Continuous monitoring of driven-dissipative quantum-optical systems is a crucial element in the implementation of quantum metrology, providing essential strategies for achieving highly precise measurements beyond the classical limit. In this context, the relevant figure of merit is the quantum Fisher information of the radiation field emitted by the driven-dissipative sensor. Saturation of the corresponding precision limit as defined by the quantum Cramér-Rao bound is typically not achieved by conventional, temporally local continuous-measurement schemes such as counting or homodyning. To address the outstanding open challenge of efficient retrieval of the quantum Fisher information of the emission field, we design a novel continuous-measurement strategy featuring temporally quasilocal measurement bases as captured by matrix-product states. Such a measurement can be implemented effectively by injecting the emission field of the sensor into an auxiliary open system, a “quantum-decoder” module, which “decodes” specific input matrix-product states into simple product states as its output field, and performing conventional continuous measurement at the output. We devise a universal recipe for the construction of the decoder by exploiting the time-reversal transformation of quantum-optical input-output channels, thereby establishing a universal method to achieve the quantum Cramér-Rao precision limit for generic sensor designs based on continuous measurement. As a by-product, we establish an effective formula for the evaluation of the quantum Fisher information of the emission field of generic driven-dissipative open sensors. We illustrate the power of our scheme with paramagnetic open sensor designs including linear force sensors, fiber-interfaced nonlinear emitters, and driven-dissipative many-body sensors, and demonstrate that it can be robustly implemented under realistic experimental imperfections.

High harmonic generation (HHG) has developed in recent years as a promising tool for ultrafast materials spectroscopy. At the forefront of these advancements, several works proposed using HHG as an all-optical probe for topology of quantum matter by identifying its signatures in the emission spectra. However, it remains unclear if such spectral signatures are indeed a robust and general approach for probing topology. To address this point, we perform a fully ab initio study of HHG from prototypical two-dimensional topological insulators in the Kane-Mele quantum spin-Hall and anomalous-Hall phases. We analyze the spectra and previously proposed topological signatures by comparing HHG from the topological and trivial phases and across the phase transition. We demonstrate and provide detailed microscopic explanations of why, in these systems, none of the observables proposed thus far uniquely and universally probes material topology. Specifically, we find that the (i) HHG helicity, (ii) anomalous HHG ellipticity, (iii) HHG elliptical dichroism, and (iv) temporal delays in HHG emission are all unreliable signatures of topological phases. Our results suggest that extreme care must be taken when interpreting HHG spectra for topological signatures and that contributions from the crystal symmetries and chemical nature might be dominant over those from topology. They hint that a truly universal topological signature in nonlinear optics is unlikely and raise important questions regarding possible utilization and detection of topology in out-of-equilibrium systems.

Electronic nematicity is the spontaneous loss of rotational symmetry in a metal, without breaking translational symmetry. In the cuprate superconductors, there is experimental evidence for nematicity, but its origin remains unclear. Here we investigate the onset of nematicity in the transport of charge by means of electric and thermoelectric measurements in underdoped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$, performed by passing the current (electrical or thermal) first along the $a$ axis then the $b$ axis of the orthorhombic structure in the same crystal, with a hole doping $p=0.12$. Upon cooling, we observe no additional in-plane anisotropy—beyond the background anisotropy due to the CuO chains—in either the resistivity $\rho$ or the Seebeck coefficient $S$ as the temperature $T^{\star }$ for the onset of the pseudogap phase is crossed. We conclude that the pseudogap phase of cuprates is not nematic. However, at temperatures much lower than $T^{\star }$, a strong additional anisotropy is observed, most clearly in the Peltier coefficient $\alpha =S/\rho$. We interpret it as nematicity associated with the development of charge order.

Exploring non-Hermitian phenomenology is an exciting frontier of modern physics. However, the demonstration of a non-Hermitian phenomenon that is quantum in nature has remained elusive. Here, we predict quantum non-Hermitian phenomena: the fractional quantum Zeno (FQZ) effect and FQZ-induced photon antibunching. We consider a quantum optics platform with reservoir engineering, where nonlinear emitters are coupled to a bath of decaying bosonic modes whose own decay rates form band structures. By engineering the dissipation band, the spontaneous emission of emitters can be suppressed by strong dissipation through an algebraic scaling with fractional exponents—the FQZ effect. This fractional scaling originates uniquely from the divergent dissipative density of states near the dissipation band edge, different from the traditional closed-bath context. We find FQZ-induced strong photon antibunching in the steady state of a driven emitter even for weak nonlinearities. Remarkably, we identify that the sub-Poissonian quantum statistics of photons, which has no classical analogs, stems here from the key role of non-Hermiticity. Our setup is experimentally feasible with the techniques used to design lattice models with dissipative couplings.

