Interlayer and Moiré excitons in atomically thin double layers: From individual quantum emitters to degenerate ensembles.

Abstract: Interlayer excitons (IXs), composed of electron and hole states localized in different layers, excel in bilayers composed of atomically thin van der Waals materials such as semiconducting transition-metal dichalcogenides (TMDs) due to drastically enlarged exciton binding energies, exciting spin-valley properties, elongated lifetimes, and large permanent dipoles. The latter allows modification by electric fields and the study of thermalized bosonic quasiparticles, from the single particle level to interacting degenerate dense ensembles. Additionally, the freedom to combine bilayers of different van der Waals materials without lattice or relative twist-angle constraints leads to layer-hybridized and Moiré excitons, which can be widely engineered. This article covers fundamental aspects of IXs, including correlation phenomena as well as the consequence of Moiré superlattices with a strong focus on TMD homo- and heterobilayers.

Spin-layer locking of interlayer excitons trapped in moiré potentials.

Van der Waals heterostructures offer attractive opportunities to design quantum materials. For instance, transition metal dichalcogenides (TMDs) possess three quantum degrees of freedom: spin, valley index and layer index. Furthermore, twisted TMD heterobilayers can form moiré patterns that modulate the electronic band structure according to the atomic registry, leading to spatial confinement of interlayer excitons (IXs). Here we report the observation of spin-layer locking of IXs trapped in moiré potentials formed in a heterostructure of bilayer 2H-MoSe2 and monolayer WSe2. The phenomenon of locked electron spin and layer index leads to two quantum-confined IX species with distinct spin-layer-valley configurations. Furthermore, we observe that the atomic registries of the moiré trapping sites in the three layers are intrinsically locked together due to the 2H-type stacking characteristic of bilayer TMDs. These results identify the layer index as a useful degree of freedom to engineer tunable few-level quantum systems in two-dimensional heterostructures.

Metasurface for characterization of the polarization state of light.

The miniaturization of measurement systems currently used to characterize the polarization state of light is limited by the bulky optical components used such as polarizers and waveplates. We propose and experimentally demonstrate a simple and compact approach to measure the ellipticity and handedness of the polarized light using an ultrathin (40 nm) gradient metasurface. A completely polarized light beam is decomposed into a left circularly polarized beam and a right circularly polarized beam, which are steered in two directions by the metasurface consisting of nanorods with spatially varying orientations. By measuring the intensities of the refracted light spots, the ellipticity and handedness of various incident polarization states are characterized at a range of wavelengths and used to determine the polarization information of the incident beam. To fully characterize the polarization state of light, an extra polarizer can be used to measure the polarization azimuth angle of the incident light.

High resolution coherent population trapping on a single hole spin in a semiconductor quantum dot.

We report high resolution coherent population trapping on a single hole spin in a semiconductor quantum dot. The absorption dip signifying the formation of a dark state exhibits an atomic physicslike dip width of just 10 MHz. We observe fluctuations in the absolute frequency of the absorption dip, evidence of very slow spin dephasing. We identify the cause of this process as charge noise by, first, demonstrating that the hole spin g factor in this configuration (in-plane magnetic field) is strongly dependent on the vertical electric field, and second, by characterizing the charge noise through its effects on the optical transition frequency. An important conclusion is that charge noise is an important hole spin dephasing process.

Optical pumping of a single hole spin in a quantum dot.

The spin of an electron is a natural two-level system for realizing a quantum bit in the solid state. For an electron trapped in a semiconductor quantum dot, strong quantum confinement highly suppresses the detrimental effect of phonon-related spin relaxation. However, this advantage is offset by the hyperfine interaction between the electron spin and the 10(4) to 10(6) spins of the host nuclei in the quantum dot. Random fluctuations in the nuclear spin ensemble lead to fast spin decoherence in about ten nanoseconds. Spin-echo techniques have been used to mitigate the hyperfine interaction, but completely cancelling the effect is more attractive. In principle, polarizing all the nuclear spins can achieve this but is very difficult to realize in practice. Exploring materials with zero-spin nuclei is another option, and carbon nanotubes, graphene quantum dots and silicon have been proposed. An alternative is to use a semiconductor hole. Unlike an electron, a valence hole in a quantum dot has an atomic p orbital which conveniently goes to zero at the location of all the nuclei, massively suppressing the interaction with the nuclear spins. Furthermore, in a quantum dot with strong strain and strong quantization, the heavy hole with spin-3/2 behaves as a spin-1/2 system and spin decoherence mechanisms are weak. We demonstrate here high fidelity (about 99 per cent) initialization of a single hole spin confined to a self-assembled quantum dot by optical pumping. Our scheme works even at zero magnetic field, demonstrating a negligible hole spin hyperfine interaction. We determine a hole spin relaxation time at low field of about one millisecond. These results suggest a route to the realization of solid-state quantum networks that can intra-convert the spin state with the polarization of a photon.

