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The sub-laser-cycle timescale of the electronic response to strong fields enables attosecond dynamical imaging in atoms, molecules and solids1–4, with optical tunnelling and high-harmonic generation the hallmarks of attosecond optical spectroscopy2,5–7. Topological insulators are intimately linked with electron dynamics, as manifested via the chiral edge currents8, but it is unclear if and how topology leaves its mark on optical tunnelling and sub-cycle electronic response. Here, we identify distinct bulk topological effects on directionality and timing of currents arising during electron injection into conduction bands. We show that electrons tunnel differently in trivial and topological insulators, for the same band structure, and identify the key role of the Berry curvature in this process. These effects map onto topologically dependent attosecond delays and helicities of emitted harmonics that record the phase diagram of the system. Our findings create new roadmaps in studies of topological systems, building on the ubiquitous properties of the sub-laser-cycle strong-field response—a unique mark of attosecond science.

It is well known that the spin angular momentum of light, and therefore that of photons, is directly related to their circular polarization. Naturally, for totally unpolarized light, polarization is undefined and the spin vanishes. However, for non-paraxial light, the recently discovered transverse spin component, orthogonal to the main propagation direction, is largely independent of the polarization state of the wave. Here, we demonstrate, both theoretically and experimentally, that this transverse spin survives even in non-paraxial fields (for example, focused or evanescent) generated from totally unpolarized paraxial light. This counterintuitive phenomenon is closely related to the fundamental difference between the meanings of ‘full depolarization’ for two-dimensional (2D) paraxial and 3D non-paraxial fields. Our results open an avenue for studies of spin-related phenomena and optical manipulation using unpolarized light.A theoretical and experimental study of the transverse spin appearing in non-paraxial light when the source is totally unpolarized is reported, in sharp contrast to the usual longitudinal spin, which is directly related to the 2D polarization and vanishes in unpolarized fields.

A powerful method to interface quantum light with matter is to propagate the light through an ensemble of atoms. Recently, a number of such interfaces have emerged, most prominently Rydberg ensembles, that enable strong nonlinear interactions between propagating photons. A largely open problem is whether these systems produce exotic many-body states of light and developing new tools to study propagation in the large photon number limit is highly desirable. Here we provide a method based on a “spin model” that maps quasi one-dimensional (1D) light propagation to the dynamics of an open 1D interacting spin system, where all photon correlations are obtained from those of the spins. The spin dynamics in turn are numerically solved using the toolbox of matrix product states. We apply this formalism to investigate vacuum induced transparency, wherein the different photon number components of a pulse propagate with number-dependent group velocity and separate at output. Numerical simulation of light propagation through 1D atomic systems in the many-body limit rapidly saturates hardware capabilities. Here, the authors tackle the problem by mapping the dynamics to an open 1D interacting spin system and solving it using the matrix product state ansatz.

Interactions between a single emitter and cavity provide the archetypical system for fundamental quantum electrodynamics. Here we show that a single molecule of Atto647 aligned using DNA origami interacts coherently with a sub-wavelength plasmonic nanocavity, approaching the cooperative regime even at room temperature. Power-dependent pulsed excitation reveals Rabi oscillations, arising from the coupling of the oscillating electric field between the ground and excited states. The observed single-molecule fluorescent emission is split into two modes resulting from anti-crossing with the plasmonic mode, indicating the molecule is strongly coupled to the cavity. The second-order correlation function of the photon emission statistics is found to be pump wavelength dependent, varying from g (2) (0) = 0.4 to 1.45, highlighting the influence of vibrational relaxation on the Jaynes-Cummings ladder. Our results show that cavity quantum electrodynamic effects can be observed in molecular systems at ambient conditions, opening significant potential for device applications. Here, the authors report the coupling between a single dye molecule and plasmonic nanocavity at room temperature. They provide insight into the statistical properties of the emission and observe non-classical emission, with photon bunching and anti-bunching regimes dependent on the excitation wavelength.

Mode-locking is a process in which different modes of an optical resonator establish stable synchronization through non-linear interactions. This self-organization underlies light sources that enable many modern scientific applications, such as ultrafast and high-field optics and frequency combs. Despite this, mode-locking has almost exclusively referred to the self-organization of light in a single dimension—time. Here we present a theoretical approach—attractor dissection—to understand three-dimensional spatiotemporal mode-locking. The key idea is to find a specific, minimal reduced model for each distinct type of three-dimensional pulse, and thus identify the important intracavity effects responsible for its formation and stability. An intuition for the results follows from the minimum loss principle, the idea that a laser strives to find the configuration of intracavity light that minimizes loss (maximizes gain extraction). Through this approach, we identify and explain several distinct forms of spatiotemporal mode-locking. These phases of coherent laser light have no analogues in one dimension and are supported by measurements of the three-dimensional field, which reveals spatiotemporal mode-locked states that comprise more than 10 7 cavity modes. Our results should facilitate the discovery and understanding of new higher-dimensional forms of coherent light which, in turn, may enable new applications. Mode-locking of lasers can be understood as self-organization, and the three-dimensional case of spatiotemporal mode-locking can described using attractor dissection theory, which helps develop an intuition for this complex case.

