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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 paper thus paves the way towards a universal understanding of boson-induced pairing across various fermionic systems at finite density, and opens perspectives towards realizing unexplored forms of electron pairing beyond the conventional paradigm of Cooper pair formation., Physical Review B, 107 (15), ISSN:1098-0121, ISSN:0163-1829, ISSN:1550-235X, ISSN:0556-2805, ISSN:2469-9969, ISSN:1095-3795, ISSN:2469-9950

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. ISSN:0028-0836 ISSN:1476-4687

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, Comptes Rendus. Physique, 22 (S4), ISSN:1631-0705, ISSN:1878-1535

Moiré superlattices in transition metal dichalcogenide bilayers provide a platform for exploring strong correlations with optical spectroscopy. Despite the 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 has ensured a classical layer degree of freedom. We investigated a MoSe2 homobilayer structure where interlayer coherent tunneling allows for electric field–controlled manipulation and measurement of the ground-state hole-layer pseudospin. We observed an electrically tunable two-dimensional Feshbach resonance in exciton-hole scattering, which allowed us to control the strength of interactions between excitons and holes located in different layers. Our results may enable the realization of degenerate Bose-Fermi mixtures with tunable interactions. ISSN:0036-8075 ISSN:1095-9203

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 moire 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. The signature of a Wigner crystal—the analogue of a solid phase for electrons—is observed via the optical reflection spectrum in a monolayer transition metal dichalcogenide.

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 periodic distribution of electrons 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 interactions between excitons and electrons in an incompressible Mott-like correlated 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 charge order. ISSN:2160-3308

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 observe the magnetic proximity effect in a gate-tunable ${\mathrm{MoSe}}_{2}/{\mathrm{CrBr}}_{3}$ heterostructure. The high quality of the interface leads to a giant zero-field splitting of the $K$ and ${K}^{\ensuremath{'}}$ valley excitons in ${\mathrm{MoSe}}_{2}$, 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 ${\mathrm{CrBr}}_{3}$ magnet, determining the easy-axis coercive field, the magnetic anisotropy energy, and critical exponents associated with spin susceptibility and magnetization.

When Landau levels (LLs) become degenerate near the Fermi energy in the quantum Hall regime, interaction effects can drastically modify the electronic ground state. We study the quantum Hall ferromagnet formed in a two-dimensional hole gas around the LL filling factor ν = 1 in the vicinity of a LL crossing in the heave-hole valence band. Cavity spectroscopy in the strong-coupling regime allows us to optically extract the spin polarization of the two-dimensional hole gas. By analyzing this polarization as a function of hole density and magnetic field, we observe a spin flip of the ferromagnet. Furthermore, the depolarization away from v=1 accelerates close to the LL crossing. This is indicative of an increase in the size of skyrmion excitations as the effective Zeeman energy vanishes at the LL crossing., Physical Review Letters, 125 (6), ISSN:0031-9007, ISSN:1079-7114

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.

Physical Review B, 101 (15), ISSN:1098-0121, ISSN:0163-1829, ISSN:1550-235X, ISSN:0556-2805, ISSN:2469-9969, ISSN:1095-3795, ISSN:2469-9950

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 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., Physical Review Letters, 124 (20), ISSN:0031-9007, ISSN:1079-7114

Nature Materials, 18 (3), ISSN:1476-1122, ISSN:1476-4660

Nature, 572 (7767), ISSN:0028-0836, ISSN:1476-4687

he realization of mixtures of excitons and charge carriers in van der Waals materials presents a 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., Physical Review B, 101 (19), ISSN:1098-0121, ISSN:0163-1829, ISSN:1550-235X, ISSN:0556-2805, ISSN:2469-9969, ISSN:1095-3795, ISSN:2469-9950

Optics Letters, 44 (15), ISSN:0146-9592, ISSN:1539-4794

Physical Review Letters, 121 (22), ISSN:0031-9007, ISSN:1079-7114

Physical Review B, 98 (24), ISSN:1098-0121, ISSN:0163-1829, ISSN:1550-235X, ISSN:0556-2805, ISSN:2469-9969, ISSN:1095-3795, ISSN:2469-9950

Physical Review Letters, 120 (5), ISSN:0031-9007, ISSN:1079-7114

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.