Understanding topological matter is an outstanding challenge across several disciplines of physical science. Programmable quantum simulators have emerged as a powerful approach to studying such systems. While quantum spin liquids of paradigmatic toric code type have recently been realized in the laboratory, controlled exploration of topological phases with non-Abelian excitations remains an open problem. We introduce and analyze a new approach to simulating topological matter based on periodic driving. Specifically, we describe a model for a so-called Floquet spin liquid, obtained through a periodic sequence of parallel quantum gate operations that effectively simulates the Hamiltonian of the non-Abelian spin liquid in Kitaev’s honeycomb model. We show that this approach, including the toolbox for preparation, control, and readout of topological states, can be efficiently implemented in state-of-the-art experimental platforms. One specific implementation scheme is based on Rydberg atom arrays and utilizes recently demonstrated coherent qubit transport combined with controlled-phase gate operations. We describe methods for probing the non-Abelian excitations, and the associated Majorana zero modes, and simulate possible fusion and braiding experiments. Our analysis demonstrates the potential of programmable quantum simulators for exploring topological phases of matter. Extensions including simulation of Kitaev materials and lattice gauge theories are also discussed.

Realizing the full potential of quantum computation requires quantum error correction (QEC), with most recent breakthrough demonstrations of QEC using the surface code. QEC codes use multiple noisy physical qubits to encode information in fewer logical qubits, enabling the identification of errors through a decoding process. This process increases the logical fidelity (or accuracy) making the computation more reliable. However, most fast (efficient run-time) decoders neglect important noise characteristics, thereby reducing their accuracy. In this work, we introduce decoders that are both fast and accurate, and can be used with a wide class of QEC codes including the surface code. Our decoders, named belief-matching and belief-find, exploit all noise information and thereby unlock higher accuracy demonstrations of QEC. Using the surface code threshold as a performance metric, we observe a threshold at 0.94% error probability for our decoders, outperforming the 0.82% threshold for a standard minimum-weight perfect matching decoder. We also test our belief-matching decoders in a theoretical case study of codes tailored to a biased noise model. We find that the decoders lead to a much higher threshold and lower qubit overhead in the tailored surface code with respect to the standard, square surface code. Surprisingly, in the well-below-threshold regime, the rectangular surface code becomes more resource efficient than the tailored surface code due to a previously unnoticed phenomenon that we call “fragile boundaries.” Our decoders outperform all other fast decoders in terms of threshold and accuracy, enabling better results in current quantum-error-correction experiments and opening up new areas for theoretical case studies.

We present a fast, hierarchical, and adaptive algorithm for Metropolis Monte Carlo simulations of systems with long-range interactions that reproduces the dynamics of a standard implementation exactly, i.e., the generated configurations and consequently all measured observables are identical, allowing in particular for nonequilibrium studies. The method is demonstrated for the power-law interacting long-range Ising and XY spin models with nonconserved order parameter and a Lennard-Jones particle system, all in two dimensions. The measured run times support an average complexity $O(N\log N)$, where $N$ is the number of spins or particles. Importantly, prefactors of this scaling behavior are small, which in practice manifests in speedup factors larger than ${10}^4$. The method is general and will allow the treatment of large systems that were out of reach before, likely enabling a more detailed understanding of physical phenomena rooted in long-range interactions.

We show how to define a quantized many-body charge polarization $\overrightarrow{𝒫}$ for $(2+1)\mathrm{D}$ topological phases of matter, even in the presence of nonzero Chern number and magnetic field. For invertible topological states, $\overrightarrow{𝒫}$ is a ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$, ${\mathbb{Z}}_3$, ${\mathbb{Z}}_2$, or ${\mathbb{Z}}_1$ topological invariant in the presence of ($M=2$, 3, 4, or 6)-fold rotational symmetry, lattice (magnetic) translational symmetry, and charge conservation. $\overrightarrow{𝒫}$ manifests in the bulk of the system as (i) a fractional quantized contribution of $\overrightarrow{𝒫}·\overrightarrow{b}\text{mod}1$ to the charge bound to lattice disclinations and dislocations with Burgers vector $\overrightarrow{b}$, (ii) a linear momentum for magnetic flux, and (iii) an oscillatory system size dependent contribution to the effective 1D polarization on a cylinder. We study $\overrightarrow{𝒫}$ in lattice models of spinless free fermions in a magnetic field. We derive predictions from topological field theory, which we match to numerical calculations for the effects (i)–(iii), demonstrating that these can be used to extract $\overrightarrow{𝒫}$ from microscopic models in an intrinsically many-body way. We show how, given a high symmetry point o, there is a topological invariant, the discrete shift ${𝒮}_{\mathrm{o}}$, such that $\overrightarrow{𝒫}$ specifies the dependence of ${𝒮}_{\mathrm{o}}$ on o. We derive colored Hofstadter butterflies, corresponding to the quantized value of $\overrightarrow{𝒫}$, which further refine the colored butterflies from the Chern number and discrete shift.

