Rayleigh’s criterion for resolving two incoherent point sources has been the most influential measure of optical imaging resolution for over a century. In the context of statistical image processing, violation of the criterion is especially detrimental to the estimation of the separation between the sources, and modern far-field superresolution techniques rely on suppressing the emission of close sources to enhance the localization precision. Using quantum optics, quantum metrology, and statistical analysis, here we show that, even if two close incoherent sources emit simultaneously, measurements with linear optics and photon counting can estimate their separation from the far field almost as precisely as conventional methods do for isolated sources, rendering Rayleigh’s criterion irrelevant to the problem. Our results demonstrate that superresolution can be achieved not only for fluorophores but also for stars.

We report a combined experimental and theoretical study of the candidate type-II Weyl semimetal ${\mathrm{MoTe}}_2$. Using laser-based angle-resolved photoemission, we resolve multiple distinct Fermi arcs on the inequivalent top and bottom (001) surfaces. All surface states observed experimentally are reproduced by an electronic structure calculation for the experimental crystal structure that predicts a topological Weyl semimetal state with eight type-II Weyl points. We further use systematic electronic structure calculations simulating different Weyl point arrangements to discuss the robustness of the identified Weyl semimetal state and the topological character of Fermi arcs in ${\mathrm{MoTe}}_2$.

Within a dense environment ($\rho \approx {10}^{14}\mathrm{atoms}/{\mathrm{cm}}^3$) at ultracold temperatures ($T<1\mu \mathrm{K}$), a single atom excited to a Rydberg state acts as a reaction center for surrounding neutral atoms. At these temperatures, almost all neutral atoms within the Rydberg orbit are bound to the Rydberg core and interact with the Rydberg atom. We have studied the reaction rate and products for $nS$ ${}^{87}\mathrm{Rb}$ Rydberg states, and we mainly observe a state change of the Rydberg electron to a high orbital angular momentum $l$, with the released energy being converted into kinetic energy of the Rydberg atom. Unexpectedly, the measurements show a threshold behavior at $n\approx 100$ for the inelastic collision time leading to increased lifetimes of the Rydberg state independent of the densities investigated. Even at very high densities ($\rho \approx 4.8\times {10}^{14}{\mathrm{cm}}^{-3}$), the lifetime of a Rydberg atom exceeds $10\mu \mathrm{s}$ at $n>140$ compared to $1\mu \mathrm{s}$ at $n=90$. In addition, a second observed reaction mechanism, namely, ${\mathrm{Rb}}_2^{+}$ molecule formation, was studied. Both reaction products are equally probable for $n=40$, but the fraction of ${\mathrm{Rb}}_2^{+}$ created drops to below 10% for $n\ge 90$.

We present an experimental realization of resonance fluorescence in squeezed vacuum. We strongly couple microwave-frequency squeezed light to a superconducting artificial atom and detect the resulting fluorescence with high resolution enabled by a broadband traveling-wave parametric amplifier. We investigate the fluorescence spectra in the weak and strong driving regimes, observing up to 3.1 dB of reduction of the fluorescence linewidth below the ordinary vacuum level and a dramatic dependence of the Mollow triplet spectrum on the relative phase of the driving and squeezed vacuum fields. Our results are in excellent agreement with predictions for spectra produced by a two-level atom in squeezed vacuum [Phys. Rev. Lett. 58, 2539 (1987)], demonstrating that resonance fluorescence offers a resource-efficient means to characterize squeezing in cryogenic environments.

Complex electrical dynamics in excitable tissues occur throughout biology, but the roles of individual ion channels can be difficult to determine due to the complex nonlinear interactions in native tissue. Here, we ask whether we can engineer a tissue capable of basic information storage and processing, where all functional components are known and well understood. We develop a cell line with four transgenic components: two to enable collective propagation of electrical waves and two to enable optical perturbation and optical readout of membrane potential. We pattern the cell growth to define simple cellular ring oscillators that run stably for $>2\mathrm{h}$ ($\sim {10}^4\text{cycles}$) and that can store data encoded in the direction of electrical circulation. Using patterned optogenetic stimulation, we probe the biophysical attributes of this synthetic excitable tissue in detail, including dispersion relations, curvature-dependent wave front propagation, electrotonic coupling, and boundary effects. We then apply the biophysical characterization to develop an optically reconfigurable bioelectric oscillator. These results demonstrate the feasibility of engineering bioelectric tissues capable of complex information processing with optical input and output.

