We explore the interplay of electron-electron correlations and spin-orbit coupling in the model Fermi liquid ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ using laser-based angle-resolved photoemission spectroscopy. Our precise measurement of the Fermi surface confirms the importance of spin-orbit coupling in this material and reveals that its effective value is enhanced by a factor of about 2, due to electronic correlations. The self-energies for the $\beta$ and $\gamma$ sheets are found to display significant angular dependence. By taking into account the multi-orbital composition of quasiparticle states, we determine self-energies associated with each orbital component directly from the experimental data. This analysis demonstrates that the perceived angular dependence does not imply momentum-dependent many-body effects but arises from a substantial orbital mixing induced by spin-orbit coupling. A comparison to single-site dynamical mean-field theory further supports the notion of dominantly local orbital self-energies and provides strong evidence for an electronic origin of the observed nonlinear frequency dependence of the self-energies, leading to “kinks” in the quasiparticle dispersion of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$.

We introduce a new class of states for bosonic quantum fields which extend tensor network states to the continuum and generalize continuous matrix product states to spatial dimensions $d\ge 2$. By construction, they are Euclidean invariant and are genuine continuum limits of discrete tensor network states. Admitting both a functional integral and an operator representation, they share the important properties of their discrete counterparts: expressiveness, invariance under gauge transformations, simple rescaling flow, and compact expressions for the $N$-point functions of local observables. While we discuss mostly the continuous tensor network states extending projected entangled-pair states, we propose a generalization bearing similarities with the continuum multiscale entanglement renormalization ansatz.

We demonstrate full quantum state control of two species of single atoms using optical tweezers and assemble the atoms into a molecule. Our demonstration includes 3D ground-state cooling of a single atom (Cs) in an optical tweezer, transport by several microns with minimal heating, and merging with a single Na atom. Subsequently, both atoms occupy the simultaneous motional ground state with 61(4)% probability. This realizes a sample of exactly two cotrapped atoms near the phase-space-density limit of one, and allows for efficient stimulated-Raman transfer of a pair of atoms into a molecular bound state of the triplet electronic ground potential $a^3{\mathrm{\Sigma }}^{+}$. The results are key steps toward coherent creation of single ultracold molecules for future exploration of quantum simulation and quantum information processing.

By combining theory and experiments, we demonstrate that dipolar quantum gases of both ${}^{166}\mathrm{Er}$ and ${}^{164}\mathrm{Dy}$ support a state with supersolid properties, where a spontaneous density modulation and a global phase coherence coexist. This paradoxical state occurs in a well-defined parameter range, separating the phases of a regular Bose-Einstein condensate and of an insulating droplet array, and is rooted in the roton mode softening, on the one side, and in the stabilization driven by quantum fluctuations, on the other side. Here, we identify the parameter regime for each of the three phases. In the experiment, we rely on a detailed analysis of the interference patterns resulting from the free expansion of the gas, quantifying both its density modulation and its global phase coherence. Reaching the phases via a slow interaction tuning, starting from a stable condensate, we observe that ${}^{166}\mathrm{Er}$ and ${}^{164}\mathrm{Dy}$ exhibit a striking difference in the lifetime of the supersolid properties, due to the different atom loss rates in the two systems. Indeed, while in ${}^{166}\mathrm{Er}$ the supersolid behavior survives only a few tens of milliseconds, we observe coherent density modulations for more than 150 ms in ${}^{164}\mathrm{Dy}$. Building on this long lifetime, we demonstrate an alternative path to reach the supersolid regime, relying solely on evaporative cooling starting from a thermal gas.

Quantum simulations with ultracold atoms typically create atomic wave functions with structures at optical length scales, where direct imaging suffers from the diffraction limit. In analogy to advances in optical microscopy for biological applications, we use a nonlinear atomic response to surpass the diffraction limit. Exploiting quantum interference, we demonstrate imaging with superresolution of $\lambda /50$ and excellent temporal resolution of 500 ns. We characterize our microscope’s performance by measuring the ensemble-averaged probability density of atoms within the unit cells of an optical lattice and observe the dynamics of atoms excited into motion. This approach can be readily applied to image any atomic or molecular system, as long as it hosts a three-level system.

