By coupling a macroscopic mechanical oscillator to two microwave cavities, we simultaneously prepare and monitor a nonclassical steady state of mechanical motion. In each cavity, correlated radiation pressure forces induced by two coherent drives engineer the coupling between the quadratures of light and motion. We, first, demonstrate the ability to perform a continuous quantum nondemolition measurement of a single mechanical quadrature at a rate that exceeds the mechanical decoherence rate, while avoiding measurement backaction by more than 13 dB. Second, we apply this measurement technique to independently verify the preparation of a squeezed state in the mechanical oscillator, resolving quadrature fluctuations 20% below the quantum noise.

The realization of nanophotonic optical isolators with high optical isolation even at ultralow light levels and low optical losses is an open problem. Here, we employ the link between the local polarization of strongly confined light and its direction of propagation to realize low-loss nonreciprocal transmission through a silica nanofiber at the single-photon level. The direction of the resulting optical isolator is controlled by the spin state of cold atoms. We perform our experiment in two qualitatively different regimes, i.e., with an ensemble of cold atoms where each atom is weakly coupled to the waveguide and with a single atom strongly coupled to the waveguide mode. In both cases, we observe simultaneously high isolation and high forward transmission. The isolator concept constitutes a nanoscale quantum optical analog of microwave ferrite resonance isolators, can be implemented with all kinds of optical waveguides and emitters, and might enable novel integrated optical devices for fiber-based classical and quantum networks.

We show that the topological Kitaev spin liquid on the honeycomb lattice is extremely fragile against the second-neighbor Kitaev coupling $K_2$, which has recently been shown to be the dominant perturbation away from the nearest-neighbor model in iridate ${\mathrm{Na}}_2{\mathrm{IrO}}_3$, and may also play a role in $\alpha \text{−}{\mathrm{RuCl}}_3$ and ${\mathrm{Li}}_2{\mathrm{IrO}}_3$. This coupling naturally explains the zigzag ordering (without introducing unrealistically large longer-range Heisenberg exchange terms) and the special entanglement between real and spin space observed recently in ${\mathrm{Na}}_2{\mathrm{IrO}}_3$. Moreover, the minimal $K_1-K_2$ model that we present here holds the unique property that the classical and quantum phase diagrams and their respective order-by-disorder mechanisms are qualitatively different due to the fundamentally different symmetries of the classical and quantum counterparts.

It is well known that unitary symmetries can be “gauged,” i.e., defined to act in a local way, which leads to a corresponding gauge field. Gauging, for example, the charge-conservation symmetry leads to electromagnetic gauge fields. It is an open question whether an analogous process is possible for time reversal which is an antiunitary symmetry. Here, we discuss a route to gauging time-reversal symmetry that applies to gapped quantum ground states that admit a tensor network representation. The tensor network representation of quantum states provides a notion of locality for the wave function coefficient and hence a notion of locality for the action of complex conjugation in antiunitary symmetries. Based on that, we show how time reversal can be applied locally and also describe time-reversal symmetry twists that act as gauge fluxes through nontrivial loops in the system. As with unitary symmetries, gauging time reversal provides useful access to the physical properties of the system. We show how topological invariants of certain time-reversal symmetric topological phases in $D=1$, 2 are readily extracted using these ideas.

A solid—amorphous or crystalline—is defined by a finite shear modulus while a fluid lacks such. We thus experimentally investigate the elastic properties of a colloidal glass former near the glass transition: Spectroscopy of vibrational excitations yields the dispersion relations of longitudinal and transverse phonons in the glassy state. From the long-wavelength limit of the dispersion relation, we extract the bulk and the shear modulus. As expected, the latter disappear in a fluid and we measure a clearly resolved discontinuous behavior of the elastic moduli at the glass transition. This not only determines the transition temperature $T_G$ of the system but also directly addresses recent discussions about elasticity during vitrification. We show that low-frequency excitations in our system are plane waves such that continuum elasticity theory can be used to describe the macroscopic behavior.