Microwave photons inside lattices of coupled resonators and superconducting qubits can exhibit surprising matterlike behavior. Realizing such open-system quantum simulators presents an experimental challenge and requires new tools and measurement techniques. Here, we introduce scanning defect microscopy as one such tool and illustrate its use in mapping the normal-mode structure of microwave photons inside a 49-site kagome lattice of coplanar waveguide resonators. Scanning is accomplished by moving a probe equipped with a sapphire tip across the lattice. This locally perturbs resonator frequencies and induces shifts of the lattice resonance frequencies, which we determine by measuring the transmission spectrum. From the magnitude of mode shifts, we can reconstruct photon field amplitudes at each lattice site and thus create spatial images of the photon-lattice normal modes.

The realization of a network of quantum registers is an outstanding challenge in quantum science and technology. We experimentally investigate a network node that consists of a single nitrogen-vacancy center electronic spin hyperfine coupled to nearby nuclear spins. We demonstrate individual control and readout of five nuclear spin qubits within one node. We then characterize the storage of quantum superpositions in individual nuclear spins under repeated application of a probabilistic optical internode entangling protocol. We find that the storage fidelity is limited by dephasing during the electronic spin reset after failed attempts. By encoding quantum states into a decoherence-protected subspace of two nuclear spins, we show that quantum coherence can be maintained for over 1000 repetitions of the remote entangling protocol. These results and insights pave the way towards remote entanglement purification and the realization of a quantum repeater using nitrogen-vacancy center quantum-network nodes.

We provide general sufficient conditions for the efficient classical simulation of quantum-optics experiments that involve inputting states to a quantum process and making measurements at the output. The first condition is based on the negativity of phase-space quasiprobability distributions (PQDs) of the output state of the process and the output measurements; the second one is based on the negativity of PQDs of the input states, the output measurements, and the transition function associated with the process. We show that these conditions provide useful practical tools for investigating the effects of imperfections in implementations of boson sampling. In particular, we apply our formalism to boson-sampling experiments that use single-photon or spontaneous-parametric-down-conversion sources and on-off photodetectors. Considering simple models for loss and noise, we show that above some threshold for the probability of random counts in the photodetectors, these boson-sampling experiments are classically simulatable. We identify mode mismatching as the major source of error contributing to random counts and suggest that this is the chief challenge for implementations of boson sampling of interesting size.

The magnetic surfaces of modern stellarators are characterized by complex, carefully optimized shaping and exhibit locally compressed regions of strong turbulence drive. Massively parallel computer simulations of plasma turbulence reveal, however, that stellarators also possess two intrinsic mechanisms to mitigate the effect of this drive. In the regime where the length scale of the turbulence is very small compared to the equilibrium scale set by the variation of the magnetic field, the strongest fluctuations form narrow bandlike structures on the magnetic surfaces. Thanks to this localization, the average transport through the surface is significantly smaller than that predicted at locations of peak turbulence. This feature results in a numerically observed upshift of the onset of turbulence on the surface towards higher ion temperature gradients as compared with the prediction from the most unstable regions. In a second regime lacking scale separation, the localization is lost and the fluctuations spread out on the magnetic surface. Nonetheless, stabilization persists through the suppression of the large eddies (relative to the equilibrium scale), leading to a reduced stiffness for the heat flux dependence on the ion temperature gradient. These fundamental differences with tokamak turbulence are exemplified for the QUASAR stellarator [G. H. Neilson et al., IEEE Trans. Plasma Sci. 42, 489 (2014)].