Physical Review A, 98 (5), ISSN:1094-1622, ISSN:0556-2791, ISSN:1050-2947

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 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 phenomenon that demonstrates the presence of a strong coupling between transport and magnetism in magnetic van der Waals semiconductors., Nature Communications, 9 (1), ISSN:2041-1723

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., SciPost Physics, 5 (1), ISSN:2542-4653

Physical Review B, 96 (24), ISSN:1098-0121, ISSN:0163-1829, ISSN:1550-235X, ISSN:0556-2805, ISSN:2469-9969, ISSN:1095-3795, ISSN:2469-9950

A monolayer of a transition metal dichalcogenide such as WSe2 is a two-dimensional direct-bandgap valley-semiconductor(1,2) having an effective honeycomb lattice structure with broken inversion symmetry. The inequivalent valleys in the Brillouin zone could be selectively addressed using circularly polarized light fields', suggesting the possibility for magneto-optical measurement and manipulation of the valley pseudospin degree of freedom(6-8). Here we report such experiments that demonstrate the valley Zeeman effect-strongly anisotropic lifting of the degeneracy of the valley pseudospin degree of freedom using an external magnetic field. The valley-splitting measured using the exciton transition deviates appreciably from values calculated using a three-band tight-binding model(9) for an independent electron-hole pair at +/- K valleys. We show, on the other hand, that a theoretical model taking into account the strongly bound nature of the exciton yields an excellent agreement with the experimentally observed splitting. In contrast to the exciton, the trion transition exhibits an unexpectedly large valley Zeeman effect that cannot be understood within the same framework, hinting at a different contribution to the trion magnetic moment. Our results raise the possibility of controlling the valley degree of freedom using magnetic fields in monolayer transition metal dichalcogenides or observing topological states of photons strongly coupled to elementary optical excitations in a microcavity(10).

Physical Review B, 96 (16), ISSN:1098-0121, ISSN:0163-1829, ISSN:1550-235X, ISSN:0556-2805, ISSN:2469-9969, ISSN:1095-3795, ISSN:2469-9950

The efficient conversion of thermal energy to mechanical work by a heat engine is an ongoing technological challenge. Since the pioneering work of Carnot, it has been known that the efficiency of heat engines is bounded by a fundamental upper limit—the Carnot limit. Theoretical studies suggest that heat engines may be operated beyond the Carnot limit by exploiting stationary, nonequilibrium reservoirs that are characterized by a temperature as well as further parameters. In a proof-of-principle experiment, we demonstrate that the efficiency of a nanobeam heat engine coupled to squeezed thermal noise is not bounded by the standard Carnot limit. Remarkably, we also show that it is possible to design a cyclic process that allows for extraction of mechanical work from a single squeezed thermal reservoir. Our results demonstrate a qualitatively new regime of nonequilibrium thermodynamics at small scales and provide a new perspective on the design of efficient, highly miniaturized engines., Physical Review X, 7 (3), ISSN:2160-3308

Physical Review A, 96 (3), ISSN:1094-1622, ISSN:0556-2791, ISSN:1050-2947

Understanding and characterizing phase transitions in driven-dissipative systems constitutes a new frontier for many-body physics. A generic feature of dissipative phase transitions is a vanishing gap in the Liouvillian spectrum, which leads to long-lived deviations from the steady-state as the system is driven towards the transition. Here, we show that photon correlation measurements can be used to characterize the corresponding critical slowing down of nonequilibrium dynamics. We focus on the extensively studied phenomenon of optical bistability in GaAs cavity-polaritons, which can be described as a first-order dissipative phase transition. Increasing the excitation strength towards the bistable range results in an increasing photon-bunching signal along with a decay time that is prolonged by more than nine orders of magnitude as compared to that of low density polaritons. In the limit of strong polariton interactions leading to pronounced quantum fluctuations, the mean-field bistability threshold is washed out. Nevertheless, the scaling of the Liouvillian gap closing as thermodynamic limit is approached provides a signature of the emerging dissipative phase transition. Our results establish photon correlation measurements as an invaluable tool for studying dynamical properties of dissipative phase transitions without requiring phase-sensitive interferometric measurements., 10 pages, 5 figures

Physical Review B, 95 (23), ISSN:1098-0121, ISSN:0163-1829, ISSN:1550-235X, ISSN:0556-2805, ISSN:2469-9969, ISSN:1095-3795, ISSN:2469-9950