Highly tunable ground and excited state excitonic dipoles in multilayer 2H-MoSe2.

The fundamental properties of an exciton are determined by the spin, valley, energy, and spatial wavefunctions of the Coulomb-bound electron and hole. In van der Waals materials, these attributes can be widely engineered through layer stacking configuration to create highly tunable interlayer excitons with static out-of-plane electric dipoles, at the expense of the strength of the oscillating in-plane dipole responsible for light-matter coupling. Here we show that interlayer excitons in bi- and tri-layer 2H-MoSe2 crystals exhibit electric-field-driven coupling with the ground (1s) and excited states (2s) of the intralayer A excitons. We demonstrate that the hybrid states of these distinct exciton species provide strong oscillator strength, large permanent dipoles (up to 0.73 ± 0.01 enm), high energy tunability (up to ~200 meV), and full control of the spin and valley characteristics such that the exciton g-factor can be manipulated over a large range (from -4 to +14). Further, we observe the bi- and tri-layer excited state (2s) interlayer excitons and their coupling with the intralayer excitons states (1s and 2s). Our results, in good agreement with a coupled oscillator model with spin (layer)-selectivity and beyond standard density functional theory calculations, promote multilayer 2H-MoSe2 as a highly tunable platform to explore exciton-exciton interactions with strong light-matter interactions.

Electro-elastic tuning of single particles in individual self-assembled quantum dots.

We investigate the effect of uniaxial stress on InGaAs quantum dots in a charge tunable device. Using Coulomb blockade and photoluminescence, we observe that significant tuning of single particle energies (≈-0.22 meV/MPa) leads to variable tuning of exciton energies (+18 to -0.9 µeV/MPa) under tensile stress. Modest tuning of the permanent dipole, Coulomb interaction and fine-structure splitting energies is also measured. We exploit the variable exciton response to tune multiple quantum dots on the same chip into resonance.

Single-emitter quantum key distribution over 175 km of fibre with optimised finite key rates.

Quantum key distribution with solid-state single-photon emitters is gaining traction due to their rapidly improving performance and compatibility with future quantum networks. Here we emulate a quantum key distribution scheme with quantum-dot-generated single photons frequency-converted to 1550 nm, achieving count rates of 1.6 MHz with [Formula: see text] and asymptotic positive key rates over 175 km of telecom fibre. We show that the commonly used finite-key analysis for non-decoy state QKD drastically overestimates secure key acquisition times due to overly loose bounds on statistical fluctuations. Using the tighter multiplicative Chernoff bound to constrain the estimated finite key parameters, we reduce the required number of received signals by a factor 108. The resulting finite key rate approaches the asymptotic limit at all achievable distances in acquisition times of one hour, and at 100 km we generate finite keys at 13 kbps for one minute of acquisition. This result is an important step towards long-distance single-emitter quantum networking.

Coherence in cooperative photon emission from indistinguishable quantum emitters.

Photon-mediated interactions between atoms can arise via coupling to a common electromagnetic mode or by quantum interference. Here, we probe the role of coherence in cooperative emission arising from two distant but indistinguishable solid-state emitters because of path erasure. The primary signature of cooperative emission, the emergence of "bunching" at zero delay in an intensity correlation experiment, is used to characterize the indistinguishability of the emitters, their dephasing, and the degree of correlation in the joint system that can be coherently controlled. In a stark departure from a pair of uncorrelated emitters, in Hong-Ou-Mandel-type interference measurements, we observe photon statistics from a pair of indistinguishable emitters resembling that of a weak coherent state from an attenuated laser. Our experiments establish techniques to control and characterize cooperative behavior between matter qubits using the full quantum optics toolbox, a key step toward realizing large-scale quantum photonic networks.

The Magnetic Genome of Two-Dimensional van der Waals Materials.

Magnetism in two-dimensional (2D) van der Waals (vdW) materials has recently emerged as one of the most promising areas in condensed matter research, with many exciting emerging properties and significant potential for applications ranging from topological magnonics to low-power spintronics, quantum computing, and optical communications. In the brief time after their discovery, 2D magnets have blossomed into a rich area for investigation, where fundamental concepts in magnetism are challenged by the behavior of spins that can develop at the single layer limit. However, much effort is still needed in multiple fronts before 2D magnets can be routinely used for practical implementations. In this comprehensive review, prominent authors with expertise in complementary fields of 2D magnetism (i.e., synthesis, device engineering, magneto-optics, imaging, transport, mechanics, spin excitations, and theory and simulations) have joined together to provide a genome of current knowledge and a guideline for future developments in 2D magnetic materials research.