Coherent scattering of light from ultracold atoms involves an exchange of energy and momentum introducing a wealth of nonlinear dynamical phenomena. As a prominent example, particles can spontaneously form stationary periodic configurations that simultaneously maximize the light scattering and minimize the atomic potential energy in the emerging optical lattice. Such self-ordering effects resulting in periodic lattices via bimodal symmetry breaking have been experimentally observed with cold gases and Bose-Einstein condensates (BECs) inside an optical resonator. Here, we study a new regime of periodic pattern formation for an atomic BEC in free space, driven by far off-resonant counterpropagating and noninterfering lasers of orthogonal polarization. In contrast to previous works, no spatial light modes are preselected by any boundary conditions and the transition from homogeneous to periodic order amounts to a crystallization of both light and ultracold atoms breaking a continuous translational symmetry. In the crystallized state the BEC acquires a phase similar to a supersolid with an emergent intrinsic length scale whereas the light field forms an optical lattice allowing phononic excitations via collective backscattering, which are gapped due to the infinte-range interactions. The system we study constitutes a novel configuration allowing the simulation of synthetic solid-state systems with ultracold atoms including long-range phonon dynamics.

The use of optical clocks or oscillators in future ultraprecise navigation, gravitational sensing, coherent arrays, and relativity experiments will require time comparison and synchronization over terrestrial or satellite free-space links. Here, we demonstrate full unambiguous synchronization of two optical time scales across a free-space link. The time deviation between synchronized time scales is below 1 fs over durations from 0.1 to 6500 s, despite atmospheric turbulence and kilometer-scale path length variations. Over 2 days, the time wander is 40 fs peak to peak. Our approach relies on the two-way reciprocity of a single-spatial-mode optical link, valid to below 225 attoseconds across a turbulent 4-km path. This femtosecond level of time-frequency transfer should enable optical networks using state-of-the-art optical clocks or oscillators.

In cavity optomechanics, radiation pressure and photothermal forces are widely utilized to cool and control micromechanical motion, with applications ranging from precision sensing and quantum information to fundamental science. Here, we realize an alternative approach to optical forcing based on superfluid flow and evaporation in response to optical heating. We demonstrate optical forcing of the motion of a cryogenic microtoroidal resonator at a level of 1.46 nN, roughly 1 order of magnitude larger than the radiation pressure force. We use this force to feedback cool the motion of a microtoroid mechanical mode to 137 mK. The photoconvective forces we demonstrate here provide a new tool for high bandwidth control of mechanical motion in cryogenic conditions, while the ability to apply forces remotely, combined with the persistence of flow in superfluids, offers the prospect for new applications.

Quantifying the similarity between symbolic sequences is a traditional problem in information theory which requires comparing the frequencies of symbols in different sequences. In numerous modern applications, ranging from DNA over music to texts, the distribution of symbol frequencies is characterized by heavy-tailed distributions (e.g., Zipf’s law). The large number of low-frequency symbols in these distributions poses major difficulties to the estimation of the similarity between sequences; e.g., they hinder an accurate finite-size estimation of entropies. Here, we show analytically how the systematic (bias) and statistical (fluctuations) errors in these estimations depend on the sample size $N$ and on the exponent $\gamma$ of the heavy-tailed distribution. Our results are valid for the Shannon entropy ($\alpha =1$), its corresponding similarity measures (e.g., the Jensen-Shanon divergence), and also for measures based on the generalized entropy of order $\alpha$. For small $\alpha$’s, including $\alpha =1$, the errors decay slower than the $1/N$ decay observed in short-tailed distributions. For $\alpha$ larger than a critical value ${\alpha }^{*}=1+1/\gamma \le 2$, the $1/N$ decay is recovered. We show the practical significance of our results by quantifying the evolution of the English language over the last two centuries using a complete $\alpha$ spectrum of measures. We find that frequent words change more slowly than less frequent words and that $\alpha =2$ provides the most robust measure to quantify language change.