A boson sampler implements a restricted model of quantum computing. It is defined by the ability to sample from the distribution resulting from the interference of identical bosons propagating according to programmable, non-interacting dynamics 1 . An efficient exact classical simulation of boson sampling is not believed to exist, which has motivated ground-breaking boson sampling experiments in photonics with increasingly many photons 2 – 12 . However, it is difficult to generate and reliably evolve specific numbers of photons with low loss, and thus probabilistic techniques for postselection 7 or marked changes to standard boson sampling 10 – 12 are generally used. Here, we address the above challenges by implementing boson sampling using ultracold atoms 13 , 14 in a two-dimensional, tunnel-coupled optical lattice. This demonstration is enabled by a previously unrealized combination of tools involving high-fidelity optical cooling and imaging of atoms in a lattice, as well as programmable control of those atoms using optical tweezers. When extended to interacting systems, our work demonstrates the core abilities required to directly assemble ground and excited states in simulations of various Hubbard models 15 , 16 . Boson sampling using ultracold atoms in a two-dimensional, tunnel-coupled optical lattice is enabled by high-fidelity programmable control with optical tweezers of a large number of atoms trapped in an optical lattice.

The strong fields associated with few-cycle pulses can drive highly nonlinear phenomena, allowing the direct control of electrons in condensed matter systems. In this context, by employing near-infrared single-cycle pulse pairs, we measure interferometric autocorrelations of the ultrafast currents induced by optical field emission at the nanogap of a single plasmonic nanocircuit. The dynamics of this ultrafast electron nanotransport depends on the precise temporal field profile of the optical driving pulse. Current autocorrelations are acquired with sub-femtosecond temporal resolution as a function of both pulse delay and absolute carrier-envelope phase. Quantitative modelling of the experiments enables us to monitor the spatiotemporal evolution of the electron density and currents induced in the system and to elucidate the physics underlying the electron transfer driven by strong optical fields in plasmonic gaps. Specifically, we clarify the interplay between the carrier-envelope phase of the driving pulse, plasmonic resonance and quiver motion. Single-cycle interferometric autocorrelation measurements of electrons tunnelling across the gap of a plasmonic bowtie antenna and quantitative models provide insight into the physical interactions that drive the electron transfer.

A quantum computer attains computational advantage when outperforming the best classical computers running the best-known algorithms on well-defined tasks. No photonic machine offering programmability over all its quantum gates has demonstrated quantum computational advantage: previous machines 1 , 2 were largely restricted to static gate sequences. Earlier photonic demonstrations were also vulnerable to spoofing 3 , in which classical heuristics produce samples, without direct simulation, lying closer to the ideal distribution than do samples from the quantum hardware. Here we report quantum computational advantage using Borealis, a photonic processor offering dynamic programmability on all gates implemented. We carry out Gaussian boson sampling 4 (GBS) on 216 squeezed modes entangled with three-dimensional connectivity 5 , using a time-multiplexed and photon-number-resolving architecture. On average, it would take more than 9,000 years for the best available algorithms and supercomputers to produce, using exact methods, a single sample from the programmed distribution, whereas Borealis requires only 36 μs. This runtime advantage is over 50 million times as extreme as that reported from earlier photonic machines. Ours constitutes a very large GBS experiment, registering events with up to 219 photons and a mean photon number of 125. This work is a critical milestone on the path to a practical quantum computer, validating key technological features of photonics as a platform for this goal. Gaussian boson sampling is performed on 216 squeezed modes entangled with three-dimensional connectivity 5 , using Borealis, registering events with up to 219 photons and a mean photon number of 125.

Understanding excited carrier dynamics in semiconductors is crucial for the development of photovoltaics and efficient photonic devices. However, overlapping spectral features in optical pump-probe spectroscopy often render assignments of separate electron and hole carrier dynamics ambiguous. Here, ultrafast electron and hole dynamics in germanium nanocrystalline thin films are directly and simultaneously observed by ultrafast transient absorption spectroscopy in the extreme ultraviolet at the germanium M 4,5 edge. We decompose the spectra into contributions of electronic state blocking and photo-induced band shifts at a carrier density of 8 × 10 20  cm −3 . Separate electron and hole relaxation times are observed as a function of hot carrier energies. A first-order electron and hole decay of ∼1 ps suggests a Shockley–Read–Hall recombination mechanism. The simultaneous observation of electrons and holes with extreme ultraviolet transient absorption spectroscopy paves the way for investigating few- to sub-femtosecond dynamics of both holes and electrons in complex semiconductor materials and across junctions. Understanding excited carrier dynamics in semiconductors is central to the continued development of optoelectronic devices. Using extreme ultraviolet transient absorption spectroscopy, Zürch et al . directly and simultaneously observe ultrafast electron and hole dynamics in germanium thin films.

Many non-equilibrium phenomena have been discovered or predicted in optically driven quantum solids 1 . Examples include light-induced superconductivity 2 , 3 and Floquet-engineered topological phases 4 – 8 . These are short-lived effects that should lead to measurable changes in electrical transport, which can be characterized using an ultrafast device architecture based on photoconductive switches 9 . Here, we report the observation of a light-induced anomalous Hall effect in monolayer graphene driven by a femtosecond pulse of circularly polarized light. The dependence of the effect on a gate potential used to tune the Fermi level reveals multiple features that reflect a Floquet-engineered topological band structure 4 , 5 , similar to the band structure originally proposed by Haldane 10 . This includes an approximately 60 meV wide conductance plateau centred at the Dirac point, where a gap of equal magnitude is predicted to open. We find that when the Fermi level lies within this plateau the estimated anomalous Hall conductance saturates around 1.8 ± 0.4  e 2 / h . A transient topological response in graphene is driven by a short pulse of light. When the Fermi energy is in the predicted band gap the Hall conductance is around two conductance quanta. An ultrafast detection technique enables the measurement.