We present a new impurity solver for dynamical mean-field theory based on imaginary-time evolution of matrix product states. This converges the self-consistency loop on the imaginary-frequency axis and obtains real-frequency information in a final real-time evolution. Relative to computations on the real-frequency axis, required bath sizes are much smaller and no entanglement is generated, so much larger systems can be studied. The power of the method is demonstrated by solutions of a three-band model in the single- and two-site dynamical mean-field approximation. Technical issues are discussed, including details of the method, efficiency as compared to other matrix-product-state-based impurity solvers, bath construction and its relation to real-frequency computations and the analytic continuation problem of quantum Monte Carlo methods, the choice of basis in dynamical cluster approximation, and perspectives for off-diagonal hybridization functions.

We discuss a non-Fermi liquid gapless metallic surface state of the topological band insulator. It has an odd number of gapless Dirac fermions coupled to a noncompact $U(1)$ gauge field. This can be viewed as a vortex dual to the conventional Dirac fermion surface state. This surface duality is a reflection of a bulk dual description discussed recently for the gauged topological insulator. All the other known surface states can be conveniently accessed from the dual Dirac liquid, including the surface quantum Hall state, the Fu-Kane superconductor, the gapped symmetric topological order and the “composite Dirac liquid.” We also discuss the physical properties of the dual Dirac liquid and its connection to the half-filled Landau level.

Firing patterns in the central nervous system often exhibit strong temporal irregularity and considerable heterogeneity in time-averaged response properties. Previous studies suggested that these properties are the outcome of the intrinsic chaotic dynamics of the neural circuits. Indeed, simplified rate-based neuronal networks with synaptic connections drawn from Gaussian distribution and sigmoidal nonlinearity are known to exhibit chaotic dynamics when the synaptic gain (i.e., connection variance) is sufficiently large. In the limit of an infinitely large network, there is a sharp transition from a fixed point to chaos, as the synaptic gain reaches a critical value. Near the onset, chaotic fluctuations are slow, analogous to the ubiquitous, slow irregular fluctuations observed in the firing rates of many cortical circuits. However, the existence of a transition from a fixed point to chaos in neuronal circuit models with more realistic architectures and firing dynamics has not been established. In this work, we investigate rate-based dynamics of neuronal circuits composed of several subpopulations with randomly diluted connections. Nonzero connections are either positive for excitatory neurons or negative for inhibitory ones, while single neuron output is strictly positive with output rates rising as a power law above threshold, in line with known constraints in many biological systems. Using dynamic mean field theory, we find the phase diagram depicting the regimes of stable fixed-point, unstable-dynamic, and chaotic-rate fluctuations. We focus on the latter and characterize the properties of systems near this transition. We show that dilute excitatory-inhibitory architectures exhibit the same onset to chaos as the single population with Gaussian connectivity. In these architectures, the large mean excitatory and inhibitory inputs dynamically balance each other, amplifying the effect of the residual fluctuations. Importantly, the existence of a transition to chaos and its critical properties depend on the shape of the single-neuron nonlinear input-output transfer function, near firing threshold. In particular, for nonlinear transfer functions with a sharp rise near threshold, the transition to chaos disappears in the limit of a large network; instead, the system exhibits chaotic fluctuations even for small synaptic gain. Finally, we investigate transition to chaos in network models with spiking dynamics. We show that when synaptic time constants are slow relative to the mean inverse firing rates, the network undergoes a transition from fast spiking fluctuations with constant rates to a state where the firing rates exhibit chaotic fluctuations, similar to the transition predicted by rate-based dynamics. Systems with finite synaptic time constants and firing rates exhibit a smooth transition from a regime dominated by stationary firing rates to a regime of slow rate fluctuations. This smooth crossover obeys scaling properties, similar to crossover phenomena in statistical mechanics. The theoretical results are supported by computer simulations of several neuronal architectures and dynamics. Consequences for cortical circuit dynamics are discussed. These results advance our understanding of the properties of intrinsic dynamics in realistic neuronal networks and their functional consequences.

