Reservoir computing, originally referred to as an echo state network or a liquid state machine, is a brain-inspired paradigm for processing temporal information. It involves learning a “read-out” interpretation for nonlinear transients developed by high-dimensional dynamics when the latter is excited by the information signal to be processed. This novel computational paradigm is derived from recurrent neural network and machine learning techniques. It has recently been implemented in photonic hardware for a dynamical system, which opens the path to ultrafast brain-inspired computing. We report on a novel implementation involving an electro-optic phase-delay dynamics designed with off-the-shelf optoelectronic telecom devices, thus providing the targeted wide bandwidth. Computational efficiency is demonstrated experimentally with speech-recognition tasks. State-of-the-art speed performances reach one million words per second, with very low word error rate. Additionally, to record speed processing, our investigations have revealed computing-efficiency improvements through yet-unexplored temporal-information-processing techniques, such as simultaneous multisample injection and pitched sampling at the read-out compared to information “write-in”.

Circulators are nonreciprocal circuit elements that are integral to technologies including radar systems, microwave communication transceivers, and the readout of quantum information devices. Their nonreciprocity arises from the interference of microwaves over the centimeter scale of the signal wavelength, in the presence of bulky magnetic media that breaks time-reversal symmetry. Here, we realize a completely passive on-chip microwave circulator with size $1/1000\mathrm{th}$ the wavelength by exploiting the chiral, “slow-light” response of a two-dimensional electron gas in the quantum Hall regime. For an integrated GaAs device with $330\mu \mathrm{m}$ diameter and about 1-GHz center frequency, a nonreciprocity of 25 dB is observed over a 50-MHz bandwidth. Furthermore, the nonreciprocity can be dynamically tuned by varying the voltage at the port, an aspect that may enable reconfigurable passive routing of microwave signals on chip.

Understanding the general principles underlying strongly interacting quantum states out of equilibrium is one of the most important tasks of current theoretical physics. With experiments accessing the intricate dynamics of many-body quantum systems, it is paramount to develop powerful methods that encode the emergent physics. Up to now, the strong dichotomy observed between integrable and nonintegrable evolutions made an overarching theory difficult to build, especially for transport phenomena where space-time profiles are drastically different. We present a novel framework for studying transport in integrable systems: hydrodynamics with infinitely many conservation laws. This bridges the conceptual gap between integrable and nonintegrable quantum dynamics, and gives powerful tools for accurate studies of space-time profiles. We apply it to the description of energy transport between heat baths, and provide a full description of the current-carrying nonequilibrium steady state and the transition regions in a family of models including the Lieb-Liniger model of interacting Bose gases, realized in experiments.

Experimental and theoretical studies are reported, for the first time, on the observation and characterization of echo phenomena in oscillatory chemical reactions. Populations of uncoupled and coupled oscillators are globally perturbed. The macroscopic response to this perturbation dies out with time: At some time $\tau$ after the perturbation (where $\tau$ is long enough that the response has died out), the system is again perturbed, and the initial response to this second perturbation again dies out. Echoes can potentially appear as responses that arise at $2\tau ,3\tau ,\mathrm{...}$ after the first perturbation. The phase-resetting character of the chemical oscillators allows a detailed analysis, offering insights into the origin of the echo in terms of an intricate structure of phase relationships. Groups of oscillators experiencing different perturbations are analyzed with a geometric approach and in an analytical theory. The characterization of echo phenomena in populations of chemical oscillators reinforces recent theoretical studies of the behavior in populations of phase oscillators [E. Ott et al., Chaos 18, 037115 (2008)]. This indicates the generality of the behavior, including its likely occurrence in biological systems.

One major change of the future revision of the International System of Units is a new definition of the ampere based on the elementary charge $e$. Replacing the former definition based on Ampère’s force law will allow one to fully benefit from quantum physics to realize the ampere. However, a quantum realization of the ampere from $e$, accurate to within ${10}^{-8}$ in relative value and fulfilling traceability needs, is still missing despite the many efforts made for the development of single-electron tunneling devices. Starting again with Ohm’s law, applied here in a quantum circuit combining the quantum Hall resistance and Josephson voltage standards with a superconducting cryogenic amplifier, we report on a practical and universal programmable quantum current generator. We demonstrate that currents generated in the milliampere range are accurately quantized in terms of $e{f}_{\mathrm{J}}$ ($f_{\mathrm{J}}$ is the Josephson frequency) with measurement uncertainty of ${10}^{-8}$. This new quantum current source, which is able to deliver such accurate currents down to the microampere range, can greatly improve the current measurement traceability, as demonstrated with the calibrations of digital ammeters. In addition, it opens the way to further developments in metrology and in fundamental physics, such as a quantum multimeter or new accurate comparisons to single-electron pumps.

