The Petermann factor and the phase rigidity are convenient measures for various aspects of open quantum and wave systems, such as the sensitivity of energy eigenvalues to perturbations or the magnitude of quantum excess noise in lasers. We discuss the behavior of these two important quantities near non-Hermitian degeneracies, so-called exceptional points. For small generic perturbations, we derive analytically explicit formulas, which reveal a relation to the spectral response strength of the exceptional point. These formulas shed light on the possibilities for enhanced sensing in passive systems. The predictions of the general theory are successfully compared to analytical solutions of a toy model. Moreover, it is demonstrated that the connection between the Petermann factor and the spectral response strength provides the basis for an efficient numerical scheme to calculate the latter. Our theory is also important in the presence of the unavoidable imperfections in the fabrication of exceptional points as it allows to determine of what is left of the sensitivity for such imperfect exceptional points studied in experiments.

Differentiable programming has emerged as a key programming paradigm empowering rapid developments of deep learning while its applications to important computational methods such as Monte Carlo remain largely unexplored. Here we present the general theory enabling infinite-order automatic differentiation on expectations computed by Monte Carlo with unnormalized probability distributions, which we call automatic differentiable Monte Carlo (ADMC). By implementing ADMC algorithms on computational graphs, one can also leverage state-of-the-art machine learning frameworks and techniques in traditional Monte Carlo applications in statistics and physics. We illustrate the versatility of ADMC by showing some applications: fast search of phase transitions and accurately finding ground states of interacting many-body models in two dimensions. ADMC paves a promising way to innovate Monte Carlo in various aspects to achieve higher accuracy and efficiency.

Stacking-dependent physics is emerging as a fascinating research topic for two-dimensional materials. A variety of novel properties can be achieved by layer stacking according to different modes. However, most of the studies focus on the impact of electronic, superconducting, optical, and magnetic properties. In this work, we have systematically studied the stacking-dependent topological quantum states in bilayer ${\mathrm{Mn}}_2{\mathrm{Cl}}_3{\mathrm{Br}}_3$ by the first-principles electronic structure calculations. Here, ferromagnetic layer coupling is always favored in different stacking modes. Many exotic topological quantum states, such as topological nodal-ring spin-gapless semimetal state, spin-valley polarized quantum valley Hall (SVP-QVH) effect, and high Chern number quantum anomalous Hall effect can be realized in this single system. Among these states, the SVP-QVH is a new topological phase discovered for the first time, in which there are two topologically protected gapless chiral edge states that carry the same spin, localize respectively on the two polarized valleys, and propagate in opposite directions along the edges. The spin-valley polarized anomalous valley Hall effect can be further realized with electron doping or gate tuning, resulting in edge states that integrate multiple degrees of freedom of valley, spin, and charge. Our research therefore provides an idea for discovery of new topological phases and design of two-dimensional multifunctional electronic, spintronic, and topological devices.

The physics of long-range-interacting quantum systems is currently living through a renaissance driven by the fast progress in quantum simulators. In these systems many paradigms of statistical physics do not apply and also the universal long-wavelength physics gets substantially modified by the presence of long-ranged forces. Here we explore the low-energy excitations of several long-range-interacting quantum systems, including spin models and interacting Bose gases, in the ordered phase associated with the spontaneous breaking of U(1) and SU(2) symmetries. Instead of the expected Goldstone modes, we find three qualitatively different regimes, depending on the range of the interaction. In one of these regimes the Goldstone modes are gapped, via a generalization of the Higgs mechanism. Moreover, we show how this effect is realized in current experiments with ultracold atomic gases in optical cavities.