Based on the notion that the local dark-matter field of axions or axionlike particles (ALPs) in our Galaxy induces oscillating couplings to the spins of nucleons and nuclei (via the electric dipole moment of the latter and/or the paramagnetic axion-wind effect), we establish the feasibility of a new method to search for ALPs in storage rings. Based on previous work that allows us to maintain the in-plane polarization of a stored deuteron beam for a few hundred seconds, we perform a first proof-of-principle experiment at the Cooler Synchrotron (COSY) to scan momenta near $970\mathrm{MeV}/c$. This entails a scan of the spin-precession frequency. At resonance between the spin-precession frequency of deuterons and the ALP-induced electric dipole moment (EDM) oscillation frequency, there is an accumulation of the polarization component out of the ring plane. Since the axion frequency is unknown, the momentum of the beam and, consequently, the spin-precession frequency are ramped to search for a vertical polarization change that occurs when the resonance is crossed. At COSY, four beam bunches with different polarization directions are used to make sure that no resonance is missed because of the unknown relative phase between the polarization precession and the axion or ALP field. A frequency window of 1.5 kHz width around the spin-precession frequency of 121 kHz is scanned. We describe the experimental procedure and a test of the methodology with the help of a radio-frequency Wien filter located on the COSY ring. No ALP resonance is observed. As a consequence, an upper limit of the oscillating EDM component of the deuteron as well as its axion coupling constants are provided.

Pathological morphological changes in tumor tissue enable collective cancer cell unjamming, a cellular motility transition. However, fundamental questions remain: Is unjamming essential for tumor progression? Which different unjamming states can be found in patients? Here, vital cell tracking in patient-derived solid tumor explants ($N=16$) reveals that states of cell unjamming can be recognized by elongated cell and nucleus shape (CeNuS) and low nucleus number density. These static variables serve as a morphodynamic link to map the broad range of morphologies and associated motility states found in histological slides of 1380 breast cancer patients to generate a comprehensive state diagram of cancer cell unjamming. An increase in predicted cell motility in primary tumors through unjamming significantly correlates with distant metastases that may even occur a decade later. Patient risk groups are quantified via a decision boundary in the state space found by machine learning. The resulting clinical prognostic potential is evaluated using a range of quantifiers, including Harrel’s concordance index. Using multivariable Cox models, we find that cell unjamming as a prognostic parameter adds a 26% information gain in the concordance index when combined with the established prognostic criteria (tumor diameter, tumor grade, lymph node status) used in the Nottingham index. Unjamming complements the information on affected lymph nodes in patients regarding metastatic risk. The derived state diagram of cancer cell unjamming reconciles conflicting observations regarding shape- or density-induced unjamming and stresses the nuclei’s mechanical importance, which is not considered in current theories of cell unjamming. We conclude that cancer cell unjamming is part of the metastatic cascade; thus, an emergent physical phenomenon contributes to tumor progression.

The development of efficient techniques to distinguish mirror images of chiral molecules (enantiomers) is very important in both chemistry and physics. Enantiomers share most molecular properties except, for instance, the absorption of circularly polarized light. Enantiomer purification is therefore a challenging task that requires specialized equipment. Strong coupling between quantized fields and matter (e.g., in optical cavities) is a promising technique to modify molecular processes in a noninvasive way. The modulation of molecular properties is achieved by changing the field characteristics. In this work, we investigate whether strong coupling to circularly polarized electromagnetic fields is a viable way to discriminate chiral molecules. To this end, we develop a nonperturbative framework to calculate the behavior of molecules in chiral cavities. We show that in this setting the enantiomers have different energies—that is, one is more stable than the other. The field-induced energy differences are also shown to give rise to enantiospecific signatures in rotational spectra.