One of the most important problems in development is how epigenetic domains can first be established, and then maintained, within cells. To address this question, we propose a framework that couples three-dimensional chromatin folding dynamics to a “recoloring” process modeling the writing of epigenetic marks. Because many intrachromatin interactions are mediated by bridging proteins, we consider a “two-state” model with self-attractive interactions between two epigenetic marks that are alike (either active or inactive). This model displays a first-order-like transition between a swollen, epigenetically disordered phase and a compact, epigenetically coherent chromatin globule. If the self-attraction strength exceeds a threshold, the chromatin dynamics becomes glassy, and the corresponding interaction network freezes. By modifying the epigenetic read-write process according to more biologically inspired assumptions, our polymer model with recoloring recapitulates the ultrasensitive response of epigenetic switches to perturbations and accounts for long-lived multidomain conformations, strikingly similar to the topologically associating domains observed in eukaryotic chromosomes.

In contrast to classical empty space, the quantum vacuum fundamentally alters the properties of embedded particles. This paradigm shift allows one to explain the discovery of the celebrated Lamb shift in the spectrum of the hydrogen atom. Here, we engineer a synthetic vacuum, building on the unique properties of ultracold atomic gas mixtures, offering the ability to switch between empty space and quantum vacuum. Using high-precision spectroscopy, we observe the phononic Lamb shift, an intriguing many-body effect originally conjectured in the context of solid-state physics. We find good agreement with theoretical predictions based on the Fröhlich model. Our observations establish this experimental platform as a new tool for precision benchmarking of open theoretical challenges, especially in the regime of strong coupling between the particles and the quantum vacuum.

In a joint experimental and theoretical effort, we report on the formation of a macrodroplet state in an ultracold bosonic gas of erbium atoms with strong dipolar interactions. By precise tuning of the $s$-wave scattering length below the so-called dipolar length, we observe a smooth crossover of the ground state from a dilute Bose-Einstein condensate to a dense macrodroplet state of more than $2\times {10}^4\mathrm{atoms}$. Based on the study of collective excitations and loss features, we prove that quantum fluctuations stabilize the ultracold gas far beyond the instability threshold imposed by mean-field interactions. Finally, we perform expansion measurements, showing that although self-bound solutions are prevented by losses, the interplay between quantum stabilization and losses results in a minimal time-of-flight expansion velocity at a finite scattering length.

Thermal conductivity in dielectric crystals is the result of the relaxation of lattice vibrations described by the phonon Boltzmann transport equation. Remarkably, an exact microscopic definition of the heat carriers and their relaxation times is still missing: Phonons, typically regarded as the relevant excitations for thermal transport, cannot be identified as the heat carriers when most scattering events conserve momentum and do not dissipate heat flux. This is the case for two-dimensional or layered materials at room temperature, or three-dimensional crystals at cryogenic temperatures. In this work, we show that the eigenvectors of the scattering matrix in the Boltzmann equation define collective phonon excitations, which are termed here “relaxons”. These excitations have well-defined relaxation times, directly related to heat-flux dissipation, and they provide an exact description of thermal transport as a kinetic theory of the relaxon gas. We show why Matthiessen’s rule is violated, and we construct a procedure for obtaining the mean free paths and relaxation times of the relaxons. These considerations are general and would also apply to other semiclassical transport models, such as the electronic Boltzmann equation. For heat transport, they remain relevant even in conventional crystals like silicon, but they are of the utmost importance in the case of two-dimensional materials, where they can revise, by several orders of magnitude, the relevant time and length scales for thermal transport in the hydrodynamic regime.