For studies on thermalization of an isolated quantum many-body system, the fundamental issue is to determine whether a given system thermalizes or not. However, most studies tested only a small number of observables, and it was unclear whether other observables thermalize. Here, we study whether “linear thermalization” occurs for all additive observables: We consider a quantum many-body system prepared in an equilibrium state and its unitary time evolution induced by a small change $\mathrm{\Delta }f$ of a physical parameter $f$ of the Hamiltonian, and examine whether all additive observables relax to the equilibrium values in a manner fully consistent with thermodynamics up to the linear order in $\mathrm{\Delta }f$. We find that the additive observable conjugate to $f$ is key for linear thermalization in that its linear thermalization guarantees, under physically reasonable conditions, linear thermalization of all additive observables. Such a linear thermalization occurs in the timescale of $\mathcal{O}\left(\right|\mathrm{\Delta }f{|}^0)$, and lasts at least for a period of $o(1/\sqrt{\left|\mathrm{\Delta }f\right|})$. We also consider linear thermalization against the change of other parameters, and find that linear thermalization of the key observable against $\mathrm{\Delta }f$ guarantees its linear thermalization against small changes of any other parameters. Furthermore, we discuss the generalized susceptibilities for cross responses and their consistency between quantum mechanics and thermodynamics. We demonstrate our main result by performing numerical calculations for spin models. The present paper offers an efficient way of judging linear thermalization because it guarantees that examination of the single key observable is sufficient.

We consider the implementation of quantum logic gates in trapped ions using tightly focused optical tweezers. Strong polarization gradients near the tweezer focus lead to qubit-state-dependent forces on the ion. We show that these may be used to implement quantum logic gates on pairs of ion qubits in a crystal. The qubit-state-dependent forces generated by this effect are located on the plane perpendicular to the direction of propagation of the laser beams opening alternate ways of coupling to motional modes of an ion crystal. The proposed gate does not require ground-state cooling of the ions although the waist of the tightly focused beam needs to be comparable to its wavelength in order to achieve the needed field curvature. Furthermore, the gate can be implemented on both ground-state and magnetic-field-insensitive clock-state qubits without the need for counterpropagating laser fields. This simplifies the setup and eliminates errors due to phase instabilities between the gate laser beams. Finally, we show that imperfections in the gate execution, in particular, a 30-nm tweezer alignment error, lead to an infidelity of $\sim {10}^{-3}$. In the absence of experimental imperfections and within the limits of the gate model explored in this paper the fidelity is predicted to be $\sim 0.99988$ when using a Laguerre-Gaussian beam to suppress photon scattering errors.

A fruitful approach towards neuromorphic computing is to mimic mechanisms of the brain in physical devices, which has led to successful replication of neuronlike dynamics and learning in the past. However, there remains a large set of neural self-organization mechanisms whose role for neuromorphic computing has yet to be explored. One such mechanism is homeostatic plasticity, which has recently been proposed to play a key role in shaping network dynamics and correlations. Here, we study—from a statistical-physics point of view—the emergent collective dynamics in a homeostatically regulated neuromorphic device that emulates a network of excitatory and inhibitory leaky integrate-and-fire neurons. Importantly, homeostatic plasticity is only active during the training stage and results in a heterogeneous weight distribution that we fix during the analysis stage. We verify the theoretical prediction that reducing the external input in a homeostatically regulated neural network increases temporal correlations, measuring autocorrelation times exceeding $500\mathrm{m}\mathrm{s}$, despite single-neuron timescales of only $20\mathrm{m}\mathrm{s}$, both in experiments on neuromorphic hardware and in computer simulations. However, unlike theoretically predicted near-critical fluctuations, we find that temporal correlations can originate from an emergent bistability. We identify this bistability as a fluctuation-induced stochastic switching between metastable active and quiescent states in the vicinity of a nonequilibrium phase transition. Our results thereby constitute a complementary mechanism for emergent autocorrelations in networks of spiking neurons with implications for future developments in neuromorphic computing.

