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.

We present a physically intuitive matrix approach for wave imaging and characterization in scattering media. The experimental proof of concept is performed with ultrasonic waves, but this approach can be applied to any field of wave physics for which multielement technology is available. The concept is that focused beam forming enables the synthesis, in transmit and receive, of an array of virtual transducers which map the entire medium to be imaged. The interelement responses of this virtual array form a focused reflection matrix from which spatial maps of various characteristics of the propagating wave can be retrieved. Here we demonstrate (i) a local focusing criterion that enables the image quality and the wave velocity to be evaluated everywhere inside the medium, including in random speckle, and (ii) a highly resolved spatial mapping of the prevalence of multiple scattering, which constitutes a new and unique contrast for ultrasonic imaging. The approach is demonstrated for a controllable phantom system and for in vivo imaging of the human abdomen. More generally, this matrix approach opens an original and powerful route for quantitative imaging in wave physics.

Complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in the dynamics of these networks, known as critical transitions, from data is important to avert disastrous consequences of major disruptions. Predicting such changes is a major challenge as it requires forecasting the behavior for parameter ranges for which no data on the system are available. We address this issue for networks with weak individual interactions and chaotic local dynamics. We do this by building a model network, termed an effective network, consisting of the underlying local dynamics and a statistical description of their interactions. We show that behavior of such networks can be decomposed in terms of an emergent deterministic component and a fluctuation term. Traditionally, such fluctuations are filtered out. However, as we show, they are key to accessing the interaction structure. We illustrate this approach on synthetic time series of realistic neuronal interaction networks of the cat cerebral cortex and on experimental multivariate data of optoelectronic oscillators. We reconstruct the community structure by analyzing the stochastic fluctuations generated by the network and predict critical transitions for coupling parameters outside the observed range.

While a clean, driven system generically absorbs energy until it reaches “infinite temperature,” it may do so very slowly exhibiting what is known as a prethermal regime. Here, we show that the emergence of an additional approximately conserved quantity in a periodically driven (Floquet) system can give rise to an analogous long-lived regime. This can allow for nontrivial dynamics, even from initial states that are at a high or infinite temperature with respect to an effective Hamiltonian governing the prethermal dynamics. We present concrete settings with such a prethermal regime, one with a period-doubled (time-crystalline) response. We also present a direct diagnostic to distinguish this prethermal phenomenon from its infinitely long-lived many-body localized cousin. We apply these insights to a model of the recent NMR experiments by Rovny et al. [Phys. Rev. Lett. 120, 180603 (2018)] which, intriguingly, detected signatures of a Floquet time crystal in a clean three-dimensional material. We show that a mild but subtle variation of their driving protocol can increase the lifetime of the time-crystalline signal by orders of magnitude.

A lattice random walk is a mathematical representation of movement through random steps on a lattice at discrete times. It is commonly referred to as Pólya’s walk when the steps occur in either of the nearest-neighbor sites. Since Smoluchowski’s 1906 derivation of the spatiotemporal dependence of the walk occupation probability in an unbounded one-dimensional lattice, discrete random walks and their continuous counterpart, Brownian walks, have developed over the course of a century into a vast and versatile area of knowledge. Lattice random walks are now routinely employed to study stochastic processes across scales, dimensions, and disciplines, from the one-dimensional search of proteins along a DNA strand and the two-dimensional roaming of bacteria in a petri dish, to the three-dimensional motion of macromolecules inside cells and the spatial coverage of multiple robots in a disaster area. In these realistic scenarios, when the randomly moving object is constrained to remain within a finite domain, confined lattice random walks represent a powerful modeling tool. Somewhat surprisingly, and differently from Brownian walks, the spatiotemporal dependence of the confined lattice walk probability has been accessible mainly via computational techniques, and finding its analytic description has remained an open problem. Making use of a set of analytic combinatorics identities with Chebyshev polynomials, I develop a hierarchical dimensionality reduction to find the exact space and time dependence of the occupation probability for confined Pólya’s walks in arbitrary dimensions with reflective, periodic, absorbing, and mixed (reflective and absorbing) boundary conditions along each direction. The probability expressions allow one to construct the time dependence of derived quantities, explicitly in one dimension and via an integration in higher dimensions, such as the first-passage probability to a single target, return probability, average number of distinct sites visited, and absorption probability with imperfect traps. Exact mean first-passage time formulas to a single target in arbitrary dimensions are also presented. These formulas allow one to extend the so-called discrete pseudo-Green function formalism, employed to determine analytically mean first-passage time, with reflecting and periodic boundaries, and a wealth of other related quantities, to arbitrary dimensions. For multiple targets, I introduce a procedure to construct the time dependence of the first-passage probability to one of many targets. Reduction of the occupation probability expressions to the continuous time limit, the so-called continuous time random walk, and to the space-time continuous limit is also presented.