Superresolution microscopy has revolutionized the fields of chemistry and biology by resolving features at the molecular level. In atomic physics, such a scheme can be applied to resolve the atomic density distribution beyond the diffraction limit and to perform quantum control. Here we demonstrate superresolution imaging based on the nonlinear response of atoms to an optical pumping pulse. With this technique, the atomic density distribution can be imaged with a full-width-at-half-maximum resolution of 32(4) nm and a localization precision below 500 pm. The short optical pumping pulse of $1.4\mu \mathrm{s}$ enables us to resolve fast atomic dynamics within a single lattice site. A by-product of our scheme is the emergence of moiré patterns on the atomic cloud, which we show to be immensely magnified images of the atomic density in the lattice.

We study theoretically and experimentally the emergence of supersolid properties in a dipolar Bose-Einstein condensate. The theory reveals a ground state phase diagram with three distinct regimes—a regular Bose-Einstein condensate and incoherent and coherent arrays of quantum droplets. The coherent droplets are connected by a background condensate, which leads—in addition to the periodic density modulation—to a robust phase coherence throughout the whole system. We further theoretically demonstrate that we are able to dynamically approach the ground state in our experiment and that its lifetime is limited only by three-body losses. Experimentally we probe and confirm the signatures of the phase diagram by observing the in situ density modulation as well as the phase coherence using matter wave interference.

Recent research has led to the discovery of fundamental new phenomena in network synchronization, including chimera states, explosive synchronization, and asymmetry-induced synchronization. Each of these phenomena has thus far been observed only in systems designed to exhibit that one phenomenon, which raises the questions of whether they are mutually compatible and, if so, under what conditions they co-occur. Here, we introduce a class of remarkably simple oscillator networks that concurrently exhibit all of these phenomena. The dynamical units consist of pairs of nonidentical phase oscillators, which we refer to as Janus oscillators by analogy with Janus particles and the mythological figure from which their name is derived. In contrast to previous studies, these networks exhibit (i) explosive synchronization with identical oscillators; (ii) extreme multistability of chimera states, including traveling, intermittent, and bouncing chimeras; and (iii) asymmetry-induced synchronization in which synchronization is promoted by random oscillator heterogeneity. These networks also exhibit the previously unobserved possibility of inverted synchronization transitions, in which a transition to a more synchronous state is induced by a reduction rather than an increase in the coupling strength. These various phenomena are shown to emerge under rather parsimonious conditions and even in locally connected ring topologies, which has the potential to facilitate their use to control and manipulate synchronization in experiments.

We perform microwave spectroscopy of Andreev states in superconducting weak links tailored in an InAs-Al (core-full shell) epitaxially grown nanowire. The spectra present distinctive features with bundles of four lines crossing when the superconducting phase difference across the weak link is 0 or $\pi$. We interpret these features as arising from zero-field spin-split Andreev states. A simple analytical model, which takes into account the Rashba spin-orbit interaction in a nanowire containing several transverse subbands, explains these features and their evolution with magnetic field. Our results show that the spin degree of freedom is addressable in Josephson junctions and constitute a first step towards its manipulation.

Tunable directional scattering is of paramount importance for operation of antennas, routing of light, and design of topologically protected optical states. For visible light scattered on a nanoparticle, the directionality could be provided by the Kerker effect, exploiting the interference of electric and magnetic dipole emission patterns. However, magnetic optical resonances in small sub-100-nm particles are relativistically weak. Here, we predict inelastic scattering with the unexpectedly strong tunable directivity up to 5.25 driven by a trembling of a small particle without any magnetic resonance. The proposed optomechanical Kerker effect originates from the vibration-induced multipole conversion. We also put forward an optomechanical spin-Hall effect, the inelastic polarization-dependent directional scattering. Our results uncover an intrinsically multipolar nature of the interaction between light and mechanical motion and apply to a variety of systems from cold atoms to two-dimensional materials to superconducting qubits. An application for engineering of chiral optomechanical coupling and nonreciprocal transmission at nanoscale is proposed.