In force sensing, optomechanics, and quantum motion experiments, it is typically advantageous to create lightweight, compliant mechanical elements with the lowest possible force noise. Here, we report the fabrication and characterization of high-aspect-ratio, nanogram-scale ${\mathrm{Si}}_3{\mathrm{N}}_4$ “trampolines” having quality factors above $4\times {10}^7$ and ringdown times exceeding 5 min (mHz linewidth). These devices exhibit thermally limited force noise sensitivities below $20\mathrm{aN}/{\mathrm{Hz}}^{1/2}$ at room temperature, which is the lowest among solid-state mechanical sensors. We also characterize the suitability of these devices for high-finesse cavity readout and optomechanics applications, finding no evidence of surface or bulk optical losses from the processed nitride in a cavity achieving finesse 40,000. These parameters provide access to a single-photon cooperativity $C_0\sim 8$ in the resolved-sideband limit, wherein a variety of outstanding optomechanics goals become feasible.

Quantum fluctuations of the gravitational field in the early Universe, amplified by inflation, produce a primordial gravitational-wave background across a broad frequency band. We derive constraints on the spectrum of this gravitational radiation, and hence on theories of the early Universe, by combining experiments that cover 29 orders of magnitude in frequency. These include Planck observations of cosmic microwave background temperature and polarization power spectra and lensing, together with baryon acoustic oscillations and big bang nucleosynthesis measurements, as well as new pulsar timing array and ground-based interferometer limits. While individual experiments constrain the gravitational-wave energy density in specific frequency bands, the combination of experiments allows us to constrain cosmological parameters, including the inflationary spectral index $n_t$ and the tensor-to-scalar ratio $r$. Results from individual experiments include the most stringent nanohertz limit of the primordial background to date from the Parkes Pulsar Timing Array, ${\mathrm{\Omega }}_{\mathrm{GW}}(f)<2.3\times {10}^{-10}$. Observations of the cosmic microwave background alone limit the gravitational-wave spectral index at 95% confidence to $n_t\lesssim 5$ for a tensor-to-scalar ratio of $r=0.11$. However, the combination of all the above experiments limits $n_t<0.36$. Future Advanced LIGO observations are expected to further constrain $n_t<0.34$ by 2020. When cosmic microwave background experiments detect a nonzero $r$, our results will imply even more stringent constraints on $n_t$ and, hence, theories of the early Universe.

The quantized lateral motional states and the spin states of electrons trapped on the surface of superfluid helium have been proposed as basic building blocks of a scalable quantum computer. Circuit quantum electrodynamics allows strong dipole coupling between electrons and a high-$Q$ superconducting microwave resonator, enabling such sensitive detection and manipulation of electron degrees of freedom. Here, we present the first realization of a hybrid circuit in which a large number of electrons are trapped on the surface of superfluid helium inside a coplanar waveguide resonator. The high finesse of the resonator allows us to observe large dispersive shifts that are many times the linewidth and make fast and sensitive measurements on the collective vibrational modes of the electron ensemble, as well as the superfluid helium film underneath. Furthermore, a large ensemble coupling is observed in the dispersive regime during experiment, and it shows excellent agreement with our numeric model. The coupling strength of the ensemble to the cavity is found to be $\approx 1\mathrm{MHz}$ per electron, indicating the feasibility of achieving single electron strong coupling.

Progress of silicon-based technology is nearing its physical limit, as the minimum feature size of components is reaching a mere 10 nm. The resistive switching behavior of transition metal oxides and the associated memristor device is emerging as a competitive technology for next-generation electronics. Significant progress has already been made in the past decade, and devices are beginning to hit the market; however, this progress has mainly been the result of empirical trial and error. Hence, gaining theoretical insight is of the essence. In the present work, we report the striking result of a connection between the resistive switching and shock-wave formation, a classic topic of nonlinear dynamics. We argue that the profile of oxygen vacancies that migrate during the commutation forms a shock wave that propagates through a highly resistive region of the device. We validate the scenario by means of model simulations and experiments in a manganese-oxide-based memristor device, and we extend our theory to the case of binary oxides. The shock-wave scenario brings unprecedented physical insight and enables us to rationalize the process of oxygen-vacancy-driven resistive change with direct implications for a key technological aspect—the commutation speed.

