Electrically tunable quantum confinement of neutral excitons.

Confining particles to distances below their de Broglie wavelength discretizes their motional state. This fundamental effect is observed in many physical systems, ranging from electrons confined in atoms or quantum dots1,2 to ultracold atoms trapped in optical tweezers3,4. In solid-state photonics, a long-standing goal has been to achieve fully tunable quantum confinement of optically active electron-hole pairs, known as excitons. To confine excitons, existing approaches mainly rely on material modulation5, which suffers from poor control over the energy and position of trapping potentials. This has severely impeded the engineering of large-scale quantum photonic systems. Here we demonstrate electrically controlled quantum confinement of neutral excitons in 2D semiconductors. By combining gate-defined in-plane electric fields with inherent interactions between excitons and free charges in a lateral p-i-n junction, we achieve exciton confinement below 10 nm. Quantization of excitonic motion manifests in the measured optical response as a ladder of discrete voltage-dependent states below the continuum. Furthermore, we observe that our confining potentials lead to a strong modification of the relative wave function of excitons. Our technique provides an experimental route towards creating scalable arrays of identical single-photon sources and has wide-ranging implications for realizing strongly correlated photonic phases6,7 and on-chip optical quantum information processors8,9.

Signatures of Wigner crystal of electrons in a monolayer semiconductor.

When the Coulomb repulsion between electrons dominates over their kinetic energy, electrons in two-dimensional systems are predicted to spontaneously break continuous-translation symmetry and form a quantum crystal1. Efforts to observe2-12 this elusive state of matter, termed a Wigner crystal, in two-dimensional extended systems have primarily focused on conductivity measurements on electrons confined to a single Landau level at high magnetic fields. Here we use optical spectroscopy to demonstrate that electrons in a monolayer semiconductor with density lower than 3 × 1011 per centimetre squared form a Wigner crystal. The combination of a high electron effective mass and reduced dielectric screening enables us to observe electronic charge order even in the absence of a moiré potential or an external magnetic field. The interactions between a resonantly injected exciton and electrons arranged in a periodic lattice modify the exciton bandstructure so that an umklapp resonance arises in the optical reflection spectrum, heralding the presence of charge order13. Our findings demonstrate that charge-tunable transition metal dichalcogenide monolayers14 enable the investigation of previously uncharted territory for many-body physics where interaction energy dominates over kinetic energy.

Strongly correlated electrons and hybrid excitons in a moiré heterostructure.

Two-dimensional materials and their heterostructures constitute a promising platform to study correlated electronic states, as well as the many-body physics of excitons. Transport measurements on twisted graphene bilayers have revealed a plethora of intertwined electronic phases, including Mott insulators, strange metals and superconductors1-5. However, signatures of such strong electronic correlations in optical spectroscopy have hitherto remained unexplored. Here we present experiments showing how excitons that are dynamically screened by itinerant electrons to form exciton-polarons6,7 can be used as a spectroscopic tool to investigate interaction-induced incompressible states of electrons. We study a molybdenum diselenide/hexagonal boron nitride/molybdenum diselenide heterostructure that exhibits a long-period moiré superlattice, as evidenced by coherent hole-tunnelling-mediated avoided crossings of an intralayer exciton with three interlayer exciton resonances separated by about five millielectronvolts. For electron densities corresponding to half-filling of the lowest moiré subband, we observe strong layer pseudospin paramagnetism, demonstrated by an abrupt transfer of all the (roughly 1,500) electrons from one molybdenum diselenide layer to the other on application of a small perpendicular electric field. Remarkably, the electronic state at half-filling of each molybdenum diselenide 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 paves the way for investigating Bose-Fermi mixtures of degenerate electrons and dipolar excitons.

Nonlinear optics in the fractional quantum Hall regime.

Engineering strong interactions between optical photons is a challenge for quantum science. Polaritonics, which is based on the strong coupling of photons to atomic or electronic excitations in an optical resonator, has emerged as a promising approach to address this challenge, paving the way for applications such as photonic gates for quantum information processing1 and photonic quantum materials for the investigation of strongly correlated driven-dissipative systems2,3. Recent experiments have demonstrated the onset of quantum correlations in exciton-polariton systems4,5, showing that strong polariton blockade6-the prevention of resonant injection of additional polaritons in a well delimited region by the presence of a single polariton-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 cavity7, demonstrating that polariton-polariton interactions are strongly enhanced when the electrons are initially in the fractional quantum Hall regime. Our experiments indicate that, in addition to strong correlations in the electronic ground state, exciton-electron interactions leading to the formation of polaron-polaritons8-11 have a key role in enhancing the nonlinear optical response of the system. Our findings could facilitate the realization of strongly interacting photonic systems, and suggest that nonlinear optical measurements could provide information about fractional quantum Hall states that is not accessible through their linear optical response.