The Kuramoto model, originally proposed to model the dynamics of many interacting oscillators, has been used and generalized for a wide range of applications involving the collective behavior of large heterogeneous groups of dynamical units whose states are characterized by a scalar angle variable. One such application in which we are interested is the alignment of orientation vectors among members of a swarm. Despite being commonly used for this purpose, the Kuramoto model can only describe swarms in two dimensions, and hence the results obtained do not apply to the often relevant situation of swarms in three dimensions. Partly based on this motivation, as well as on relevance to the classical, mean-field, zero-temperature Heisenberg model with quenched site disorder, in this paper we study the Kuramoto model generalized to $D$ dimensions. We show that in the important case of three dimensions, as well as for any odd number of dimensions, the $D$-dimensional generalized Kuramoto model for heterogeneous units has dynamics that are remarkably different from the dynamics in two dimensions. In particular, for odd $D$ the transition to coherence occurs discontinuously as the interunit coupling constant $K$ is increased through zero, as opposed to the $D=2$ case (and, as we show, also the case of even $D$) for which the transition to coherence occurs continuously as $K$ increases through a positive critical value $K_c$. We also demonstrate the qualitative applicability of our results to related models constructed specifically to capture swarming and flocking dynamics in three dimensions.

We demonstrate single-shot imaging and narrow-line cooling of individual alkaline-earth atoms in optical tweezers; specifically, strontium trapped in $515.2\text{−}\mathrm{nm}$ light. Our approach enables high-fidelity detection of single atoms by imaging photons from the broad singlet transition while cooling on the narrow intercombination line, and we extend this technique to highly uniform two-dimensional tweezer arrays with 121 sites. Cooling during imaging is based on a previously unobserved narrow-line Sisyphus mechanism, which we predict to be applicable in a wide variety of experimental situations. Further, we demonstrate optically resolved sideband cooling of a single atom to near the motional ground state of a tweezer, which is tuned to a magic-trapping configuration achieved by elliptical polarization. Finally, we present calculations, in agreement with our experimental results, that predict a linear-polarization and polarization-independent magic crossing at 520(2) nm and 500.65(50) nm, respectively. Our results pave the way for a wide range of novel experimental avenues based on individually controlled alkaline-earth atoms in tweezers—from fundamental experiments in atomic physics to quantum computing, simulation, and metrology.

Optical tweezers provide a versatile platform for the manipulation and detection of single atoms. Here, we use optical tweezers to demonstrate a set of tools for the microscopic control of atomic strontium, which has two valence electrons. Compared to the single-valence-electron atoms typically used with tweezers, strontium has a more complex internal state structure with a variety of transition wavelengths and linewidths. We report single-atom loading into an array of subwavelength scale optical tweezers and light-shift-free control of a narrow-linewidth optical transition. We use this transition to perform three-dimensional ground-state cooling and to enable high-fidelity nondestructive imaging of single atoms on subwavelength spatial scales. These capabilities, combined with the rich internal structure of strontium, open new possibilities including tweezer-based metrology, new quantum computing architectures, and new paths to low-entropy many-body physics.

In sight of fundamental thermal limits on further substantial performance improvements of modern digital computational processing units, wave-based analog computation is becoming an enticing alternative. A wave, as it propagates through a carefully tailored medium, performs the desired computational operation. Yet, the necessary designs are so intricate that experimental demonstrations will necessitate further technological advances. Here, we show that, counterintuitively, the carefully tailored medium can be replaced with a random medium, subject to an appropriate shaping of the incident wave front. Using tunable metasurface reflect-arrays, we demonstrate our concept experimentally in a chaotic microwave cavity. We conclude that off-the-shelf wireless communication infrastructure in combination with a simple reflect-array suffices to perform analog computation with Wi-Fi waves reverberating in a room.