In ${\mathrm{ABO}}_3$ perovskites, oxygen octahedron rotations are common structural distortions that can promote large ferroelectricity in ${\text{BiFeO}}_3$ with an $R3c$ structure [1] but suppress ferroelectricity in ${\text{CaTiO}}_3$ with a $Pbnm$ symmetry [2]. For many ${\text{CaTiO}}_3$-like perovskites, the ${\text{BiFeO}}_3$ structure is a metastable phase. Here, we report the stabilization of the highly polar ${\text{BiFeO}}_3$-like phase of ${\text{CaTiO}}_3$ in a ${\text{BaTiO}}_3/{\text{CaTiO}}_3$ superlattice grown on a ${\text{SrTiO}}_3$ substrate. The stabilization is realized by a reconstruction of oxygen octahedron rotations at the interface from the pattern of nonpolar bulk ${\text{CaTiO}}_3$ to a different pattern that is characteristic of a ${\text{BiFeO}}_3$ phase. The reconstruction is interpreted through a combination of amplitude-contrast sub-0.1-nm high-resolution transmission electron microscopy and first-principles theories of the structure, energetics, and polarization of the superlattice and its constituents. We further predict a number of new artificial ferroelectric materials demonstrating that nonpolar perovskites can be turned into ferroelectrics via this interface mechanism. Therefore, a large number of perovskites with the ${\text{CaTiO}}_3$ structure type, which include many magnetic representatives, are now good candidates as novel highly polar multiferroic materials [3].

The semiconductor polariton laser promises a new source of coherent light, which, compared to conventional semiconductor photon lasers, has input-energy threshold orders of magnitude lower. However, intensity stability, a defining feature of a coherent state, has remained poor. Intensity noise many times the shot noise of a coherent state has persisted, attributed to multiple mechanisms that are difficult to separate in conventional polariton systems. The large intensity noise, in turn, limits the phase coherence. Thus, the capability of the polariton laser as a source of coherence light is limited. Here, we demonstrate a polariton laser with shot-noise-limited intensity stability, as expected from a fully coherent state. This stability is achieved by using an optical cavity with high mode selectivity to enforce single-mode lasing, suppress condensate depletion, and establish gain saturation. Moreover, the absence of spurious intensity fluctuations enables the measurement of a transition from exponential to Gaussian decay of the phase coherence of the polariton laser. It suggests large self-interaction energies in the polariton condensate, exceeding the laser bandwidth. Such strong interactions are unique to matter-wave lasers and important for nonlinear polariton devices. The results will guide future development of polariton lasers and nonlinear polariton devices.

Today’s narrowest linewidth lasers are limited by mirror motion in the reference optical resonator used to stabilize the laser’s frequency. Recent proposals suggest that superradiant lasers based on narrow dipole-forbidden transitions in cold alkaline earth atoms could offer a way around this limitation. Such lasers operating on transitions with linewidth of order mHz are predicted to achieve output spectra orders of magnitude narrower than any currently existing laser. As a step towards this goal, we demonstrate and study a laser based on the 7.5-kHz linewidth dipole-forbidden ${}^3{P}_1$ to ${}^1{S}_0$ transition in laser-cooled and tightly confined ${}^{88}\mathrm{Sr}$. We can operate this laser in the bad-cavity or superradiant regime, where coherence is primarily stored in the atoms, or continuously tune to the more conventional good-cavity regime, where coherence is primarily stored in the light field. We show that the cold-atom gain medium can be repumped to achieve quasi-steady-state lasing. We also demonstrate up to an order of magnitude suppression in the sensitivity of laser frequency to changes in cavity length, verifying a key feature of the proposed narrow linewidth lasers.