Cavity Quantum Electrodynamics with Hyperbolic van der Waals Materials.

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.

Erratum: Observation of Magnetic Proximity Effect Using Resonant Optical Spectroscopy of an Electrically Tunable MoSe_{2}/CrBr_{3} Heterostructure [Phys. Rev. Lett. 124, 197401 (2020)].

This corrects the article DOI: 10.1103/PhysRevLett.124.197401.

Optical Sensing of Fractional Quantum Hall Effect in Graphene.

Graphene and its heterostructures provide a unique and versatile playground for explorations of strongly correlated electronic phases, ranging from unconventional fractional quantum Hall (FQH) states in a monolayer system to a plethora of superconducting and insulating states in twisted bilayers. However, the access to those fascinating phases has been thus far entirely restricted to transport techniques, due to the lack of a robust energy bandgap that makes graphene hard to access optically. Here we demonstrate an all-optical, noninvasive spectroscopic tool for probing electronic correlations in graphene using excited Rydberg excitons in an adjacent transition metal dichalcogenide monolayer. These excitons are highly susceptible to the compressibility of graphene electrons, allowing us to detect the formation of odd-denominator FQH states at high magnetic fields. Owing to its submicron spatial resolution, the technique we demonstrate circumvents spatial inhomogeneities and paves the way for optical studies of correlated states in optically inactive atomically thin materials.

Optical Signatures of Periodic Magnetization: The Moiré Zeeman Effect.

Detecting magnetic order at the nanoscale is of central interest for the study of quantum magnetism in general, and the emerging field of moiré 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 moiré magnets realized by periodic ordering of electron spins in Mott-Wigner states of transition metal dichalcogenide 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 Néel order in a honeycomb lattice. We then focus on semiclassical moiré magnets realized in twisted bilayers of ferromagnetic materials: we propose a detection scheme for moiré magnetism that is based on interlayer exchange coupling between spins in a moiré magnet and excitons in a transition metal dichalcogenide monolayer.

Tunable Feshbach Resonances and Their Spectral Signatures in Bilayer Semiconductors.

Feshbach resonances provide 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 analog of a Feshbach resonance in two dimensional semiconductor heterostructures. In the presence of interlayer 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 interlayer 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.

Cavity Quantum Electrodynamics at Arbitrary Light-Matter Coupling Strengths.

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 or 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.

Towards polariton blockade of confined exciton-polaritons.

Cavity-polaritons in semiconductor microstructures have emerged as a promising system for exploring non-equilibrium dynamics of many-body systems1. Key advances in this field, including the observation of polariton condensation2, superfluidity3, realization of topological photonic bands4, and dissipative phase transitions5-7, generically allow for a description based on a mean-field Gross-Pitaevskii formalism. Observation of polariton intensity squeezing8,9 and decoherence of a polarization entangled photon pair by a polariton condensate10, on the other hand, demonstrate quantum effects that show up at high polariton occupancy. Going beyond and into the regime of strongly correlated polaritons requires the observation of a photon blockade effect11,12 where interactions are strong enough to suppress double occupancy of a photonic lattice site. Here, we report evidence of quantum correlations between polaritons spatially confined in a fibre cavity. Photon correlation measurements show that careful tuning of the coupled system can lead to a modest reduction of simultaneous two-polariton generation probability by 5%. Concurrently, our experiments allow us to measure the polariton interaction strength, thereby resolving the controversy stemming from recent experimental reports13. Our findings constitute an essential step towards the realization of strongly interacting photonic systems.

Tunable Flux Vortices in Two-Dimensional Dirac Superconductors.

