We present a joint theoretical and experimental analysis of thermorefractive noise in high-quality-factor ($Q$), small-mode-volume ($V$) optical microcavities. Analogous to well-studied stability limits imposed by Brownian motion in macroscopic Fabry-Perot resonators, we show that microcavity thermorefractive noise gives rise to a mode-volume-dependent maximum effective quality factor. State-of-the-art fabricated microcavities are found to be within one order of magnitude of this bound. By measuring the first thermodynamically limited frequency noise spectra of wavelength-scale high-$Q/V$ silicon photonic crystal cavities, we confirm the assumptions of our theory, demonstrate a broadband sub-$\mu \mathrm{K}/\sqrt{\mathrm{Hz}}$ temperature sensitivity, and unveil a new technique for discerning subwavelength changes in microcavity mode volumes. To illustrate the immediate implications of these results, we show that thermorefractive noise limits the optimal performance of recently proposed room-temperature, all-optical qubits using cavity-enhanced bulk material nonlinearities. Looking forward, we propose and analyze coherent thermo-optic noise cancellation as one potential avenue toward violating these bounds, thereby enabling continued development in quantum optical measurement, precision sensing, and low-noise integrated photonics.

We present an ab initio correlated approach to study molecules that interact strongly with quantum fields in an optical cavity. Quantum electrodynamics coupled cluster theory provides a nonperturbative description of cavity-induced effects in ground and excited states. Using this theory, we show how quantum fields can be used to manipulate charge transfer and photochemical properties of molecules. We propose a strategy to lift electronic degeneracies and induce modifications in the ground-state potential energy surface close to a conical intersection.

In recent years, social media has become an important platform for political discourse, being a site of both political conversations between voters and political advertisements from campaigns. While their individual influences on public discourse are well documented, the interplay between individual-level cognitive biases, social influence processes, dueling campaign efforts, and social media platforms remains unexamined. We introduce an agent-based model that integrates these dynamics and illustrates how their combination can lead to the formation of echo chambers. We find that the range of political viewpoints that individuals are willing to consider is a key determinant in the formation of polarized networks and the emergence of echo chambers and show that aggressive political campaigns can have counterproductive outcomes by radicalizing supporters and alienating moderates. Our model results demonstrate how certain elements of public discourse and political polarization can be understood as the result of an interactive process of shifting individual opinions, evolving social networks, and political campaigns. We also introduce a dynamic empirical case, retweet networks from the final stage of the 2016 U.S. presidential election, to show how our proposed model can be calibrated with real-world behavior.

An ultimate goal of quantum computing is to perform calculations beyond the reach of any classical computer. It is therefore imperative that useful quantum computers be very difficult to simulate classically, otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably exponentially difficult to simulate: the classical resources required grow exponentially with the number of qubits $N$ or the depth $D$ of the circuit. This difficulty has triggered recent experiments on deep, random circuits that aim to demonstrate that quantum devices may already perform tasks beyond the reach of classical computing. These real quantum computing devices, however, suffer from many sources of decoherence and imprecision which limit the degree of entanglement that can actually be reached to a fraction of its theoretical maximum. They are characterized by an exponentially decaying fidelity $\mathcal{F}\sim (1-\epsilon {)}^{ND}$ with an error rate $\epsilon$ per operation as small as $\approx 1\%$ for current devices with several dozen qubits or even smaller for smaller devices. In this work, we provide new insight on the computing capabilities of real quantum computers by demonstrating that they can be simulated at a tiny fraction of the cost that would be needed for a perfect quantum computer. Our algorithms compress the representations of quantum wave functions using matrix product states, which are able to capture states with low to moderate entanglement very accurately. This compression introduces a finite error rate $\epsilon$ so that the algorithms closely mimic the behavior of real quantum computing devices. The computing time of our algorithm increases only linearly with $N$ and $D$ in sharp contrast with exact simulation algorithms. We illustrate our algorithms with simulations of random circuits for qubits connected in both one- and two-dimensional lattices. We find that $\epsilon$ can be decreased at a polynomial cost in computing power down to a minimum error ${\epsilon }_{\infty }$. Getting below ${\epsilon }_{\infty }$ requires computing resources that increase exponentially with ${\epsilon }_{\infty }/\epsilon$. For a two-dimensional array of $N=54$ qubits and a circuit with control-$Z$ gates, error rates better than state-of-the-art devices can be obtained on a laptop in a few hours. For more complex gates such as a swap gate followed by a controlled rotation, the error rate increases by a factor 3 for similar computing time. Our results suggest that, despite the high fidelity reached by quantum devices, only a tiny fraction $(\sim {10}^{-8})$ of the system Hilbert space is actually being exploited.