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.

We show that Hamiltonian nonlinear dispersive wave systems with cubic nonlinearity and random initial data develop, during their evolution, anomalous correlators. These are responsible for the appearance of “ghost” excitations, i.e., those characterized by negative frequencies, in addition to the positive ones predicted by the linear dispersion relation. We use generalization of the Wick’s decomposition and the wave turbulence theory to explain theoretically the existence of anomalous correlators. We test our theory on the celebrated $\beta$-Fermi-Pasta-Ulam-Tsingou chain and show that numerically measured values of the anomalous correlators agree, in the weakly nonlinear regime, with our analytical predictions. We also predict that similar phenomena will occur in other nonlinear systems dominated by nonlinear interactions, including surface gravity waves. Our results pave the road to study phase correlations in the Fourier space for weakly nonlinear dispersive wave systems.

Motivated by experimental studies that have found signatures of a quantum spin liquid phase in organic crystals whose structure is well described by the two-dimensional triangular lattice, we study the Hubbard model on this lattice at half filling using the infinite-system density matrix renormalization group (iDMRG) method. On infinite cylinders with finite circumference, we identify an intermediate phase between observed metallic behavior at low interaction strength and Mott insulating spin-ordered behavior at strong interactions. Chiral ordering from spontaneous breaking of time-reversal symmetry, a fractionally quantized spin Hall response, and characteristic level statistics in the entanglement spectrum in the intermediate phase provide strong evidence for the existence of a chiral spin liquid in the full two-dimensional limit of the model.

Gauge theories are the cornerstone of our understanding of fundamental interactions among elementary particles. Their properties are often probed in dynamical experiments, such as those performed at ion colliders and high-intensity laser facilities. Describing the evolution of these strongly coupled systems is a formidable challenge for classical computers and represents one of the key open quests for quantum simulation approaches to particle physics phenomena. In this work, we show how recent experiments done on Rydberg atom chains naturally realize the real-time dynamics of a lattice gauge theory at system sizes at the boundary of classical computational methods. We prove that the constrained Hamiltonian dynamics induced by strong Rydberg interactions maps exactly onto the one of a U(1) lattice gauge theory. Building on this correspondence, we show that the recently observed anomalously slow dynamics corresponds to a string-inversion mechanism, reminiscent of the string breaking typically observed in gauge theories. This underlies the generality of this slow dynamics, which we illustrate in the context of one-dimensional quantum electrodynamics on the lattice. Within the same platform, we propose a set of experiments that generically show long-lived oscillations, including the evolution of particle-antiparticle pairs, and discuss how a tunable topological angle can be realized, further affecting the dynamics following a quench. Our work shows that the state of the art for quantum simulation of lattice gauge theories is at 51 qubits and connects the recently observed slow dynamics in atomic systems to archetypal phenomena in particle physics.

Hybrid functionals have proven to be of immense practical value in density-functional-theory calculations. While they are often thought to be a heuristic construct, it has been established that this is in fact not the case. Here, we present a rigorous and formally exact analysis of generalized Kohn-Sham (GKS) density-functional theory of hybrid functionals, in which exact remainder exchange-correlation potentials combine with a fraction of Fock exchange to produce the correct ground-state density. First, we extend formal GKS theory by proving a generalized adiabatic connection theorem. We then use this extension to derive two different definitions for a rigorous distinction between multiplicative exchange and correlation components—one new and one previously postulated. We examine their density-scaling behavior and discuss their similarities and differences. We then present a new algorithm for obtaining exact GKS potentials by inversion of accurate reference electron densities and employ this algorithm to obtain exact potentials for simple atoms and ions. We establish that an equivalent description of the many-electron problem is indeed obtained with any arbitrary global fraction of Fock exchange, and we rationalize the Fock-fraction dependence of the computed remainder exchange-correlation potentials in terms of the new formal theory. Finally, we use the exact theoretical framework and numerical results to shed light on the exchange-correlation potential used in approximate hybrid functional calculations and to assess the consequences of different choices of fractional exchange.

A scheme for controlling the polarization of a light wave via its interaction with an auxiliary beam in a nonlinear optical medium is proposed. We first present the linear theory of polarization-dependent wave mixing, where the “probe” beam, whose polarization is to be manipulated, is less intense than the auxiliary beam. Then we show that a simple geometrical arrangement, where the auxiliary and probe are crossing at 90° and the auxiliary is linearly $s$ polarized (orthogonal to the plane of incidence), enables us to control the probe’s polarization even when its intensity exceeds the auxiliary’s intensity. These schemes are of particular interest when the nonlinear optical medium is a plasma, as it might enable dynamic polarization manipulations at ultrafast timescales and far beyond the optics damage threshold of crystal-based photonics devices.

