have emerged as a promising system for exploring nonequilibrium dynamics of many-body systems. Key advances in this field, including the observation of polariton condensation, superfluidity, realization of topological photonic bands, and dissipative phase transitions, generically allow for a description based on a mean-field Gross-Pitaevskii formalism. While observation of polariton intensity squeezing and decoherence of a polarization entangled photon pair by a polariton condensate provide counter-examples, quantum effects in these experiments show up at high polariton occupancy. Going beyond into the regime of strongly correlated polaritons requires the observation of a photon blockade effect where interactions are strong enough to suppress double occupancy of a photonic lattice site. Here, we report the observation of quantum correlations between polaritons in a fiber cavity which spatially confines polaritons into an area of 3 $\mu$m$^2$. Photon correlation measurements show that careful tuning of the coupled system allows for a modest photon blockade effect as evidenced by a reduction of simultaneous two-polariton generation probability by 5 %. Concurrently, our experiments provide an unequivocal measurement of the polariton interaction strength, thereby resolving the controversy stemming from recent experimental reports. Our findings constitute a first essential step towards the realization of strongly interacting photonic systems.

Narrow dark resonances associated with electromagnetically induced transparency play a key role in enhancing photon-photon interactions. The schemes realized to date relied on the existence of long-lived atomic states with strong van der Waals interactions. Here, we show that by placing an atomically thin semiconductor with ultra-fast radiative decay rate inside a \textcolor{black}{0D} cavity, it is possible to obtain narrow dark or bright resonances in transmission whose width could be much smaller than that of the cavity and bare exciton decay rates. While breaking of translational invariance places a limit on the width of the dark resonance width, it is possible to obtain a narrow bright resonance that is resilient against disorder by tuning the cavity away from the excitonic transition. Resonant excitation of this bright resonance yields strong photon antibunching even in the limit where the interaction strength is arbitrarily smaller than the non-Markovian disorder broadening and the radiative decay rate of the bare exciton. Our findings suggest that atomically thin semiconductors could pave the way for realization of strongly interacting photonic systems in the solid-state., Comment: 4 pages, 3 figures, Comments welcome

Nonperturbative coupling between cavity photons and excitons leads to formation of hybrid light-matter excitations termed polaritons. In structures where photon absorption leads to creation of excitons with aligned permanent dipoles, the elementary excitations, termed dipolar polaritons, are expected to exhibit enhanced interactions. Here, we report a substantial increase in interaction strength between dipolar polaritons as the size of the dipole is increased by tuning the applied gate voltage. To this end, we use coupled quantum well structures embedded inside a microcavity where coherent electron tunneling between the wells controls the size of the excitonic dipole. Modifications of the interaction strength are characterized by measuring the changes in the reflected intensity of light when polaritons are driven with a resonant laser. Factor of 6.5 increase in the interaction strength to linewidth ratio that we obtain indicates that dipolar polaritons could be used to demonstrate a polariton blockade effect and thereby form the building blocks of many-body states of light., Comment: 12 pages, 4 figures. Supplementary note

Two dimensional heterostructures are likely to provide new avenues for the manipulation of magnetization that is crucial for spintronics or magnetoelectronics. Here, we demonstrate that optical spin pumping can generate a large effective magnetic field in two dimensional MoSe2/WSe2 heterostructures. We determine the strength of the generated field by polarization-resolved measurement of the interlayer exciton photoluminescence spectrum: the measured splitting exceeding 10 milli-electron volts (meV) between the emission originating from the two valleys corresponds to an effective magnetic field of ~ 30 T. The strength of this optically induced field can be controlled by the excitation light polarization. Our finding opens up new possibilities for optically controlled spintronic devices based on van der Waals heterostructures.

Mobile quantum impurities interacting with a fermionic bath form quasiparticles known as Fermi polarons. We demonstrate that a force applied to the bath particles can generate a drag force of similar magnitude acting on the impurities, realizing a novel, nonperturbative Coulomb drag effect. To prove this, we calculate the fully self-consistent, frequency-dependent transconductivity at zero temperature in the Baym-Kadanoff conserving approximation. We apply our theory to excitons and exciton polaritons interacting with a bath of charge carriers in a doped semiconductor embedded in a microcavity. In external electric and magnetic fields, the drag effect enables electrical control of excitons and may pave the way for the implementation of gauge fields for excitons and polaritons. Moreover, a reciprocal effect may facilitate optical manipulation of electron transport. Our findings establish transport measurements as a novel, powerful tool for probing the many-body physics of mobile quantum impurities., Comment: 18 + 11 pages, 4 figures

Magnetic layered van der Waals crystals are an emerging class of materials giving access to new physical phenomena, as illustrated by the recent observation of 2D ferromagnetism in Cr2Ge2Te6 and CrI3. Of particular interest in semiconductors is the interplay between magnetism and transport, which has remained unexplored. Here we report first magneto-transport measurements on exfoliated CrI3 crystals. We find that tunneling conduction in the direction perpendicular to the crystalline planes exhibits a magnetoresistance as large as 10 000 %. The evolution of the magnetoresistance with magnetic field and temperature reveals that the phenomenon originates from multiple transitions to different magnetic states, whose possible microscopic nature is discussed on the basis of all existing experimental observations. This observed dependence of the conductance of a tunnel barrier on its magnetic state is a new phenomenon that demonstrates the presence of a strong coupling between transport and magnetism in magnetic van der Waals semiconductors.

Quantum fluids of light in a nonlinear planar microcavity can exhibit antibunched photon statistics at short distances due to repulsive polariton interactions. We show that, despite the weakness of the nonlinearity, the antibunching signal can be amplified orders of magnitude with an appropriate free-space optics scheme to select and interfere output modes. Our results are understood from the unconventional photon blockade perspective by analyzing the approximate Gaussian output state of the microcavity. In a second part, we illustrate how the temporal and spatial profile of the density-density correlation function of a fluid of light can be reconstructed with free-space optics. Also here the nontrivial (anti)bunching signal can be amplified significantly by shaping the light emitted by the microcavity.