Radiation-pressure-induced optomechanical coupling permits exquisite control of micro- and mesoscopic mechanical oscillators. This ability to manipulate and even damp mechanical motion with light—a process known as dynamical backaction cooling—has become the basis for a range of novel phenomena within the burgeoning field of cavity optomechanics, spanning from dissipation engineering to quantum-state preparation. As this field moves toward more complex systems and dynamics, there has been growing interest in the prospect of cooling traveling-wave phonons in continuous optomechanical waveguides. Here, we demonstrate optomechanical cooling in a continuous system for the first time. By leveraging the dispersive symmetry breaking produced by intermodal Brillouin scattering, we achieve continuous-mode optomechanical cooling in an extended 2.3-cm silicon waveguide, reducing the temperature of a band of traveling-wave phonons by more than 30 K from room temperature. This work reveals that optomechanical cooling is possible in macroscopic linear waveguide systems without an optical cavity or discrete acoustic modes. Moreover, through an intriguing type of wave-vector-resolved phonon spectroscopy, we show that this system permits optomechanical control over continuously accessible groups of phonons and produces a new form of nonreciprocal reservoir engineering. Beyond this study, this work represents a first step toward a range of classical and quantum traveling-wave operations in continuous optomechanical systems.

Photosynthetic water oxidation is a fundamental process that sustains the biosphere. A ${\mathrm{Mn}}_4\mathrm{Ca}$ cluster embedded in the photosystem II protein environment is responsible for the production of atmospheric oxygen. Here, time-resolved x-ray emission spectroscopy (XES) is used to observe the process of oxygen formation in real time. These experiments reveal that the oxygen evolution step, initiated by three sequential laser flashes, is accompanied by rapid (within $50\mu \mathrm{s}$) changes to the Mn $K\beta$ XES spectrum. However, no oxidation of the ${\mathrm{Mn}}_4\mathrm{Ca}$ core above the all-${\mathrm{Mn}}^{\mathrm{IV}}$ state is detected to precede $\mathrm{O}─\mathrm{O}$ bond formation, and the observed changes are therefore assigned to $\mathrm{O}─\mathrm{O}$ bond-formation dynamics. We propose that $\mathrm{O}─\mathrm{O}$ bond formation occurs prior to the transfer of the final (fourth) electron from the ${\mathrm{Mn}}_4\mathrm{Ca}$ cluster to the oxidized tyrosine ${\mathrm{Tyr}}_Z$ residue. This model resolves the kinetic limitations associated with $\mathrm{O}─\mathrm{O}$ bond formation and suggests an evolutionary adaptation to avoid releasing harmful peroxide species.

We demonstrate that the pulsed-time structure and high-peak ion intensity provided by the laser-ablation process can be directly combined with the high resolution, high efficiency, and low background offered by collinear resonance ionization spectroscopy. This simple, versatile, and powerful method offers new and unique opportunities for high-precision studies of atomic and molecular structures, impacting fundamental and applied physics research. We show that even for ion beams possessing a relatively large energy spread, high-resolution hyperfine-structure measurements can be achieved by correcting the observed line shapes with the time-of-flight information of the resonantly ionized ions. This approach offers exceptional advantages for performing precision measurements on beams with large energy spreads and allows measurements of atomic parameters of previously inaccessible electronic states. The potential of this experimental method in multidisciplinary research is illustrated by performing, for the first time, hyperfine-structure measurements of selected states in the naturally occurring isotopes of indium, ${}^{113,115}\mathrm{In}$. Ab initio atomic-physics calculations have been performed to highlight the importance of our findings in the development of state-of-the-art atomic many-body methods, nuclear structure, and fundamental-physics studies.