Optical read-out of Coulomb staircases in a moiré superlattice via trapped interlayer trions.

Moiré patterns with a superlattice potential can be formed by vertically stacking two layered materials with a relative twist or lattice constant mismatch. In transition metal dichalcogenide-based systems, the moiré potential landscape can trap interlayer excitons (IXs) at specific atomic registries. Here, we report that spatially isolated trapped IXs in a molybdenum diselenide/tungsten diselenide heterobilayer device provide a sensitive optical probe of carrier filling in their immediate environment. By mapping the spatial positions of individual trapped IXs, we are able to spectrally track the emitters as the moiré lattice is filled with excess carriers. Upon initial doping of the heterobilayer, neutral trapped IXs form charged IXs (IX trions) uniformly with a binding energy of ~7 meV. Upon further doping, the empty superlattice sites sequentially fill, creating a Coulomb staircase: stepwise changes in the IX trion emission energy due to Coulomb interactions with carriers at nearest-neighbour moiré sites. This non-invasive, highly local technique can complement transport and non-local optical sensing techniques to characterize Coulomb interaction energies, visualize charge correlated states, or probe local disorder in a moiré superlattice.

Resonance Fluorescence from Waveguide-Coupled, Strain-Localized, Two-Dimensional Quantum Emitters.

Efficient on-chip integration of single-photon emitters imposes a major bottleneck for applications of photonic integrated circuits in quantum technologies. Resonantly excited solid-state emitters are emerging as near-optimal quantum light sources, if not for the lack of scalability of current devices. Current integration approaches rely on cost-inefficient individual emitter placement in photonic integrated circuits, rendering applications impossible. A promising scalable platform is based on two-dimensional (2D) semiconductors. However, resonant excitation and single-photon emission of waveguide-coupled 2D emitters have proven to be elusive. Here, we show a scalable approach using a silicon nitride photonic waveguide to simultaneously strain-localize single-photon emitters from a tungsten diselenide (WSe2) monolayer and to couple them into a waveguide mode. We demonstrate the guiding of single photons in the photonic circuit by measuring second-order autocorrelation of g(2)(0) = 0.150 ± 0.093 and perform on-chip resonant excitation, yielding a g(2)(0) = 0.377 ± 0.081. Our results are an important step to enable coherent control of quantum states and multiplexing of high-quality single photons in a scalable photonic quantum circuit.

Hybridization of electronic states in quantum dots through photon emission.

The self-assembly of semiconductor quantum dots has opened up new opportunities in photonics. Quantum dots are usually described as 'artificial atoms', because electron and hole confinement gives rise to discrete energy levels. This picture can be justified from the shell structure observed as a quantum dot is filled either with excitons (bound electron-hole pairs) or with electrons. The discrete energy levels have been most spectacularly exploited in single photon sources that use a single quantum dot as emitter. At low temperatures, the artificial atom picture is strengthened by the long coherence times of excitons in quantum dots, motivating the application of quantum dots in quantum optics and quantum information processing. In this context, excitons in quantum dots have already been manipulated coherently. We show here that quantum dots can also possess electronic states that go far beyond the artificial atom model. These states are a coherent hybridization of localized quantum dot states and extended continuum states: they have no analogue in atomic physics. The states are generated by the emission of a photon from a quantum dot. We show how a new version of the Anderson model that describes interactions between localized and extended states can account for the observed hybridization.

Author Correction: Towards spontaneous parametric down conversion from monolayer MoS2.

A correction to this article has been published and is linked from the HTML and PDF versions of this paper. The error has been fixed in the paper.

Coulomb blockade in an atomically thin quantum dot coupled to a tunable Fermi reservoir.

