We present a general theory of classical metastability in open quantum systems. Metastability is a consequence of a large separation in timescales in the dynamics, leading to the existence of a regime when states of the system appear stationary, before eventual relaxation toward a true stationary state at much larger times. In this work, we focus on the emergence of classical metastability, i.e., when metastable states of an open quantum system with separation of timescales can be approximated as probabilistic mixtures of a finite number of states. We find that a number of classical features follow from this approximation, for the manifold of metastable states, long-time dynamics between them, and symmetries of the dynamics. Namely, those states are approximately disjoint and thus play the role of metastable phases, the relaxation toward the stationary state is approximated by a classical stochastic dynamics between them, and weak symmetries correspond to their permutations. Importantly, the classical dynamics is observed not only on average but also at the level of individual quantum trajectories: We show that time coarse-grained continuous measurement records can be viewed as noisy classical trajectories, while their statistics can be approximated by that of the classical dynamics. Among others, this explains how first-order dynamical phase transitions arise from metastability. Finally, to verify the presence of classical metastability in a given open quantum system, we develop an efficient numerical approach that delivers the set of metastable phases together with the effective classical dynamics. Since the proximity to a first-order dissipative phase transition manifests as metastability, the theory and tools introduced in this work can be used to investigate such transitions—which occur in the large size limit—through the metastable behavior of many-body systems of moderate sizes accessible to numerics.

In ${\mathrm{BaV}}_{10}{\mathrm{O}}_{15}$ with quasitriangular V lattices, we found unique superstructures characterized by $\left(qq0\right)$-type peaks in the momentum space, where $q$ varies continuously with temperature between $q=0$ and $1/3$ and locks at $1/3$. Such a threefold superstructure is likely caused by the dense arrangement of the V trimers associated with the orbital ordering of V. The results indicate that the superstructure of the V trimers, each of which is also a superstructure, gives rise to the ordered phases with peculiar characteristics.

We study the generalization of the three-dimensional two-band Hopf insulator to the case of many bands, where all the bands are separated from each other by band gaps. The obtained $\mathbb{Z}$ classification of such an $N$-band Hopf insulator is related to the quantized isotropic magnetoelectric coefficient of its bulk. The boundary of an $N$-band Hopf insulator can be fully gapped, and we find that there is no unique way of dividing a finite system into bulk and boundary. Despite this nonuniqueness, we find that the magnetoelectric coefficient of the bulk and the anomalous Hall conductivity of the boundary are quantized to the same integer value. We propose an experiment where the quantized boundary effect can be measured in a nonequilibrium state.

Adiabatically exchanging anyons gives rise to topologically protected operations on the quantum state of the system, but the desired result is only achieved if the anyons are well separated, which requires a sufficiently large area. Being able to reduce the area needed for the exchange, however, would have several advantages such as enabling a larger number of operations per area and allowing anyon exchange to be studied in smaller systems that are easier to handle. Here, we use optimization techniques to squeeze the charge distribution of Abelian anyons in lattice fractional quantum Hall models, and we show that the squeezed anyons can be exchanged within a smaller area with a close to ideal outcome. We first use a toy model consisting of a modified Laughlin trial state to show that one can shape the anyons without altering the exchange statistics under certain conditions. We then squeeze and braid anyons in the Kapit-Mueller model and an interacting Hofstadter model by adding suitable potentials. We consider a fixed system size, for which the charge distributions of the normal anyons overlap, and we find that the outcome of the exchange process is closer to the ideal value for the squeezed anyons. The time needed for the exchange is also important, and for a particular example we find that the duration needed for the process to be close to the adiabatic limit is about five times longer for the squeezed anyons when the path length is the same. Finally, we show that the exchange outcome is robust with respect to small modifications of the potential away from the optimized value.

As strength of disorder enhances beyond a threshold value in many-body systems, a fundamental transformation happens through which the entire spectrum localizes, a phenomenon known as many-body localization. This has profound implications as it breaks down fundamental principles of statistical mechanics, such as thermalization and ergodicity. Due to the complexity of the problem, the investigation of the many-body localization transition has remained a big challenge. The experimental exploration of the transition point is even more challenging as most of the proposed quantities for studying such an effect are practically infeasible. Here, we experimentally implement a scalable protocol for detecting the many-body localization transition point, using the dynamics of an $N=12$ superconducting qubit array. We show that the sensitivity of the dynamics to random samples becomes maximum at the transition point, which leaves its fingerprints in all spatial scales. By exploiting three quantities, each with a different spatial resolution, we identify the transition point with an excellent match between simulation and experiment. In addition, one can detect the evidence of a mobility edge through slight variation of the transition point as the initial state varies. The protocol is easily scalable and can be performed across various physical platforms.