We show that for ultracold magnetic lanthanide atoms chaotic scattering emerges due to a combination of anisotropic interaction potentials and Zeeman coupling under an external magnetic field. This scattering is studied in a collaborative experimental and theoretical effort for both dysprosium and erbium. We present extensive atom-loss measurements of their dense magnetic Feshbach-resonance spectra, analyze their statistical properties, and compare to predictions from a random-matrix-theory-inspired model. Furthermore, theoretical coupled-channels simulations of the anisotropic molecular Hamiltonian at zero magnetic field show that weakly bound, near threshold diatomic levels form overlapping, uncoupled chaotic series that when combined are randomly distributed. The Zeeman interaction shifts and couples these levels, leading to a Feshbach spectrum of zero-energy bound states with nearest-neighbor spacings that changes from randomly to chaotically distributed for increasing magnetic field. Finally, we show that the extreme temperature sensitivity of a small, but sizable fraction of the resonances in the Dy and Er atom-loss spectra is due to resonant nonzero partial-wave collisions. Our threshold analysis for these resonances indicates a large collision-energy dependence of the three-body recombination rate.

The Berezinskii-Kosterlitz-Thouless mechanism, in which a phase transition is mediated by the proliferation of topological defects, governs the critical behavior of a wide range of equilibrium two-dimensional systems with a continuous symmetry, ranging from spin systems to superconducting thin films and two-dimensional Bose fluids, such as liquid helium and ultracold atoms. We show here that this phenomenon is not restricted to thermal equilibrium, rather it survives more generally in a dissipative highly nonequilibrium system driven into a steady state. By considering a quantum fluid of polaritons of an experimentally relevant size, in the so-called optical parametric oscillator regime, we demonstrate that it indeed undergoes a phase transition associated with a vortex binding-unbinding mechanism. Yet, the exponent of the power-law decay of the first-order correlation function in the (algebraically) ordered phase can exceed the equilibrium upper limit: this shows that the ordered phase of driven-dissipative systems can sustain a higher level of collective excitations before the order is destroyed by topological defects. Our work suggests that the macroscopic coherence phenomena, observed recently in interacting two-dimensional light-matter systems, result from a nonequilibrium phase transition of the Berezinskii-Kosterlitz-Thouless rather than the Bose-Einstein condensation type.

As the basis of a diverse set of photonic applications, such as hologram imaging, polarization, and wave front manipulation, the local phase control of electromagnetic waves is fundamental in photonic research. However, currently available bulky, passive, range-limited phase modulators pose an obstacle in photonic applications. Here, we propose a new mechanism to achieve a wide phase modulation range, with graphene used as a tunable loss to drive an underdamped to overdamped resonator transition. Based on this mechanism, we present widely tunable phase modulation in the terahertz regime, realized in gate-tuned ultrathin reflective graphene metasurfaces. A one-port resonator model, supported by full-wave simulations, explains the underlying physics of the discovered extreme phase modulation and indicates general strategies for designing tunable photonic devices. As an example, we demonstrate a gate-tunable terahertz (THz) polarization modulator with a graphene metasurface. Our findings establish the possibility for photonic applications based on active phase manipulation.

Since the 1960s, the Benjamin-Feir (or modulation) instability (MI) has been considered as the self-modulation of the continuous “envelope waves” with respect to small periodic perturbations that precedes the emergence of highly localized wave structures. Nowadays, the universal nature of MI is established through numerous observations in physics. However, even now, 50 years later, more practical but complex forms of this old physical phenomenon at the frontier of nonlinear wave theory have still not been revealed (i.e., when perturbations beyond simple harmonic are involved). Here, we report the evidence of the broadest class of creation and annihilation dynamics of MI, also called superregular breathers. Observations are done in two different branches of wave physics, namely, in optics and hydrodynamics. Based on the common framework of the nonlinear Schrödinger equation, this multidisciplinary approach proves universality and reversibility of nonlinear wave formations from localized perturbations for drastically different spatial and temporal scales.