The nontrivial geometry encoded in the quantum mechanical wave function has important consequences for both noninteracting and interacting systems. Yet, our understanding of the relationship between geometrical effects in noninteracting systems and their interacting counterparts is far from complete. Here, we demonstrate how the single-particle Berry curvature associated with the normal phase in two dimensions modifies the fluxoid quantization of a Bardeen-Cooper-Schrieffer superconductor. A discussion of the experimental scenarios where this anomalous quantization is expected is provided. Our work demonstrates the importance of variational Ansätze in making a clear connection between the Berry phases of single-particle and many-body wave functions.

Polariton Electric-Field Sensor.

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 modifies the electric field in a spatial region much larger than the optical excitation spot.

Observation of Magnetic Proximity Effect Using Resonant Optical Spectroscopy of an Electrically Tunable MoSe_{2}/CrBr_{3} Heterostructure.

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 observe the magnetic proximity effect in a gate-tunable MoSe_{2}/CrBr_{3} heterostructure. The 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.

Second-order photon correlation measurement with picosecond resolution using frequency upconversion.

The second-order correlation function of light g(2)(τ) 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)(τ) is usually limited by the jitter of available single-photon detectors. Here, we present a versatile technique allowing g(2)(τ) to be measured 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)(τ) 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.

Enhanced Interactions between Dipolar Polaritons.

Nonperturbative coupling between cavity photons and excitons leads to the formation of hybrid light-matter excitations, termed polaritons. In structures where photon absorption leads to the 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 creates the excitonic dipole. Modifications of the interaction strength are characterized by measuring the changes in the reflected light intensity when polaritons are driven with a resonant laser. The factor of 6.5 increase in the interaction-strength-to-linewidth ratio that we obtain indicates that dipolar polaritons could constitute an important step towards a demonstration of the polariton blockade effect, and thereby to form the building blocks of many-body states of light.

Realization of an Electrically Tunable Narrow-Bandwidth Atomically Thin Mirror Using Monolayer MoSe_{2}.

The advent of two-dimensional semiconductors, such as van der Waals heterostructures, propels new research directions in condensed matter physics and enables development of novel devices with unique functionalities. Here, we show experimentally that a monolayer of MoSe_{2} embedded in a charge controlled heterostructure can be used to realize an electrically tunable atomically thin mirror, which effects 87% extinction of an incident field that is resonant with its exciton transition. The corresponding maximum reflection coefficient of 41% is only limited by the ratio of the radiative decay rate to the nonradiative linewidth of exciton transition and is independent of incident light intensity up to 400 W/cm^{2}. We demonstrate that the reflectivity of the mirror can be drastically modified by applying a gate voltage that modifies the monolayer charge density. Our findings could find applications ranging from fast programable spatial light modulators to suspended ultralight mirrors for optomechanical devices.

Polaron Polaritons in the Integer and Fractional Quantum Hall Regimes.

Elementary quasiparticles in a two-dimensional electron system can be described as exciton polarons since electron-exciton interactions ensures dressing of excitons by Fermi-sea electron-hole pair excitations. A relevant open question is the modification of this description when the electrons occupy flat bands and electron-electron interactions become prominent. Here, we perform cavity spectroscopy of a two-dimensional electron system in the strong coupling regime, where polariton resonances carry signatures of strongly correlated quantum Hall phases. By measuring the evolution of the polariton splitting under an external magnetic field, we demonstrate the modification of polaron dressing that we associate with filling factor dependent electron-exciton interactions.

Interactions and Magnetotransport through Spin-Valley Coupled Landau Levels in Monolayer MoS_{2}.

The strong spin-orbit coupling and the broken inversion symmetry in monolayer transition metal dichalcogenides 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 0.7m_{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 of 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}.

Realization of a Cascaded Quantum System: Heralded Absorption of a Single Photon Qubit by a Single-Electron Charged Quantum Dot.

Photonic losses pose a major limitation for the implementation of a quantum state transfer between nodes of a quantum network. A measurement that heralds a successful transfer without revealing any information about the qubit may alleviate this limitation. Here, we demonstrate the heralded absorption of a single photonic qubit, generated by a single neutral quantum dot, by a single-electron charged quantum dot that is located 5 m away. The transfer of quantum information to the spin degree of freedom takes place upon the emission of a photon; for a properly chosen or prepared quantum dot, the detection of this photon yields no information about the qubit. We show that this process can be combined with local operations optically performed on the destination node by measuring classical correlations between the absorbed photon color and the final state of the electron spin. Our work suggests alternative avenues for the realization of quantum information protocols based on cascaded quantum systems.