Single photon detection is a key resource for sensing at the quantum limit and the enabling technology for measurement-based quantum computing. Photon detection at optical frequencies relies on irreversible photoassisted ionization of various natural materials. However, microwave photons have energies 5 orders of magnitude lower than optical photons, and are therefore ineffective at triggering measurable phenomena at macroscopic scales. Here, we report the observation of a new type of interaction between a single two-level system (qubit) and a microwave resonator. These two quantum systems do not interact coherently; instead, they share a common dissipative mechanism to a cold bath: the qubit irreversibly switches to its excited state if and only if a photon enters the resonator. We have used this highly correlated dissipation mechanism to detect itinerant photons impinging on the resonator. This scheme does not require any prior knowledge of the photon waveform nor its arrival time, and dominant decoherence mechanisms do not trigger spurious detection events (dark counts). We demonstrate a detection efficiency of 58% and a record low dark count rate of 1.4 per millisecond. This work establishes engineered nonlinear dissipation as a key enabling resource for a new class of low-noise nonlinear microwave detectors.

Black-hole solutions to general relativity carry a thermodynamic entropy, discovered by Bekenstein and Hawking to be proportional to the area of the event horizon, at leading order in the semiclassical expansion. In a theory of quantum gravity, black holes must constitute ensembles of quantum microstates whose large number accounts for the entropy. We study this issue in the context of gravity with a negative cosmological constant. We exploit the most basic example of the holographic description of gravity ($\mathrm{AdS}/\mathrm{CFT}$): type IIB string theory on ${\mathrm{AdS}}_5\times S^5$, equivalent to maximally supersymmetric Yang-Mills theory in four dimensions. We thus resolve a long-standing question: Does the four-dimensional $\mathcal{N}=4$ $\mathrm{SU}(N)$ Super-Yang-Mills theory on $S^3$ at large $N$ contain enough states to account for the entropy of rotating electrically charged supersymmetric black holes in 5D anti–de Sitter space? Our answer is positive. By reconsidering the large $N$ limit of the superconformal index, using the so-called Bethe-ansatz formulation, we find an exponentially large contribution which exactly reproduces the Bekenstein-Hawking entropy of the black holes. Besides, the large $N$ limit exhibits a complicated structure, with many competing exponential contributions and Stokes lines, hinting at new physics. Our method opens the way toward a quantitative study of quantum properties of black holes in anti–de Sitter space.

Understanding mechanisms for rectifying stochastic fluctuations has been a long-standing problem in nonequilibrium statistical mechanics. Here, we explore an opportunity provided by nonequilibrium parity-violating metamaterials to uncover new mechanisms for rectification of energy and motion. Using a parity-violating gyroscopic metamaterial that is allowed to interact with a bath of active particles as a model system, we develop an analytic diagrammatic theory that compactly elucidates how the rectification results from an interplay between gyroscopic forces, nonequilibrium activity, and network structure. Our active metamaterial model can generate energy flows through an object in the absence of any temperature gradient. The nonreciprocal microscopic fluctuations responsible for generating the energy flows can further be used to power locomotion in, or exert forces on, a viscous fluid. Taken together, our analytical and numerical results elucidate how the geometry and interparticle interactions of the parity-violating material can couple with the nonequilibrium fluctuations of an active bath and enable rectification of energy and motion.

We characterize the motility of athermal swimming droplets within the framework of a persistent random walk. Just like active colloids, their trajectories can be modeled with a constant velocity $V$ and a slow angular diffusion, but the random changes in direction are not thermally driven. Instead, $V$ is determined by the interfacial tension gradient along the droplet surface, while reorientation of the surfactant gradient leads to changes in direction with a persistence time $\tau$. We show that the origin of locomotion is the difference in the critical micellar concentration in the front and the back of the droplet, $\mathrm{\Delta }\mathrm{CMC}$. Tuning this parameter by salt controls $V$ from 3 to 15 diameters $d/s$. Surfactant concentration has little effect on speed, but leads to a dramatic decrease in $\tau$ over 4 orders of magnitude. The corresponding range of the persistence length $\ell =V\tau$ extends beyond the realm of synthetic or living swimmers, in which $V$ is limited by fuel consumption and $\tau$ is set by thermal fluctuations or biological activity, respectively. Our tunable swimmers are ideal candidates for the study of the departure from equilibrium to high levels of activity. We show that their collective behavior exhibits the formation of active clusters of a well-defined size.