The composition of a genome with respect to all possible short DNA motifs impacts the ability of DNA binding proteins to locate and bind their target sites. Since nonfunctional DNA binding can be detrimental to cellular functions and ultimately to organismal fitness, organisms could benefit from reducing the number of nonfunctional DNA binding sites genome wide. Using in vitro measurements of binding affinities for a large collection of DNA binding proteins, in multiple species, we detect a significant global avoidance of weak binding sites in genomes. We demonstrate that the underlying evolutionary process leaves a distinct genomic hallmark in that similar words have correlated frequencies, a signal that we detect in all species across domains of life. We consider the possibility that natural selection against weak binding sites contributes to this process, and using an evolutionary model we show that the strength of selection needed to maintain global word compositions is on the order of point mutation rates. Likewise, we show that evolutionary mechanisms based on interference of protein-DNA binding with replication and mutational repair processes could yield similar results and operate with similar rates. On the basis of these modeling and bioinformatic results, we conclude that genome-wide word compositions have been molded by DNA binding proteins acting through tiny evolutionary steps over time scales spanning millions of generations.

Herbertsmithite, ${\mathrm{ZnCu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$, is a two-dimensional kagome lattice realization of a spin liquid, with evidence for fractionalized excitations and a gapped ground state. Such a quantum spin liquid has been proposed to underlie high-temperature superconductivity and is predicted to produce a wealth of new states, including a Dirac metal at $1/3$ electron doping. Here, we report the topochemical synthesis of electron-doped ${\mathrm{ZnLi}}_x{\mathrm{Cu}}_3(\mathrm{OH}{)}_6{\mathrm{Cl}}_2$ from $x=0$ to $x=1.8$ ($3/5$ per ${\mathrm{Cu}}^{2+}$). Contrary to expectations, no metallicity or superconductivity is induced. Instead, we find a systematic suppression of magnetic behavior across the phase diagram. Our results demonstrate that significant theoretical work is needed to understand and predict the role of doping in magnetically frustrated narrow band insulators, particularly the interplay between local structural disorder and tendency toward electron localization, and pave the way for future studies of doped spin liquids.

Ultracold atoms, produced by laser cooling and trapping, have led to recent advances in quantum information, quantum chemistry, and quantum sensors. A lack of ultraviolet narrow-band lasers precludes laser cooling of prevalent atoms such as hydrogen, carbon, oxygen, and nitrogen. Broadband pulsed lasers can produce high power in the ultraviolet, and we demonstrate that the entire spectrum of an optical frequency comb can cool atoms when used to drive a narrow two-photon transition. This multiphoton optical force is also used to make a magneto-optical trap. These techniques may provide a route to ultracold samples of nature’s most abundant building blocks for studies of pure-state chemistry and precision measurement.

The art of imparting information onto a light wave by optical signal modulation is fundamental to all forms of optical communication. Among many schemes, direct modulation of laser diodes stands out as a simple, robust, and cost-effective method. However, the simultaneous changes in intensity, frequency, and phase have prevented its application in the field of secure quantum communication. Here, we propose and experimentally demonstrate a directly phase-modulated light source which overcomes the main disadvantages associated with direct modulation and is suitable for diverse applications such as coherent communications and quantum cryptography. The source separates the tasks of phase preparation and pulse generation between a pair of semiconductor lasers leading to very pure phase states. Moreover, the cavity-enhanced electro-optic effect enables the first example of subvolt half-wave phase modulation at high signal rates. The source is compact, stable, and versatile, and we show its potential to become the standard transmitter for future quantum communication networks based on attenuated laser pulses.

We present the first experimental evidence, supported by theory and simulation, of spatiotemporal optical vortices (STOVs). A STOV is an optical vortex with phase and energy circulation in a spatiotemporal plane. Depending on the sign of the material dispersion, the local electromagnetic energy flow is saddle or spiral about the STOV. STOVs are a fundamental element of the nonlinear collapse and subsequent propagation of short optical pulses in material media, and conserve topological charge, constraining their birth, evolution, and annihilation. We measure a self-generated STOV consisting of a ring-shaped null in the electromagnetic field about which the phase is spiral, forming a dynamic torus that is concentric with and tracks the propagating pulse. Our results, here obtained for optical pulse collapse and filamentation in air, are generalizable to a broad class of nonlinearly propagating waves.

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.