We examine models of fermions with infinite-range interactions that realize non-Fermi liquids with a continuously variable U(1) charge density $\mathcal{Q}$ and a nonzero entropy density $\mathcal{S}$ at vanishing temperature. Real-time correlators of operators carrying U(1) charge $q$ at a low temperature $T$ are characterized by a $\mathcal{Q}$-dependent frequency ${\omega }_{\mathcal{S}}=(qT/\hslash )(\partial \mathcal{S}/\partial \mathcal{Q})$, which determines a spectral asymmetry. We show that the correlators match precisely with those of the two-dimensional anti–de Sitter (${\mathrm{AdS}}_2$) horizons of extremal charged black holes. On the black hole side, the matching employs $\mathcal{S}$ as the Bekenstein-Hawking entropy density and the laws of black hole thermodynamics that relate $(\partial \mathcal{S}/\partial \mathcal{Q})/(2\pi )$ to the electric field strength in ${\mathrm{AdS}}_2$. The fermion model entropy is computed using the microscopic degrees of freedom of a UV complete theory without supersymmetry.

We present the design, fabrication, and characterization of a planar silicon photonic crystal cavity in which large position-squared optomechanical coupling is realized. The device consists of a double-slotted photonic crystal structure in which motion of a central beam mode couples to two high-$Q$ optical modes localized around each slot. Electrostatic tuning of the structure is used to controllably hybridize the optical modes into supermodes that couple in a quadratic fashion to the motion of the beam. From independent measurements of the anticrossing of the optical modes and of the dynamic optical spring effect, a position-squared vacuum coupling rate as large as ${\tilde{g}}^{\prime }/2\pi =245\mathrm{Hz}$ is inferred between the optical supermodes and the fundamental in-plane mechanical resonance of the structure at ${\omega }_m/2\pi =8.7\mathrm{MHz}$, which in displacement units corresponds to a coupling coefficient of $g^{\prime }/2\pi =1\mathrm{THz}/{\mathrm{nm}}^2$. For larger supermode splittings, selective excitation of the individual optical supermodes is used to demonstrate optical trapping of the mechanical resonator with measured ${\tilde{g}}^{\prime }/2\pi =46\mathrm{Hz}$.

The observed magnetoresistance (MR) in three-terminal (3T) ferromagnet-nonmagnet (FM-NM) tunnel junctions has historically been assigned to ensemble dephasing (Hanle effect) of a spin accumulation, thus offering a powerful approach for characterizing the spin lifetime of candidate materials for spintronics applications. However, due to crucial discrepancies of the extracted spin parameters with known materials properties, this interpretation has come under intense scrutiny. By employing epitaxial artificial dipoles as the tunnel barrier in oxide heterostructures, the band alignments between the FM and NM channels can be controllably engineered, providing an experimental platform for testing the predictions of the various spin accumulation models. Using this approach, we have been able to definitively rule out spin accumulation as the origin of the 3T MR. Instead, we assign the origin of the magnetoresistance to spin-dependent hopping through defect states in the barrier, a fundamental phenomenon seen across diverse systems. A theoretical framework is developed that can account for the signal amplitude, linewidth, and anisotropy.

In most theoretical descriptions of collective strong coupling of organic molecules to a cavity mode, the molecules are modeled as simple two-level systems. This picture fails to describe the rich structure provided by their internal rovibrational (nuclear) degrees of freedom. We investigate a first-principles model that fully takes into account both electronic and nuclear degrees of freedom, allowing an exploration of the phenomenon of strong coupling from an entirely new perspective. First, we demonstrate the limitations of applicability of the Born-Oppenheimer approximation in strongly coupled molecule-cavity structures. For the case of two molecules, we also show how dark states, which within the two-level picture are effectively decoupled from the cavity, are indeed affected by the formation of collective strong coupling. Finally, we discuss ground-state modifications in the ultrastrong-coupling regime and show that some molecular observables are affected by the collective coupling strength, while others depend only on the single-molecule coupling constant.