A Kitaev quantum spin liquid is a prime example of novel quantum magnetism of spin-orbit entangled pseudospin-$1/2$ moments in a honeycomb lattice. Most candidate materials such as ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ have many competing exchange interactions beyond the minimal Kitaev-Heisenberg model whose small variations in the strength of the interactions produce huge differences in low-energy dynamics. Our incomplete knowledge of dynamic spin correlations hampers identification of a minimal model and quantification of the proximity to the Kitaev quantum spin-liquid phase. Here, we report momentum- and energy-resolved magnetic excitation spectra in a honeycomb lattice ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ measured using a resonant inelastic x-ray scattering spectrometer capable of 12 meV resolution. Measured spectra at a low temperature show that the dynamic response lacks resolution-limited coherent spin waves in most parts of the Brillouin zone but has a discernible dispersion and spectral weight distribution within the energy window of 60 meV. A systematic investigation using the exact diagonalization method and direct comparison of high-resolution experimental spectra and theoretical simulations allow us to confine a parameter regime in which the extended Kitaev-Heisenberg model reasonably reproduces the main feature of the observed magnetic excitations. Hidden Kitaev quantum spin-liquid and Heisenberg phases found in the complex parameter space are used as references to propose the picture of renormalized magnons as explaining the incoherent nature of magnetic excitations. Magnetic excitation spectra are taken at elevated temperatures to follow the temperature evolution of the resonant inelastic x-ray scattering dynamic response in the paramagnetic state. Whereas the low-energy excitation progressively diminishes as the zigzag order disappears, the broad high-energy excitation maintains its spectral weight up to a much higher temperature of 160 K. We suggest that the dominant nearest-neighbor interactions keep short-range correlations up to quite high temperatures with a specific short-range dynamics which has a possible connection to a proximate spin-liquid phase.

We describe the phase diagram of electrons on a fully connected lattice with random hopping, subject to a random Heisenberg spin exchange interaction between any pair of sites and a constraint of no double occupancy. A perturbative renormalization group analysis yields a critical point with fractionalized excitations at a nonzero critical value $p_c$ of the hole doping $p$ away from the half-filled insulator. We compute the renormalization group to two loops, but some exponents are obtained to all loop order. We argue that the critical point $p_c$ is flanked by confining phases: a disordered Fermi liquid with carrier density $1+p$ for $p>p_c$ and a metallic spin glass with carrier density $p$ for $p<p_c$. Additional evidence for the critical behavior is obtained from a large-$M$ analysis of a model which extends the SU(2) spin symmetry to $\mathrm{SU}(M)$. We discuss the relationship of the vicinity of this deconfined quantum critical point to key aspects of cuprate phenomenology.

We show how a large family of interacting nonequilibrium phases of matter can arise from the presence of multiple time-translation symmetries, which occur by quasiperiodically driving an isolated, quantum many-body system with two or more incommensurate frequencies. These phases are fundamentally different from those realizable in time-independent or periodically driven (Floquet) settings. Focusing on high-frequency drives with smooth time dependence, we rigorously establish general conditions for which these phases are stable in a parametrically long-lived “preheating” regime. We develop a formalism to analyze the effect of the multiple time-translation symmetries on the dynamics of the system, which we use to classify and construct explicit examples of the emergent phases. In particular, we discuss time quasicrystals which spontaneously break the time-translation symmetries, as well as time-translation symmetry-protected topological phases.

We experimentally realize a Peierls phase in the hopping amplitude of excitations carried by Rydberg atoms, and observe the resulting characteristic chiral motion in a minimal setup of three sites. Our demonstration relies on the intrinsic spin-orbit coupling of the dipolar exchange interaction combined with time-reversal symmetry breaking by a homogeneous external magnetic field. Remarkably, the phase of the hopping amplitude between two sites strongly depends on the occupancy of the third site, thus leading to a correlated hopping associated with a density-dependent Peierls phase. We experimentally observe this density-dependent hopping and show that the excitations behave as anyonic particles with a nontrivial phase under exchange. Finally, we confirm the dependence of the Peierls phase on the geometrical arrangement of the Rydberg atoms.

Epitaxial strain provides important pathways to control the magnetic and electronic states in transition-metal oxides. However, the large strain is usually accompanied by a strong reduction of the oxygen-vacancy formation energy, which hinders the direct manipulation of their intrinsic properties. Here, using a postdeposition ozone annealing method, we obtain a series of oxygen stoichiometric ${\mathrm{SrCoO}}_3$ thin films with the tensile strain up to 3.0%. We observe a robust ferromagnetic ground state in all strained thin films, while interestingly the tensile strain triggers a distinct metal-to-insulator transition along with the increase of the tensile strain. The persistent ferromagnetic state across the electrical transition therefore suggests that the magnetic state is directly correlated with the localized electrons, rather than the itinerant ones, which then calls for further investigation of the intrinsic mechanism of this magnetic compound beyond the double-exchange mechanism.