We investigate many-body dynamics in a one-dimensional interacting periodically driven system, based on a partially filled version of Thouless’s topologically quantized adiabatic pump. The corresponding single-particle Floquet bands are chiral, with the Floquet spectrum realizing nontrivial cycles around the quasienergy Brillouin zone. For generic filling, with either bosons or fermions, the system is gapless and is expected to rapidly absorb energy from the driving field. We identify parameter regimes where scattering between Floquet bands of opposite chirality is exponentially suppressed, opening a long time window in which the system prethermalizes to an infinite-temperature state restricted to a single Floquet band. In this quasi-steady state, the time-averaged current takes a universal value determined solely by the density of particles and the topological winding number of the populated Floquet band. This remarkable behavior may be readily studied experimentally in recently developed cold atom systems.

Electrides are intrinsic electron-rich materials enabling applications as excellent electron emitters, superior catalysts, and strong reducing agents. There are a number of organic electrides; however, their instability at room temperature and sensitivity to moisture are bottlenecks for their practical uses. Known inorganic electrides are rare, but they appear to have greater thermal stability at ambient conditions and are thus better characterized for application. Here, we develop a computer-assisted inverse-design method for searching for a large variety of inorganic electrides unbiased by any known electride structures. It uses the intrinsic property of interstitial electron localization of electrides as the global variable function for swarm intelligence structure searches. We construct two rules of thumb on the design of inorganic electrides pointing to electron-rich ionic systems and low electronegativity of the cationic elements involved. By screening 99 such binary compounds through large-scale computer simulations, we identify 24 stable and 65 metastable new inorganic electrides that show distinct three-, two-, and zero-dimensional conductive properties, among which 18 are existing compounds that have not been pointed to as electrides. Our work reveals the rich abundance of inorganic electrides by providing 33 hitherto unexpected structure prototypes of electrides, of which 19 are not in the known structure databases.

Condensed matter physics has been driven forward by significant experimental and theoretical progress in the study and understanding of equilibrium phase transitions based on symmetry and topology. However, nonequilibrium phase transitions have remained a challenge, in part due to their complexity in theoretical descriptions and the additional experimental difficulties in systematically controlling systems out of equilibrium. Here, we study a one-dimensional chain of 72 microwave cavities, each coupled to a superconducting qubit, and coherently drive the system into a nonequilibrium steady state. We find experimental evidence for a dissipative phase transition in the system in which the steady state changes dramatically as the mean photon number is increased. Near the boundary between the two observed phases, the system demonstrates bistability, with characteristic switching times as long as 60 ms—far longer than any of the intrinsic rates known for the system. This experiment demonstrates the power of circuit QED systems for studying nonequilibrium condensed matter physics and paves the way for future experiments exploring nonequilbrium physics with many-body quantum optics.

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”.

We present a continuous formulation of epidemic spreading on multilayer networks using a tensorial representation, extending the models of monoplex networks to this context. We derive analytical expressions for the epidemic threshold of the susceptible-infected-susceptible (SIS) and susceptible-infected-recovered dynamics, as well as upper and lower bounds for the disease prevalence in the steady state for the SIS scenario. Using the quasistationary state method, we numerically show the existence of disease localization and the emergence of two or more susceptibility peaks, which are characterized analytically and numerically through the inverse participation ratio. At variance with what is observed in single-layer networks, we show that disease localization takes place on the layers and not on the nodes of a given layer. Furthermore, when mapping the critical dynamics to an eigenvalue problem, we observe a characteristic transition in the eigenvalue spectra of the supra-contact tensor as a function of the ratio of two spreading rates: If the rate at which the disease spreads within a layer is comparable to the spreading rate across layers, the individual spectra of each layer merge with the coupling between layers. Finally, we report on an interesting phenomenon, the barrier effect; i.e., for a three-layer configuration, when the layer with the lowest eigenvalue is located at the center of the line, it can effectively act as a barrier to the disease. The formalism introduced here provides a unifying mathematical approach to disease contagion in multiplex systems, opening new possibilities for the study of spreading processes.