We present modeling of the COVID-19 epidemic in Illinois, USA, capturing the implementation of a stay-at-home order and scenarios for its eventual release. We use a non-Markovian age-of-infection model that is capable of handling long and variable time delays without changing its model topology. Bayesian estimation of model parameters is carried out using Markov chain Monte Carlo methods. This framework allows us to treat all available input information, including both the previously published parameters of the epidemic and available local data, in a uniform manner. To accurately model deaths as well as demand on the healthcare system, we calibrate our predictions to total and in-hospital deaths as well as hospital and ICU bed occupancy by COVID-19 patients. We apply this model not only to the state as a whole but also its subregions in order to account for the wide disparities in population size and density. Without prior information on nonpharmaceutical interventions, the model independently reproduces a mitigation trend closely matching mobility data reported by Google and Unacast. Forward predictions of the model provide robust estimates of the peak position and severity and also enable forecasting the regional-dependent results of releasing stay-at-home orders. The resulting highly constrained narrative of the epidemic is able to provide estimates of its unseen progression and inform scenarios for sustainable monitoring and control of the epidemic.

Understanding the behavior of an impurity strongly interacting with a Fermi sea is a long-standing challenge in many-body physics. When the interactions are short ranged, two vastly different ground states exist: a polaron quasiparticle and a molecule dressed by the majority atoms. In the single-impurity limit, it is predicted that at a critical interaction strength, a first-order transition occurs between these two states. Experiments, however, are always conducted in the finite temperature and impurity density regime. The fate of the polaron-to-molecule transition under these conditions, where the statistics of quantum impurities and thermal effects become relevant, is still unknown. Here, we address this question experimentally and theoretically. Our experiments are performed with a spin-imbalanced ultracold Fermi gas with tunable interactions. Utilizing a novel Raman spectroscopy combined with a high-sensitivity fluorescence detection technique, we isolate the quasiparticle contribution and extract the polaron energy, spectral weight, and the contact parameter. As the interaction strength is increased, we observe a continuous variation of all observables, in particular a smooth reduction of the quasiparticle weight as it goes to zero beyond the transition point. Our observation is in good agreement with a theoretical model where polaron and molecule quasiparticle states are thermally occupied according to their quantum statistics. At the experimental conditions, polaron states are hence populated even at interactions where the molecule is the ground state and vice versa. The emerging physical picture is thus that of a smooth transition between polarons and molecules and a coexistence of both in the region around the expected transition. Our findings establish Raman spectroscopy as a powerful experimental tool for probing the physics of mobile quantum impurities and shed new light on the competition between emerging fermionic and bosonic quasiparticles in non-Fermi-liquid phases.

Accurate and predictive computations of the quantum-mechanical behavior of many interacting electrons in realistic atomic environments are critical for the theoretical design of materials with desired properties, and they require solving the grand-challenge problem of the many-electron Schrödinger equation. An infinite chain of equispaced hydrogen atoms is perhaps the simplest realistic model for a bulk material, embodying several central themes of modern condensed-matter physics and chemistry while retaining a connection to the paradigmatic Hubbard model. Here, we report a combined application of cutting-edge computational methods to determine the properties of the hydrogen chain in its quantum-mechanical ground state. Varying the separation between the nuclei leads to a rich phase diagram, including a Mott phase with quasi-long-range antiferromagnetic order, electron density dimerization with power-law correlations, an insulator-to-metal transition, and an intricate set of intertwined magnetic orders.

We construct quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of rotational states of a rigid body. These codes, which protect against both drift in the body’s orientation and small changes in its angular momentum, may be well suited for robust storage and coherent processing of quantum information using rotational states of a polyatomic molecule. Extensions of such codes to rigid bodies with a symmetry axis are compatible with rotational states of diatomic molecules as well as nuclear states of molecules and atoms. We also describe codes associated with general non-Abelian groups and develop orthogonality relations for coset spaces, laying the groundwork for quantum information processing with exotic configuration spaces.