In 1933, Meissner and Ochsenfeld reported the expulsion of magnetic flux—the diamagnetic Meissner effect—from the interior of superconducting lead. This discovery was crucial in formulating the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity. In exotic superconducting systems BCS theory does not strictly apply. A classical example is a superconductor-magnet hybrid system where magnetic ordering breaks time-reversal symmetry of the superconducting condensate and results in the stabilization of an odd-frequency superconducting state. It has been predicted that under appropriate conditions, odd-frequency superconductivity should manifest in the Meissner state as fluctuations in the sign of the magnetic susceptibility, meaning that the superconductivity can either repel (diamagnetic) or attract (paramagnetic) external magnetic flux. Here, we report local probe measurements of faint magnetic fields in a $\mathrm{Au}/\mathrm{Ho}/\mathrm{Nb}$ trilayer system using low-energy muons, where antiferromagnetic Ho (4.5 nm) breaks time-reversal symmetry of the proximity-induced pair correlations in Au. From depth-resolved measurements below the superconducting transition of Nb, we observe a local enhancement of the magnetic field in Au that exceeds the externally applied field, thus proving the existence of an intrinsic paramagnetic Meissner effect arising from an odd-frequency superconducting state.

Circulators and directional amplifiers are crucial nonreciprocal signal routing and processing components involved in microwave read-out chains for a variety of applications. They are particularly important in the field of superconducting quantum information, where the devices also need to have minimal photon losses to preserve the quantum coherence of signals. Conventional commercial implementations of each device suffer from losses and are built from very different physical principles, which has led to separate strategies for the construction of their quantum-limited versions. However, as recently theoretically, by establishing simultaneous pairwise conversion and/or gain processes between three modes of a Josephson-junction-based superconducting microwave circuit, it is possible to endow the circuit with the functions of either a phase-preserving directional amplifier or a circulator. Here, we experimentally demonstrate these two modes of operation of the same circuit. Furthermore, in the directional amplifier mode, we show that the noise performance is comparable to standard nondirectional superconducting amplifiers, while in the circulator mode, we show that the sense of circulation is fully reversible. Our device is far simpler in both modes of operation than previous proposals and implementations, requiring only three microwave pumps. It offers the advantage of flexibility, as it can dynamically switch between modes of operation as its pump conditions are changed. Moreover, by demonstrating that a single three-wave process yields nonreciprocal devices with reconfigurable functions, our work breaks the ground for the development of future, more complex directional circuits, and has excellent prospects for on-chip integration.

Simple chiroptically active metamaterials are difficult to realize in practice but could pave the way for a range of important applications, such as sensitive optical biosensors, asymmetric catalysis, and novel polarization manipulation devices. We show that a metasurface based on a random arrangement of anisotropic but aligned gold nanoparticles can exhibit an almost perfect selectivity towards incident photon spin for evanescent excitation with visible to near-infrared light. The experimentally attained reflection contrast between left- and right-handed circularly polarized light peaks at $\sim 90\%$, in excellent agreement with analytical theory. These results are important for the development of future photonic and plasmonic polarization-based technologies.

${\mathrm{Sr}}_2\mathrm{Ir}{\mathrm{O}}_4$ was predicted to be a high-temperature superconductor upon electron doping since it highly resembles the cuprates in crystal structure, electronic structure, and magnetic coupling constants. Here, we report a scanning tunneling microscopy/spectroscopy (STM/STS) study of ${\mathrm{Sr}}_2\mathrm{Ir}{\mathrm{O}}_4$ with surface electron doping by depositing potassium (K) atoms. We find that as the electron doping increases, the system gradually evolves from an insulating state to a normal metallic state, via a pseudogaplike phase, and a phase with a sharp, V-shaped low-energy gap with about 95% loss of density of state (DOS) at ${\mathrm{E}}_F$. At certain K coverage (0.5–0.6 monolayer), the magnitude of the low-energy gap is 25–30 meV, and it closes at around 50 K. Our observations show that the electron-doped ${\mathrm{Sr}}_2\mathrm{Ir}{\mathrm{O}}_4$ remarkably resembles hole-doped cuprate superconductors.