In the analysis of the robustness of multiplex networks, it is commonly assumed that a node is functioning only if its interdependent nodes are simultaneously functioning. According to this model, a multiplex network becomes more and more fragile as the number of layers increases. In this respect, the addition of a new layer of interdependent nodes to a preexisting multiplex network will never improve its robustness. Whereas such a model seems appropriate to understand the effect of interdependencies in the simplest scenario of a network composed of only two layers, it may seem unsuitable to characterize the robustness of real systems formed by multiple network layers. In fact, it seems unrealistic that a real system evolved, through the development of multiple layers of interactions, towards a fragile structure. In this paper, we introduce a model of percolation where the condition that makes a node functional is that the node is functioning in at least two of the layers of the network. The model reduces to the commonly adopted percolation model for multiplex networks when the number of layers equals two. For larger numbers of layers, however, the model describes a scenario where the addition of new layers boosts the robustness of the system by creating redundant interdependencies among layers. We prove this fact thanks to the development of a message-passing theory that is able to characterize the model in both synthetic and real-world multiplex graphs.

Nonequilibrium phase transitions exist in damped-driven open quantum systems when the continuous tuning of an external parameter leads to a transition between two robust steady states. In second-order transitions this change is abrupt at a critical point, whereas in first-order transitions the two phases can coexist in a critical hysteresis domain. Here, we report the observation of a first-order dissipative quantum phase transition in a driven circuit quantum electrodynamics system. It takes place when the photon blockade of the driven cavity-atom system is broken by increasing the drive power. The observed experimental signature is a bimodal phase space distribution with varying weights controlled by the drive strength. Our measurements show an improved stabilization of the classical attractors up to the millisecond range when the size of the quantum system is increased from one to three artificial atoms. The formation of such robust pointer states could be used for new quantum measurement schemes or to investigate multiphoton phases of finite-size, nonlinear, open quantum systems.

We develop a theory of amorphous interfaces in glass-forming liquids. We show that the statistical properties of these surfaces, which separate regions characterized by different amorphous arrangements of particles, coincide with the ones of domain walls in the random field Ising model. A major consequence of our results is that supercooled liquids are characterized by two different static lengths: the point-to-set ${\xi }_{\mathrm{PS}}$, which is a measure of the spatial extent of cooperative rearranging regions, and the wandering length ${\xi }_{\perp }$, which is related to the fluctuations of their shape. We find that ${\xi }_{\perp }$ grows when approaching the glass transition but slower than ${\xi }_{\mathrm{PS}}$. The wandering length increases as $s_c^{-1/2}$, where $s_c$ is the configurational entropy. Our results strengthen the relationship with the random field Ising model found in recent works. They are in agreement with previous numerical studies of amorphous interfaces and provide a theoretical framework for explaining numerical and experimental findings on pinned particle systems and static lengths in glass-forming liquids.

Self-propelled particles, both biological and synthetic, are stably trapped by walls and develop high concentration peaks over bounding surfaces. In swimming bacteria, like E. coli, the physical mechanism behind wall entrapment is an intricate mixture of hydrodynamic and steric interactions with a strongly anisotropic character. The building of a clear physical picture of this phenomenon demands direct and full three-dimensional experimental observations of individual wall entrapment events. Here, we demonstrate that, by using a combination of three-axis holographic microscopy and optical tweezers, it is possible to obtain volumetric reconstructions of individual E. coli cells that are sequentially released at a controlled distance and angle from a flat solid wall. We find that hydrodynamic couplings can slow down the cell before collision, but reorientation only occurs while the cell is in constant contact with the wall. In the trapped state, all cells swim with the average body axis pointing into the surface. The amplitude of this pitch angle is anticorrelated to the amplitude of wobbling, thus indicating that entrapment is dominated by near-field couplings between the cell body and the wall. Our approach opens the way to three-dimensional quantitative studies of a broad range of fast dynamical processes in motile bacteria and eukaryotic cells.