Topological edge modes, which are robust against disorders, have been used to enhance the spatial stability of lasers. Recently, it was revealed that topological lasers can be further stabilized using a topological phase in non-Hermitian photonic topological insulators. Here we propose a procedure to realize topologically protected modes extended over a $d$-dimensional bulk by introducing an imaginary gauge field. This generalizes the idea of zero-energy extended modes in the one-dimensional Su-Schrieffer-Heeger lattice into higher dimensional lattices, allowing a $d$-dimensional bulk mode that is topologically protected. Furthermore, we numerically demonstrate that the topological bulk lasing mode can facilitate high temporal stability superior to topological edge-mode lasers. Using an exemplified topological extended mode in the kagome lattice, we show that large regions of stability exist in its parameter space.

Neurons are traditionally grouped in two excitability classes, which correspond to two different responses to external inputs, called phase response curves (PRCs). In this paper we have considered a network of two neural populations with delayed couplings, bound in a negative feedback loop by a positive PRC (type I). Making use of both analytical and numerical techniques, we derived the boundaries of stable incoherence in the continuum limit, studying their dependance on the time delay and the strengths of both interpopulation and intrapopulation couplings. This led us to discover, in a system with stronger delayed external compared to internal couplings, the coexistence of areas of coherence and incoherence, called chimera states, that were robust to noise. On the other hand, in the absence of time delays and with negligible internal couplings, the system portrays a family of neutrally stable periodic orbits, known as “breathing chimeras.”

We derive a unified amplitude-phase decomposition for both noisy limit cycles and quasicycles; in the latter case, the oscillatory motion has no deterministic counterpart. We extend a previous amplitude-phase decomposition approach using the stochastic averaging method (SAM) for quasicycles by taking into account nonlinear terms up to order 3. We further take into account the case of coupled networks where each isolated network can be in a quasi- or noisy limit-cycle regime. The method is illustrated on two models which exhibit a deterministic supercritical Hopf bifurcation: the Stochastic Wilson-Cowan model of neural rhythms, and the Stochastic Stuart-Landau model in physics. At the level of a single oscillatory module, the amplitude process of each of these models decouples from the phase process to the lowest order, allowing a Fokker-Planck estimate of the amplitude probability density. The peak of this density captures well the transition between the two regimes. The model describes accurately the effect of Gaussian white noise as well as of correlated noise. Bursting epochs in the limit-cycle regime are in fact favored by noise with shorter correlation time or stronger intensity. Quasicycle and noisy limit-cycle dynamics are associated with, respectively, Rayleigh-type and Gaussian-like amplitude densities. This provides an additional tool to distinguish quasicycle from limit-cycle origins of bursty rhythms. The case of multiple oscillatory modules with excitatory all-to-all delayed coupling results in a system of stochastic coupled amplitude-phase equations that keeps all the biophysical parameters of the initial networks and again works across the Hopf bifurcation. The theory is illustrated for small heterogeneous networks of oscillatory modules. Numerical simulations of the amplitude-phase dynamics obtained through the SAM are in good agreement with those of the original oscillatory networks. In the deterministic and nearly identical oscillators limits, the stochastic Stuart-Landau model leads to the stochastic Kuramoto model of interacting phases. The approach can be tailored to networks with different frequency, topology, and stochastic inputs, thus providing a general and flexible framework to analyze noisy oscillations continuously across the underlying deterministic bifurcation.

The purpose of fingerprinting is to compare long messages with low communication complexity. Compared with its classical version, quantum fingerprinting can realize exponential reduction in communication complexity. Recently, multiparty quantum fingerprinting is studied to determine whether the messages from many parties are all the same. However, the complete relationships among them, including which ones are the same, are more general for future applications. Here, we propose the relationship state $\mathcal{G}$ to describe all possible relationships among $N$ messages. Based on this, we provide a general quantum fingerprinting network and then take the four-party quantum fingerprinting protocol as an example for detailed analysis. We take the full parameter optimization for the quantum fingerprinting protocol through asymmetric channel. The method of encoding more than one bit on each coherent state is used to further improve the performance of our protocol. Compared with other protocols, our protocol provides more relationships among different parties with only linear increase in communication complexity.

Randomized benchmarking is a powerful technique to efficiently estimate the performance and reliability of quantum gates, circuits, and devices. Here, we propose to perform randomized benchmarking in a coherent way, where superpositions of different random sequences rather than independent samples are used. We show that this leads to a uniform and simple protocol having significant advantages with respect to gates that can be benchmarked, and in terms of efficiency and scalability. We show that, e.g., universal gate sets, the set of $n$-qudit Pauli operators or more general sets including arbitrary unitaries, as well as a particular $n$-qudit Clifford gate using only the Pauli set, can be efficiently benchmarked. The price to pay is an additional complexity to add control to the involved quantum operations. However, we demonstrate that this can be done by using auxiliary degrees of freedom that are naturally available in basically any physical realization, and are independent of the gates to be tested.