Degeneracies play a crucial rule in precise scientific measurements as well as in sensing applications. Spherical resonators have a high degree of degeneracy thanks to their highest symmetry; yet, fabricating perfect spheres is challenging because even a stem to hold the sphere breaks the symmetry. Here we fabricate a levitating spherical resonator that is evanescently coupled to a standard optical fiber. We characterize the resonators to exhibit an optical quality factor exceeding a billion, $10\mu \mathrm{m}$ radius, and sphericity to within less than 1 Å. Using our high quality and sphericity, we experimentally lift degeneracies of orders higher than 200, which we resolve with optical finesse exceeding 10 000 000. We then present our experimentally measured degenerate modes as well as their density of states next to our corresponding theoretical calculation. Our contactless photonic resonator is compatible with standard telecom fiber technology, exhibits the highest resonance enhancement as defined by (quality factor)/(mode volume), and the modes populating our cavity show the highest order of degeneracy reported in any system ever studied. This is in comparison with other settings that typically utilize the lowest-order twofold degeneracy.

In practically all branches of physics, different types of solitons, with a number of them enjoying topological protection, are found. Here we explore how one- and two-dimensional topological solitons formed by spatially localized continuous orientational patterns of optical axis in uniaxial birefringent media interact with light. These solitons, in the forms of one-dimensional twist walls and two-dimensional skyrmions, are controllably generated in thin films of cholesteric liquid crystals to introduce spatially localized patterns of effective refractive index. Laser light interacts with these solitons as quasiparticles or extended interfaces of different effective refractive indices seen by ordinary and extraordinary waves propagating within the liquid-crystal medium. Despite our system’s complex nature, our findings can be paralleled with the familiar phenomena of total reflection and refraction at interfaces of optically distinct media, albeit these behaviors arise in a medium with homogeneous density and chemical composition but with spatial variations of molecular and optical-axis orientations. By exploiting the facile response of liquid crystals to external stimuli, we show that the twist walls and skyrmions can be used to steer laser beams and to act as lenses and other optical elements, which can be reconfigured by low-voltage fields and other means. Analytical and numerical modeling, with the latter based on free-energy-minimizing configurations of the topological solitons, closely reproduce our experimental findings. The fundamental insights provided by this work potentially can be extended also to three-dimensional solitons, such as Hopfions, and may lead to technological applications of optical-axis topological solitons in telecommunications, nanophotonics, electro-optics, and so on.

We present a methodology to simulate the quantum thermodynamics of thermal machines which are built from an interacting working medium in contact with fermionic reservoirs at a fixed temperature and chemical potential. Our method works at a finite temperature, beyond linear response and weak system-reservoir coupling, and allows for nonquadratic interactions in the working medium. The method uses mesoscopic reservoirs, continuously damped toward thermal equilibrium, in order to represent continuum baths and a novel tensor-network algorithm to simulate the steady-state thermodynamics. Using the example of a quantum-dot heat engine, we demonstrate that our technique replicates the well-known Landauer-Büttiker theory for efficiency and power. We then go beyond the quadratic limit to demonstrate the capability of our method by simulating a three-site machine with nonquadratic interactions. Remarkably, we find that such interactions lead to power enhancement, without being detrimental to the efficiency. Furthermore, we demonstrate the capability of our method to tackle complex many-body systems by extracting the superdiffusive exponent for high-temperature transport in the isotropic Heisenberg model. Finally, we discuss transport in the gapless phase of the anisotropic Heisenberg model at a finite temperature and its connection to charge conjugation parity, going beyond the predictions of single-site boundary driving configurations.

Seeing and recognizing an object whose size is much smaller than the illumination wavelength is a challenging task for an observer placed in the far field, due to the diffraction limit. Recent advances in near- and far-field microscopy have offered several ways to overcome this limitation; however, they often use invasive markers and require intricate equipment with complicated image postprocessing. On the other hand, a simple marker-free solution for high-resolution imaging may be found by exploiting resonant metamaterial lenses that can convert the subwavelength image information contained in the near field of the object to propagating field components that can reach the far field. Unfortunately, resonant metalenses are inevitably sensitive to absorption losses, which has so far largely hindered their practical applications. Here, we solve this vexing problem and show that this limitation can be turned into an advantage when metalenses are combined with deep learning techniques. We demonstrate that combining deep learning with lossy metalenses allows recognizing and imaging largely subwavelength features directly from the far field. Our acoustic learning experiment shows that, despite being 30 times smaller than the wavelength of sound, the fine details of images can be successfully reconstructed and recognized in the far field, which is crucially favored by the presence of absorption. We envision applications in acoustic image analysis, feature detection, object classification, or as a novel noninvasive acoustic sensing tool in biomedical applications.