The search for unconventional superconductivity has been focused on materials with strong spin-orbit coupling and unique crystal lattices. Doped bismuth selenide (${\mathrm{Bi}}_2{\mathrm{Se}}_3$) is a strong candidate, given the topological insulator nature of the parent compound and its triangular lattice. The coupling between the physical properties in the superconducting state and its underlying crystal symmetry is a crucial test for unconventional superconductivity. In this paper, we report direct evidence that the superconducting magnetic response couples strongly to the underlying trigonal crystal symmetry in the recently discovered superconductor with trigonal crystal structure, niobium (Nb)-doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$. As a result, the in-plane magnetic torque signal vanishes every 60°. More importantly, the superconducting hysteresis loop amplitude is enhanced along one preferred direction, spontaneously breaking the rotational symmetry. This observation indicates the presence of nematic order in the superconducting ground state of Nb-doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$.

We develop a thermodynamic framework that describes a classical system of interest $\mathcal{S}$ that is strongly coupled to its thermal environment $\mathcal{E}$. Within this framework, seven key thermodynamic quantities—internal energy, entropy, volume, enthalpy, Gibbs free energy, heat, and work—are defined microscopically. These quantities obey thermodynamic relations including both the first and second law, and they satisfy nonequilibrium fluctuation theorems. We additionally impose a macroscopic consistency condition: When $\mathcal{S}$ is large, the quantities defined within our framework scale up to their macroscopic counterparts. By satisfying this condition, we demonstrate that a unifying framework can be developed, which encompasses both stochastic thermodynamics at one end, and macroscopic thermodynamics at the other. A central element in our approach is a thermodynamic definition of the volume of the system of interest, which converges to the usual geometric definition when $\mathcal{S}$ is large. We also sketch an alternative framework that satisfies the same consistency conditions. The dynamics of the system and environment are modeled using Hamilton’s equations in the full phase space.

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.

Topological solitons are knots in continuous physical fields classified by nonzero Hopf index values. Despite arising in theories that span many branches of physics, from elementary particles to condensed matter and cosmology, they remain experimentally elusive and poorly understood. We introduce a method of experimental and numerical analysis of such localized structures in liquid crystals that, similar to the mathematical Hopf maps, relates all points of the medium’s order parameter space to their closed-loop preimages within the three-dimensional solitons. We uncover a surprisingly large diversity of naturally occurring and laser-generated topologically nontrivial solitons with differently knotted nematic fields, which previously have not been realized in theories and experiments alike. We discuss the implications of the liquid crystal’s nonpolar nature on the knot soliton topology and how the medium’s chirality, confinement, and elastic anisotropy help to overcome the constraints of the Hobart-Derrick theorem, yielding static three-dimensional solitons without or with additional defects. Our findings will establish chiral nematics as a model system for experimental exploration of topological solitons and may impinge on understanding of such nonsingular field configurations in other branches of physics, as well as may lead to technological applications.

In optics, the interaction of atoms with the magnetic field of light is almost always ignored since its strength is many orders of magnitude weaker compared to the interaction with the electric field. In this article, by using a magnetic-dipole transition within the $4f$ shell of europium ions, we show a strong interaction between a green laser and an ensemble of atomic ions. The electrons move coherently between the ground and excited ionic levels (Rabi flopping) by interacting with the magnetic field of the laser. By measuring the Rabi flopping frequency as the laser intensity is varied, we report the first direct measurement of a magnetic-dipole matrix element in the optical region of the spectrum. Using density-matrix simulations of the ensemble, we infer the generation of coherent magnetization with magnitude $5.5\times {10}^{-3}\mathrm{A}/\mathrm{m}$, which is capable of generating left-handed electromagnetic waves of intensity $1\mathrm{nW}/{\mathrm{cm}}^2$. These results open up the prospect of constructing left-handed materials using sharp transitions of atoms.