We measure the colloidal interaction between two silica microspheres in an aqueous solution in the distance range from 0.2 to $0.5\mu \mathrm{m}$ with the help of optical tweezers. When employing a sample with a low salt concentration, the resulting interaction is dominated by the repulsive double-layer interaction which is fully characterized. The double-layer interaction is suppressed when adding $0.22\mathrm{M}$ of salt to our sample, thus leading to a purely attractive Casimir signal. When analyzing the experimental data for the potential energy and force, we find good agreement with theoretical results based on the scattering approach. At the distance range probed experimentally, the interaction arises mainly from the unscreened transverse magnetic contribution in the zero-frequency limit, with nonzero Matsubara frequencies providing a negligible contribution. In contrast, such unscreened contribution is not included by the standard theoretical model of the Casimir interaction in electrolyte solutions, in which the zero-frequency term is treated separately as an electrostatic fluctuational effect. As a consequence, the resulting attraction is too weak in this standard model, by approximately one order of magnitude, to explain the experimental data. Overall, our experimental results shed light on the nature of the thermal zero-frequency contribution and indicate that the Casimir attraction across polar liquids has a longer range than previously predicted.

Understanding magnonic properties of nonperiodic magnetic nanostructures requires real-space imaging of ferromagnetic resonance modes with spatial resolution well below the optical diffraction limit and sampling rates in the 5–100 GHz range. Here, we demonstrate element-specific scanning transmission x-ray microscopy-detected ferromagnetic resonance (STXM-FMR) applied to a chain of dipolarly coupled ${\mathrm{Fe}}_3{\mathrm{O}}_4$ nano-particles (40–50 nm particle size) inside a single cell of a magnetotactic bacterium Magnetospirillum magnetotacticum. The ferromagnetic resonance mode of the nano-particle chain driven at 6.748 GHz and probed with 50 nm x-ray focus size was found to have a uniform phase response but non-uniform amplitude response along the chain segments due to the superposition of dipolar coupled modes of chain segments and individual particles, in agreement with micromagnetic simulations.

We experimentally emulate interaction induced blockade and local spin freezing in two and three qubit NMR architecture. These phenomena are identical to the Rydberg blockade and Rydberg biased freezing. In Rydberg blockade, the simultaneous excitation of two or more atoms is blocked due to the level shift induced by the strong van der Waal's interaction. In such a strong interaction regime, one can also observe Rydberg biased freezing, wherein the dynamics is confined to a subspace, with the help of multiple drives with unequal amplitudes. Here we drive NMR qubits with specific transition-selective radio waves, while intermittently characterizing the quantum states via quantum state tomography. This not only allows us to track the population dynamics, but also helps to probe quantum correlations, by means of quantum discord, evolving under blockade and freezing phenomena. Our work constitutes experimental simulations of these phenomena in the NMR platform. Moreover, these studies open up interesting quantum control perspectives in exploiting the above phenomena for entanglement generation as well as subspace manipulations.

We present measurements of the spatiotemporal evolution of a hot-dense plasma generated by the interaction of an intense 25 fs laser pulse with a solid target, using pump-probe two-dimensional (2D) Doppler spectrometry. Measuring the time-dependent Doppler shifts at different positions across the probe beam, we achieve velocity mapping at hundreds of femtoseconds time resolution simultaneously with a few micrometer spatial resolution across the transverse length of the plasma. Simulations of the interaction using a combination of 2D particle-in-cell and 2D radiation hydrodynamics codes agree well with the experiment.

Using determinant quantum Monte Carlo, we compare three methods of evaluating the dc Hall coefficient $R_H$ of the Hubbard model: the direct measurement of the off-diagonal current-current correlator ${\chi }_{xy}$ in a system coupled to a finite magnetic field (FF), ${\chi }_{xy}^{\text{FF}}$; the three-current linear response to an infinitesimal field as measured in the zero-field (ZF) Hubbard Hamiltonian, ${\chi }_{xy}^{\text{ZF}}$; and the leading order of the recurrent expansion $R_H^{\left(0\right)}$ in terms of thermodynamic susceptibilities. The two quantities ${\chi }_{xy}^{\text{FF}}$ and ${\chi }_{xy}^{\text{ZF}}$ can be compared directly in imaginary time. Proxies for $R_H$ constructed from the three-current correlator ${\chi }_{xy}^{\text{ZF}}$ can be determined under different simplifying assumptions and compared with $R_H^{\left(0\right)}$. We find these different quantities to be consistent with one another, validating previous conclusions about the close correspondence between Fermi surface topology and the sign of $R_H$, even for strongly correlated systems. These various quantities also provide a useful set of numerical tools for testing theoretical predictions about the full behavior of the Hall conductivity for strong correlations.