Gate-tunable quantum-mechanical tunnelling of particles between a quantum confined state and a nearby Fermi reservoir of delocalized states has underpinned many advances in spintronics and solid-state quantum optics. The prototypical example is a semiconductor quantum dot separated from a gated contact by a tunnel barrier. This enables Coulomb blockade, the phenomenon whereby electrons or holes can be loaded one-by-one into a quantum dot1,2. Depending on the tunnel-coupling strength3,4, this capability facilitates single spin quantum bits1,2,5 or coherent many-body interactions between the confined spin and the Fermi reservoir6,7. Van der Waals (vdW) heterostructures, in which a wide range of unique atomic layers can easily be combined, offer novel prospects to engineer coherent quantum confined spins8,9, tunnel barriers down to the atomic limit10 or a Fermi reservoir beyond the conventional flat density of states11. However, gate-control of vdW nanostructures12-16 at the single particle level is needed to unlock their potential. Here we report Coulomb blockade in a vdW heterostructure consisting of a transition metal dichalcogenide quantum dot coupled to a graphene contact through an atomically thin hexagonal boron nitride (hBN) tunnel barrier. Thanks to a tunable Fermi reservoir, we can deterministically load either a single electron or a single hole into the quantum dot. We observe hybrid excitons, composed of localized quantum dot states and delocalized continuum states, arising from ultra-strong spin-conserving tunnel coupling through the atomically thin tunnel barrier. Probing the charged excitons in applied magnetic fields, we observe large gyromagnetic ratios (∼8). Our results establish a foundation for engineering next-generation devices to investigate either novel regimes of Kondo physics or isolated quantum bits in a vdW heterostructure platform.

Out-of-plane orientation of luminescent excitons in two-dimensional indium selenide.

Van der Waals materials offer a wide range of atomic layers with unique properties that can be easily combined to engineer novel electronic and photonic devices. A missing ingredient of the van der Waals platform is a two-dimensional crystal with naturally occurring out-of-plane luminescent dipole orientation. Here we measure the far-field photoluminescence intensity distribution of bulk InSe and two-dimensional InSe, WSe2 and MoSe2. We demonstrate, with the support of ab-initio calculations, that layered InSe flakes sustain luminescent excitons with an intrinsic out-of-plane orientation, in contrast with the in-plane orientation of dipoles we find in two-dimensional WSe2 and MoSe2 at room-temperature. These results, combined with the high tunability of the optical response and outstanding transport properties, position layered InSe as a promising semiconductor for novel optoelectronic devices, in particular for hybrid integrated photonic chips which exploit the out-of-plane dipole orientation.

Towards spontaneous parametric down conversion from monolayer MoS2.

We present a detailed study of the second order nonlinearity of 2D (mono-atomic layer) dichalcogenide MoS2, both in the visible and in the IR regime, and test its potential for spontaneous parametric down-conversion (SPDC), the amplification of vacuum fluctuations mediated by optical nonlinearity. We develop a model of SPDC from a deeply subwavelength nonlinear medium, where phase matching conditions are completely relaxed, and make predictions about the rate of emitted photons, their momentum, polarisation and spectrum. We show that detection in the visible spectral region is hindered by the strong photoluminescence background. Moving to the IR regime we observe indications of SPDC by performing polarization, power dependence and lifetime measurements around 1560 nm. We show that the signal from a single monolayer is qualitatively different from that generated by multi-layer MoS2. Finally, we characterize the latter as a new kind of photo-luminescence emission which is enhanced at the edges of multi-layer MoS2.

High-resolution grayscale image hidden in a laser beam.

Images perceived by human eyes or recorded by cameras are usually optical patterns with spatially varying intensity or color profiles. In addition to the intensity and color, the information of an image can be encoded in a spatially varying distribution of phase or polarization state. Interestingly, such images might not be able to be directly viewed by human eyes or cameras because they may exhibit highly uniform intensity profiles. Here, we propose and experimentally demonstrate an approach to hide a high-resolution grayscale image in a square laser beam with a size of less than half a millimeter. An image with a pixel size of 300 × 300 nm is encoded into the spatially variant polarization states of the laser beam, which can be revealed after passing through a linear polarizer. This unique technology for hiding grayscale images and polarization manipulation provides new opportunities for various applications, including encryption, imaging, optical communications, quantum science and fundamental physics.

Deterministic strain-induced arrays of quantum emitters in a two-dimensional semiconductor.

An outstanding challenge in quantum photonics is scalability, which requires positioning of single quantum emitters in a deterministic fashion. Site positioning progress has been made in established platforms including defects in diamond and self-assembled quantum dots, albeit often with compromised coherence and optical quality. The emergence of single quantum emitters in layered transition metal dichalcogenide semiconductors offers new opportunities to construct a scalable quantum architecture. Here, using nanoscale strain engineering, we deterministically achieve a two-dimensional lattice of quantum emitters in an atomically thin semiconductor. We create point-like strain perturbations in mono- and bi-layer WSe2 which locally modify the band-gap, leading to efficient funnelling of excitons towards isolated strain-tuned quantum emitters that exhibit high-purity single photon emission. We achieve near unity emitter creation probability and a mean positioning accuracy of 120±32 nm, which may be improved with further optimization of the nanopillar dimensions.