Virtually all interactions that are relevant for atomic and condensed matter physics are mediated by quantum fluctuations of the electromagnetic field vacuum. Consequently, controlling the vacuum fluctuations can be used to engineer the strength and the range of interactions. Recent experiments have used this premise to demonstrate novel quantum phases or entangling gates by embedding electric dipoles in photonic cavities or wave guides, which modify the electromagnetic fluctuations. Here, we show theoretically that the enhanced fluctuations in the antisqueezed quadrature of a squeezed vacuum state allow for engineering interactions between electric dipoles without the need for a photonic structure. Thus, the strength and range of the interactions can be engineered in a time-dependent way by changing the spatial profile of the squeezed vacuum in a traveling-wave geometry, which also allows the implementation of chiral dissipative interactions. Using experimentally realized squeezing parameters and including realistic losses, we predict single-atom cooperativities C of up to 10 for the squeezed-vacuum-enhanced interactions., Physical Review X, 7 (2), ISSN:2160-3308

Elementary excitations of a two-dimensional electron system (2DES) can be described in terms of exciton-polarons, i.e. excitons dressed by Fermi-sea electron-hole pairs due to interactions between excitons and the surrounding electrons [1,2]. An interesting open problem is the modification of this description in the quantum Hall regime, where electrons occupy flat-bands and electron-electron interactions become important. Here, we perform cavity spectroscopy, in the strong-coupling regime, of a two-dimensional electron system embedded in a semiconductor microcavity [3,4]. We observe exciton-polaron-polariton resonances in the regime of integer and fractional quantum Hall effect (FQHE).

Neutral particles subject to artificial gauge potentials can behave as charged particles in magnetic fields. This fascinating premise has led to demonstrations of one-way waveguides, topologically protected edge states and Landau levels for photons. In ultracold neutral atoms, effective gauge fields have allowed the emulation of matter under strong magnetic fields leading to realization of Harper-Hofstadter and Haldane models. Here we show that application of perpendicular electric and magnetic fields effects a tunable artificial gauge potential for two-dimensional microcavity exciton polaritons. For verification, we perform interferometric measurements of the associated phase accumulated during coherent polariton transport. Since the gauge potential originates from the magnetoelectric Stark effect, it can be realized for photons strongly coupled to excitations in any polarizable medium. Together with strong polariton–polariton interactions and engineered polariton lattices, artificial gauge fields could play a key role in investigation of non-equilibrium dynamics of strongly correlated photons., Nature Communications, 8, ISSN:2041-1723

Physical Review Letters, 118 (23), ISSN:0031-9007, ISSN:1079-7114

Nano-Optics and Nanophotonics, Quantum Dots for Quantum Information Technologies, ISBN:978-3-319-56377-0, ISBN:978-3-319-56378-7

We present an excerpt of the document "Quantum Information Processing and Communication: Strategic report on current status, visions and goals for research in Europe", which has been recently published in electronic form at the website of FET (the Future and Emerging Technologies Unit of the Directorate General Information Society of the European Commission, http://www.cordis.lu/ist/fet/qipc-sr.htm). This document has been elaborated, following a former suggestion by FET, by a committee of QIPC scientists to provide input towards the European Commission for the preparation of the Seventh Framework Program. Besides being a document addressed to policy makers and funding agencies (both at the European and national level), the document contains a detailed scientific assessment of the state-of-the-art, main research goals, challenges, strengths, weaknesses, visions and perspectives of all the most relevant QIPC sub-fields, that we report here. Dedicated to the memory of Prof. Th. Beth, one of the pioneers of QIPC, whose contributions have had a significant scientific impact on the development as well as on the visibility of a field that he enthusiastically helped to shape since its early days. © EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2005.

Physical Review B, 93 (24), ISSN:1098-0121, ISSN:0163-1829, ISSN:1550-235X, ISSN:0556-2805, ISSN:2469-9969, ISSN:1095-3795, ISSN:2469-9950

Physical Review B, 93 (8), ISSN:1098-0121, ISSN:0163-1829, ISSN:1550-235X, ISSN:0556-2805, ISSN:2469-9969, ISSN:1095-3795, ISSN:2469-9950