We theoretically study the few- and many-body dynamics of photons in chiral waveguides. In particular, we examine pulse propagation through an ensemble of $N$ two-level systems chirally coupled to a waveguide. We show that the system supports correlated multiphoton bound states, which have a well-defined photon number $n$ and propagate through the system with a group delay scaling as $1/n^2$. This has the interesting consequence that, during propagation, an incident coherent-state pulse breaks up into different bound-state components that can become spatially separated at the output in a sufficiently long system. For sufficiently many photons and sufficiently short systems, we show that linear combinations of $n$-body bound states recover the well-known phenomenon of mean-field solitons in self-induced transparency. Our work thus covers the entire spectrum from few-photon quantum propagation, to genuine quantum many-body (atom and photon) phenomena, and ultimately the quantum-to-classical transition. Finally, we demonstrate that the bound states can undergo elastic scattering with additional photons. Together, our results demonstrate that photon bound states are truly distinct physical objects emerging from the most elementary light-matter interaction between photons and two-level emitters. Our work opens the door to studying quantum many-body physics and soliton physics with photons in chiral waveguide QED.

In locally interacting quantum many-body systems, the velocity of information propagation is finitely bounded, and a linear light cone can be defined. Outside the light cone, the amount of information rapidly decays with distance. When systems have long-range interactions, it is highly nontrivial whether such a linear light cone exists. Herein, we consider generic long-range interacting systems with decaying interactions, such as $R^{-\alpha }$ with distance $R$. We prove the existence of the linear light cone for $\alpha >2D+1$ ($D$, the spatial dimension), where we obtain the Lieb-Robinson bound as $\parallel [O_i(t),O_j]\parallel \lesssim t^{2D+1}(R-\overline{v}t{)}^{-\alpha }$ with $\overline{v}=\mathcal{O}(1)$ for two arbitrary operators $O_i$ and $O_j$ separated by a distance $R$. Moreover, we provide an explicit quantum-state transfer protocol that achieves the above bound up to a constant coefficient and violates the linear light cone for $\alpha <2D+1$. In the regime of $\alpha >2D+1$, our result characterizes the best general constraints on the information spreading.

In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a linear light cone, which expands at an emergent velocity analogous to the speed of light. Local operations at sufficiently separated spacetime points approximately commute—given a many-body state $|\psi ⟩$, ${\mathcal{O}}_x(t){\mathcal{O}}_y|\psi ⟩\approx {\mathcal{O}}_y{\mathcal{O}}_x(t)|\psi ⟩$ with arbitrarily small errors—so long as $|x-y|\gtrsim vt$, where $v$ is finite. Yet, most nonrelativistic physical systems realized in nature have long-range interactions: Two degrees of freedom separated by a distance $r$ interact with potential energy $V(r)\propto 1/r^{\alpha }$. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: At the same $\alpha$, some quantum information processing tasks are constrained by a linear light cone, while others are not. In one spatial dimension, this linear light cone exists for every many-body state $|\psi ⟩$ when $\alpha >3$ (Lieb-Robinson light cone); for a typical state $|\psi ⟩$ chosen uniformly at random from the Hilbert space when $\alpha >\frac{5}{2}$ (Frobenius light cone); and for every state of a noninteracting system when $\alpha >2$ (free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones—and their tightness—also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that universal quantum state transfer, as well as many-body quantum chaos, is bounded by the Frobenius light cone and, therefore, is poorly constrained by all Lieb-Robinson bounds.

Active matter, composed of self-propelled entities, forms a wide class of out-of-equilibrium systems that display striking collective behaviors, among which, the so-called active turbulence where spatially and time-disordered flow patterns spontaneously arise in a variety of active systems. De facto, the active turbulence naming suggests a connection with a second seminal class of out-of-equilibrium systems, inertial turbulence, even though the latter is of very different nature with energy injected at global system scale rather than at the elementary scale of single constituents. Indeed, the existence of a possible strong tie between active and canonical turbulence remains an open question and a field of profuse research. Using an assembly of self-propelled interfacial particles, we show experimentally that the statistical properties of particles’ velocities display a turbulentlike behavior, as described by the celebrated 1941 phenomenology of Kolmogorov. Moreover, the analogy between the dynamics of the self-propelled particles and inertial turbulence is observed to hold consistently both in the Eulerian and Lagrangian frameworks. Unlike the swimmers’ velocities distribution, the subsurface fluid flow is found not turbulent, thus making Marangoni surfers’ assemblies different from other active systems generating turbulence, such as living matter. Identifying an active system in the universality class of inertial turbulence not only benefits its future development but may also provide new insights into the long-standing description of turbulent flows, arguably one of the biggest remaining mysteries in classical physics.