Cat states and Gottesman-Kitaev-Preskill (GKP) states play a key role in quantum computation and communication with continuous variables. The creation of such states relies on strong nonlinear light-matter interactions, which are widely available in microwave frequencies as in circuit quantum electrodynamics platforms. However, strong nonlinearities are hard to come by in optical frequencies, severely limiting the development and applications of quantum-information science with continuous variable in the optical range. Here we propose using the strong interaction of free electrons with light to implement the desired nonlinear mechanism, showing its implication by creating optical cat and GKP states. The key to our finding is identifying conditions on the electron for which its interaction mimics the conditional displacement quantum gate. The strong interactions can be realized by phase matching of free electrons with photonic structures such as optical waveguides and photonic crystals in an ultrafast transmission electron microscope (UTEM). Our approach enables the generation of optical GKP states with above 10 dB squeezing and fidelities above 90% at postselection probability of 10%, even reaching $>30\%$ using an initially squeezed-vacuum state. We analyze the different factors that affect the fidelity, such as electron dispersion, inhomogeneity, nonideal interaction, and limited detection efficiency. Furthermore, the free-electron interaction allows two qubit gates between a pair of GKP states, which can entangle them into a GKP Bell state. We present a roadmap for realizing such experiments in a UTEM. Since electrons can interact resonantly with light across the electromagnetic spectrum, our approach could apply for a generation of cat and GKP states also in other platforms of free-electron radiation, from klystrons to free-electron lasers.

The Mott-insulating phase of the two-dimensional (2D) Bose-Hubbard model is expected to be characterized by a nonlocal brane parity order. Parity order captures the presence of microscopic particle-hole fluctuations and entanglement, whose properties depend on the underlying lattice geometry. We realize 2D Bose-Hubbard models in dynamically tunable lattice geometries, using neutral atoms in a passively phase-stable tunable optical lattice in combination with programmable site-blocking potentials. We benchmark the performance of our system by single-particle quantum walks in the square, triangular, kagome, and Lieb lattices. In the strongly correlated regime, we microscopically characterize the geometry dependence of the quantum fluctuations and experimentally validate brane parity as a proxy for the nonlocal order parameter signaling the superfluid–to–Mott-insulating phase transition.

We lay the foundation of a circuit theory for chemical reaction networks. Chemical reactions are grouped into chemical modules solely characterized by their current-concentration characteristic—as electrical devices by their current-voltage ($\mathrm{I}\text{−}\mathrm{V}$) curve in electronic circuit theory. Combined with the chemical analog of Kirchhoff’s current and voltage laws, this provides a powerful tool to predict reaction currents and dissipation across complex chemical networks. The theory can serve to build accurate reduced models of complex networks as well as to design networks to perform desired tasks.

The modern thermodynamics of discrete systems is based on graph theory, which provides both algebraic methods to define observables and a geometric intuition of their meaning and role. However, because chemical reactions usually have many-to-many interactions, chemical networks are described by hypergraphs, which lack a systematized algebraic treatment and a clear geometric intuition. Here, we fill this gap by building fundamental bases of chemical cycles (encoding stationary behavior) and cocycles (encoding finite-time relaxation). We interpret them in terms of circulations and gradients on the hypergraph and use them to properly identify nonequilibrium observables. As an application, we unveil hidden symmetries in linear response and, within this regime, propose a reconstruction algorithm for large metabolic networks consistent with Kirchhoff’s voltage and current laws.

We demonstrate a superconducting artificial atom with strong unidirectional coupling to a microwave photonic waveguide. Our artificial atom is realized by coupling a transmon qubit to the waveguide at two spatially separated points with time-modulated interactions. Direction-sensitive interference arising from the parametric couplings in our scheme results in a nonreciprocal response, where we measure a forward/backward ratio of spontaneous emission exceeding 100. We verify the quantum nonlinear behavior of this artificial chiral atom by measuring the resonance fluorescence spectrum under a strong resonant drive and observing well-resolved Mollow triplets. Further, we demonstrate chirality for the second transition energy of the artificial atom and control it with a pulse sequence to realize a qubit-state-dependent nonreciprocal phase on itinerant photons. Our demonstration puts forth a superconducting hardware platform for the scalable realization of several key functionalities pursued within the paradigm of chiral quantum optics, including quantum networks with all-to-all connectivity, driven-dissipative stabilization of many-body entanglement, and the generation of complex nonclassical states of light.