The basic physics of sound waves enables ultrasound to visualize biological tissues with high spatial and temporal resolution. Recently, this capability was enhanced with the development of acoustic biomolecules—proteins with physical properties enabling them to scatter sound. The expression of these unique air-filled proteins, known as gas vesicles (GVs), in cells allows ultrasound to image cellular functions such as gene expression in vivo, providing ultrasound with its analog of optical fluorescent proteins. Acoustical methods for the in vivo detection of GVs are now required to maximize the impact of this technology in biology and medicine. We previously engineered GVs exhibiting a nonlinear scattering behavior in response to acoustic pressures above 300 kPa and showed that amplitude-modulated (AM) ultrasound pulse sequences that excite both the linear and nonlinear GV scattering regimes were highly effective at distinguishing GVs from linear scatterers like soft biological tissues. Unfortunately, the in vivo specificity of AM ultrasound imaging is systematically compromised by the nonlinearity added by the GVs to propagating waves, resulting in strong image artifacts from linear scatterers downstream of GV inclusions. To address this issue, we present an imaging paradigm, cross-amplitude modulation (xAM), which relies on cross-propagating plane-wave transmissions of finite aperture X waves to achieve quasi-artifact-free in vivo imaging of GVs. The xAM method derives from counterpropagating wave interaction theory, which predicts that, in media exhibiting quadratic elastic nonlinearity like biological tissue, the nonlinear interaction of counterpropagating acoustic waves is inefficient. By transmitting cross-propagating plane waves, we minimize cumulative nonlinear interaction effects due to collinear wave propagation while generating a transient wave-amplitude modulation at the two plane waves’ intersection. In both simulations and experiments, we show that residual xAM nonlinearity due to wave propagation decreases as the plane-wave cross-propagation angle increases. We demonstrate in tissue-mimicking phantoms that imaging artifacts distal to GV inclusions decrease as the plane-wave cross-propagation angle opens, nearing complete extinction at angles above 16.5 degrees. Finally, we demonstrate that xAM enables highly specific in vivo imaging of GVs located in the gastrointestinal tract, a target of prime interest for future cellular imaging. These results advance the physical facet of the emerging field of biomolecular ultrasound and are also relevant to synthetic ultrasound contrast agents.

Ultrahigh-field (UHF) magnetic resonance imaging (MRI) systems are getting a lot of attention as they ensure high intrinsic signal-to-noise ratio resulting in higher spatial and temporal resolutions as well as better contrast. This promises improved clinical results with regard to morphological as well as functional and metabolic capabilities. Traditionally, MRI relies on volume coils (birdcage) able to deliver a homogeneous radio frequency field exciting the nuclei magnetic spin. However, this strategy is hindered at UHF because of the rf field inhomogeneities yielded by the increased Larmor frequency. A standard approach consists of inserting passive dielectric elements within the volume coil in order to locally enhance the rf field and mitigate these inhomogeneities. However, the lack of control over their electromagnetic properties prevents the development of optimal solutions. Here, a single meta-atom is used to achieve efficient and tunable rf field control in UHF MRI. We demonstrate theoretically and experimentally a full overlap between the electric dipolar and magnetic dipolar resonances of the meta-atom. This interaction is precisely tuned to reach the so-called Kerker scattering conditions when illuminated in the near field by a birdcage coil. At these conditions, a strong enhancement or suppression of the rf field is achieved in the vicinity of the meta-atom within the MRI volume coil.

While Hermiticity lies at the heart of quantum mechanics, recent experimental advances in controlling dissipation have brought about unprecedented flexibility in engineering non-Hermitian Hamiltonians in open classical and quantum systems. Examples include parity-time-symmetric optical systems with gain and loss, dissipative Bose-Einstein condensates, exciton-polariton systems, and biological networks. A particular interest centers on the topological properties of non-Hermitian systems, which exhibit unique phases with no Hermitian counterparts. However, no systematic understanding in analogy with the periodic table of topological insulators and superconductors has been achieved. In this paper, we develop a coherent framework of topological phases of non-Hermitian systems. After elucidating the physical meaning and the mathematical definition of non-Hermitian topological phases, we start with one-dimensional lattices, which exhibit topological phases with no Hermitian counterparts and are found to be characterized by an integer topological winding number even with no symmetry constraint, reminiscent of the quantum-Hall insulator in Hermitian systems. A system with a nonzero winding number, which is experimentally measurable from the wave-packet dynamics, is shown to be robust against disorder, a phenomenon observed in the Hatano-Nelson model with asymmetric hopping amplitudes. We also unveil a novel bulk-edge correspondence that features an infinite number of (quasi)edge modes. We then apply the $K$ theory to systematically classify all the non-Hermitian topological phases in the Altland-Zirnbauer (AZ) classes in all dimensions. The obtained periodic table unifies time-reversal and particle-hole symmetries, leading to highly nontrivial predictions such as the absence of non-Hermitian topological phases in two dimensions. We provide concrete examples for all the nontrivial non-Hermitian AZ classes in zero and one dimensions. In particular, we identify a ${\mathbb{Z}}_2$ topological index for arbitrary quantum channels (completely positive trace-preserving maps). Our work lays the cornerstone for a unified understanding of the role of topology in non-Hermitian systems.