The efficient simulation of quantum systems is a primary motivating factor for developing controllable quantum machines. For addressing systems with underlying bosonic structure, it is advantageous to utilize a naturally bosonic platform. Optical photons passing through linear networks may be configured to perform quantum simulation tasks, but the efficient preparation and detection of multiphoton quantum states of light in linear optical systems are challenging. Here, we experimentally implement a boson sampling protocol for simulating molecular vibronic spectra [J. Huh et al., Nat. Photonics 9, 615 (2015)] in a two-mode superconducting device. In addition to enacting the requisite set of Gaussian operations across both modes, we fulfill the scalability requirement by demonstrating, for the first time in any platform, a high-fidelity single-shot photon number resolving detection scheme capable of resolving up to 15 photons per mode. Furthermore, we exercise the capability of synthesizing non-Gaussian input states to simulate spectra of molecular ensembles in vibrational excited states. We show the reprogrammability of our implementation by extracting the spectra of photoelectron processes in ${\mathrm{H}}_2\mathrm{O}$, ${\mathrm{O}}_3$, ${\mathrm{NO}}_2$, and ${\mathrm{SO}}_2$. The capabilities highlighted in this work establish the superconducting architecture as a promising platform for bosonic simulations, and by combining them with tools such as Kerr interactions and engineered dissipation, enable the simulation of a wider class of bosonic systems.

Using the deterministic, on-demand generation of two entangled phonons, we demonstrate a quantum eraser protocol in a phononic interferometer where the which-path information can be heralded during the interference process. Omitting the heralding step yields a clear interference pattern in the interfering half-quanta pathways; including the heralding step suppresses this pattern. If we erase the heralded information after the interference has been measured, the interference pattern is recovered, thereby implementing a delayed-choice quantum erasure. The test is implemented using a closed surface acoustic wave communication channel into which one superconducting qubit can emit itinerant phonons that the same or a second qubit can later recapture. If the first qubit releases only half of a phonon, the system follows a superposition of paths during the phonon propagation: either an itinerant phonon is in the channel or the first qubit remains in its excited state. These two paths are made to constructively or destructively interfere by changing the relative phase of the two intermediate states, resulting in a phase-dependent modulation of the first qubit’s final state, following interaction with the half-phonon. A heralding mechanism is added to this construct, entangling a heralding phonon with the signaling phonon. The first qubit emits a phonon herald conditioned on the qubit being in its excited state, with no signaling phonon, and the second qubit catches this heralding phonon, storing which-path information which can either be read out, destroying the signaling phonon’s self-interference, or erased.

Complex molecular structure demands customized solutions to laser cooling by extending its general set of principles and practices. Compared with other laser-cooled molecules, yttrium monoxide (YO) exhibits a large electron-nucleus interaction, resulting in a dominant hyperfine interaction over the electron spin-rotation coupling. The YO ground state is thus comprised of two manifolds of closely spaced states, with one of them possessing a negligible Landé $g$ factor. This unique energy level structure favors dual-frequency dc magneto-optical trapping (MOT) and gray molasses cooling (GMC). We report exceptionally robust cooling of YO at $4\mu \mathrm{K}$ over a wide range of laser intensity, detunings (one- and two-photon), and magnetic field. The magnetic insensitivity enables the spatial compression of the molecular cloud by alternating GMC and MOT under the continuous operation of the quadrupole magnetic field. A combination of these techniques produces a laser-cooled molecular sample with the highest phase space density in free space.

Periodic driving has emerged as a powerful tool in the quest to engineer new and exotic quantum phases. While driven many-body systems are generically expected to absorb energy indefinitely and reach an infinite-temperature state, the rate of heating can be exponentially suppressed when the drive frequency is large compared to the local energy scales of the system—leading to long-lived “prethermal” regimes. In this work, we experimentally study a bosonic cloud of ultracold atoms in a driven optical lattice and identify such a prethermal regime in the Bose-Hubbard model. By measuring the energy absorption of the cloud as the driving frequency is increased, we observe an exponential-in-frequency reduction of the heating rate persisting over more than 2 orders of magnitude. The tunability of the lattice potentials allows us to explore one- and two-dimensional systems in a range of different interacting regimes. Alongside the exponential decrease, the dependence of the heating rate on the frequency displays features characteristic of the phase diagram of the Bose-Hubbard model, whose understanding is additionally supported by numerical simulations in one dimension. Our results show experimental evidence of the phenomenon of Floquet prethermalization and provide insight into the characterization of heating for driven bosonic systems.