Turing patterns, arising from the interplay between competing species of diffusive particles, have long been an important concept for describing nonequilibrium self-organization in nature and have been extensively investigated in many chemical and biological systems. Historically, these patterns have been studied in extended systems and lattices. Recently, the Turing instability was found to produce topological patterns in networks with scale-free degree distributions and the small-world property, although with an apparent absence of geometric organization. While hints of explicitly geometric patterns in simple network models (e.g., Watts-Strogatz) have been found, the question of the exact nature and morphology of geometric Turing patterns in heterogeneous complex networks remained unresolved. In this work, we study the Turing instability in the framework of geometric random graph models, where the network topology is explained using an underlying geometric space. We demonstrate that not only can geometric patterns be observed, their wavelength can also be estimated by studying the eigenvectors of the annealed graph Laplacian. Finally, we show that Turing patterns can be found in geometric embeddings of real networks. These results indicate that there is a profound connection between the function of a network and its hidden geometry, even when the associated dynamical processes are exclusively determined by the network topology.

Ferromagnetism is an iconic example of a first-order phase transition taking place in spatially extended systems and is characterized by hysteresis and the formation of domain walls. We demonstrate that an extended atomic superfluid in the presence of a coherent coupling between two internal states exhibits a quantum phase transition from a paramagnetic to a ferromagnetic state. The nature of the transition is experimentally assessed by looking at the phase diagram as a function of the control parameters, at hysteresis phenomena, and at the magnetic susceptibility and the magnetization fluctuations around the critical point. We show that the observed features are in good agreement with mean-field calculations. Additionally, we develop experimental protocols to deterministically generate domain walls that separate spatial regions of opposite magnetization in the ferromagnetic state. Thanks to the enhanced coherence properties of our atomic superfluid system compared to standard condensed matter systems, our results open the way toward the study of different aspects of the relaxation dynamics in isolated coherent many-body quantum systems.

Transitions between the extreme angular-momentum states of alkali D lines hold the potential for enabling accurate high-field optical magnetometry because of their very simple magnetic field dependence described only by a linear and a quadratic term, characterized by the two coefficients ${\gamma }_1$ and ${\gamma }_2$. Here, we present very accurate measurements of these coefficients, for the cesium ${\mathrm{D}}_2$ line, thereby overcoming a major obstacle for the realization of this future technology. By means of saturated absorption spectroscopy on a cesium gas, in 3 T and 7 T magnetic fields, we measure the linear magnetic frequency shift of the transition to be ${\gamma }_1=13.994301(11)\mathrm{GHz}/\mathrm{T}$. This measurement corresponds to an optical magnetic field determination of better than 1 ppm accuracy. From this value, we can calculate the fine-structure Landé g-factor $g_J(6^2{P}_{3/2})=1.33408749(52)$. This result is consistent with the previous best measurement, and it improves the accuracy by more than 2 orders of magnitude. We also measure, for the first time, the quadratic diamagnetic shift as ${\gamma }_2=0.4644(35)\mathrm{MHz}/{\mathrm{T}}^2$. Our work opens up the field of accurate high-field optical magnetometry using atomic cesium, with possible applications in, e.g., medical MRI, fusion reactors, and particle accelerators. These high-accuracy measurements also allow for testing of advanced atomic structure models, as our results are incompatible with the Russel-Saunders coupling value and the hydrogen-constant-core-model value by 31 and 7 standard deviations, respectively.

Gravitational-wave observations of extreme mass ratio inspirals (EMRIs) offer the opportunity to probe the environments of active galactic nuclei (AGN) through the torques that accretion disks induce on the binary. Within a Bayesian framework, we study how well such environmental effects can be measured using gravitational wave observations from the Laser Interferometer Space Antenna (LISA). We focus on the torque induced by planetary-type migration on quasicircular inspirals and use different prescriptions for geometrically thin and radiatively efficient disks. We find that LISA could detect migration for a wide range of disk viscosities and accretion rates, for both $\alpha$ and $\beta$ disk prescriptions. For a typical EMRI with masses $50M_{\odot }+{10}^6{M}_{\odot }$, we find that LISA could distinguish between migration in $\alpha$ and $\beta$ disks and measure the torque amplitude with $\sim 20\%$ relative precision. Provided an accurate torque model, we also show how to turn gravitational-wave measurements of the torque into constraints on the disk properties. Furthermore, we show that, if an electromagnetic counterpart is identified, the multimessenger observations of the AGN EMRI system will yield direct measurements of the disk viscosity. Finally, we investigate the impact of neglecting environmental effects in the analysis of the gravitational-wave signal, finding $3\sigma$ biases in the primary mass and spin, and showing that ignoring such effects can lead to false detection of a deviation from general relativity. This work demonstrates the scientific potential of gravitational observations as probes of accretion-disk physics, accessible so far through electromagnetic observations only.