Electronic heating of cold crystal lattices in nonlinear multiphoton excitation can transiently alter their physical and chemical properties. In metals where free electron densities are high and the relative fraction of photoexcited hot electrons is low, the effects are small, but in semimetals, where the free electron densities are low and the photoexcited densities can overwhelm them, the intense femtosecond laser excitation can induce profound changes. In semimetal graphite and its derivatives, strong optical absorption, weak screening of the Coulomb potential, and high cohesive energy enable extreme hot electron generation and thermalization to be realized under femtosecond laser excitation. We investigate the nonlinear interactions within a hot electron gas in graphite through multiphoton-induced thermionic emission. Unlike the conventional photoelectric effect, within about 25 fs, the memory of the excitation process, where resonant dipole transitions absorb up to eight quanta of light, is erased to produce statistical Boltzmann electron distributions with temperatures exceeding 5000 K; this ultrafast electronic heating causes thermionic emission to occur from the interlayer band of graphite. The nearly instantaneous thermalization of the photoexcited carriers through Coulomb scattering to extreme electronic temperatures characterized by separate electron and hole chemical potentials can enhance hot electron surface femtochemistry, photovoltaic energy conversion, and incandescence, and drive graphite-to-diamond electronic phase transition.

Electrons interacting with plasmonic structures can give rise to resonant excitations in localized plasmonic cavities and to collective excitations in periodic structures. We investigate the presence of resonant features and disorder in the conventional Smith-Purcell effect (electrons interacting with periodic structures) and observe the simultaneous excitation of both the plasmonic resonances and the collective excitations. For this purpose, we introduce a new scanning-electron-microscope-based setup that allows us to probe and directly image new features of electron-photon interactions in nanophotonic structures like plasmonic crystals with strong disorder. Our work creates new possibilities for probing nanostructures with free electrons, with potential applications that include tunable sources of short-wavelength radiation and plasmonic-based particle accelerators.

We explore how thermal fluctuations affect the mechanics of thin amorphous spherical shells. In flat membranes with a shear modulus, thermal fluctuations increase the bending rigidity and reduce the in-plane elastic moduli in a scale-dependent fashion. This is still true for spherical shells. However, the additional coupling between the shell curvature, the local in-plane stretching modes, and the local out-of-plane undulations leads to novel phenomena. In spherical shells, thermal fluctuations produce a radius-dependent negative effective surface tension, equivalent to applying an inward external pressure. By adapting renormalization group calculations to allow for a spherical background curvature, we show that while small spherical shells are stable, sufficiently large shells are crushed by this thermally generated “pressure.” Such shells can be stabilized by an outward osmotic pressure, but the effective shell size grows nonlinearly with increasing outward pressure, with the same universal power-law exponent that characterizes the response of fluctuating flat membranes to a uniform tension.

Quantum correlations between imprecision and backaction are a hallmark of continuous linear measurements. Here, we study how measurement-based feedback can be used to improve the visibility of quantum correlations due to the interaction of a laser field with a nanomechanical oscillator. Backaction imparted by the meter laser, due to radiation-pressure quantum fluctuations, gives rise to correlations between its phase and amplitude quadratures. These quantum correlations are observed in the experiment both as squeezing of the meter field fluctuations below the vacuum level in a homodyne measurement and as sideband asymmetry in a heterodyne measurement, demonstrating the common origin of both phenomena. We show that quantum feedback, i.e., feedback that suppresses measurement backaction, can be used to increase the visibility of the sideband asymmetry ratio. In contrast, by operating the feedback loop in the regime of noise squashing, where the in-loop photocurrent variance is reduced below the vacuum level, the visibility of the sideband asymmetry is reduced. This is due to backaction arising from vacuum noise in the homodyne detector. These experiments demonstrate the possibility, as well as the fundamental limits, of measurement-based feedback as a tool to manipulate quantum correlations.