Reinforcement learning has revolutionized our understanding of evolved systems and our ability to engineer systems based on a theoretical framework for understanding how to maximize expected reward. However, time delays between the observation and action are estimated to be roughly $\sim 150\mathrm{ms}$ for humans, and this should affect reinforcement learning algorithms. We reformulate the Markov Decision Process framework to include time delays in action, first deriving a new Bellman equation in a way that unifies previous attempts and then implementing the corresponding SARSA-like algorithm. The main ramification—potentially useful for both evolved and engineered systems—is that, when the size of the state space is lower than that of the action space, the modified reinforcement learning algorithms will prefer to operate on sequences of states rather than just the present state with the length of the sequence equal to 1 plus the time delay.

The bulk helimagnet ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ represents a unique example in the family of B20 cubic helimagnets exhibiting a tilted spiral and skyrmion phase at low temperatures when the magnetic field is applied along the easy $\langle 001\rangle$ crystallographic direction. Here we present a systematic study of the stability and ordering of these low-temperature magnetic states. We focus our attention on the temperature and field dependencies of the tilted spiral state that we observe persisting up to above $T=35 \mathrm{K}$, i.e., up to higher temperatures than reported so far. We discuss these results in the frame of the phenomenological theory introduced by Dzyaloshinskii in an attempt to reach a quantitative description of the experimental findings. We find that the anisotropy constants, which are the drivers behind the observed behavior, exhibit a pronounced temperature dependence. This explains the differences in the behavior observed at high temperatures (above $T=18 \mathrm{K}$), where the cubic anisotropy is weak, and at low temperatures (below $T=18 \mathrm{K}$), where a strong cubic anisotropy induces an abrupt appearance of the tilted spirals out of the conical state and enhances the stability of skyrmions.

Highly excited Rydberg atoms inherit their level structure, symmetries, and scaling behavior from the hydrogen atom. We demonstrate that these fundamental properties enable a thermodynamic limit of a single Rydberg atom subjected to interactions with nearby ground-state atoms. The limit is reached by simultaneously increasing the number of ground-state atoms and the level of excitation of the Rydberg atom, for which the Coulomb potential supplies infinitely many and highly degenerate excited states. Our study reveals a surprising connection to an archetypal concept of condensed matter physics, Anderson localization, facilitated by a direct mapping between the Rydberg atom's electronic spectrum and the spectrum of a tight-binding Hamiltonian. The hopping amplitudes of this tight-binding system are determined by the arrangement of ground-state atoms and can range from oscillatory and long-ranged to nearest-neighbor. In the latter we identify clear signatures of the Anderson localization of the Rydberg electron.

Topologically-ordered phases of matter at nonzero temperature are conjectured to exhibit universal patterns of long-range entanglement, which can be detected using the entanglement negativity, a mixed-state entanglement measure. In this paper, we show that the entanglement negativity in certain topological orders can be understood through the properties of an emergent symmetry-protected topological (SPT) order that is localized on the entanglement bipartition. This connection leads to an understanding of (i) universal contributions to the entanglement negativity, which diagnose finite-temperature topological order and (ii) the behavior of the entanglement negativity across certain phase transitions in which thermal fluctuations eventually destroy long-range entanglement across the bipartition surface. Within this correspondence, the universal patterns of entanglement in the finite-temperature topological order are related to the stability of an emergent SPT order against a symmetry-breaking field. SPT orders protected by higher-form symmetries—which arise, for example, in the description of the entanglement negativity for ${\mathbb{Z}}_2$ topological order in $d=4$ spatial dimensions—remain robust even in the presence of a weak symmetry-breaking perturbation, leading to long-range entanglement at nonzero temperature for certain topological orders.

The Green's function plays an important role in many areas of physical sciences and is a prime tool for solving diverse hydrodynamic equations in the linear regime. In the present contribution, the axisymmetric low-Reynolds-number Brinkman flow induced by monopole and dipole singularities in proximity of a stationary plate of circular shape is theoretically investigated. The flow singularities are directed along the central axis of the plate. No-slip boundary conditions are assumed to hold at the surface of the plate. The Green's functions are determined to a large extent analytically, reducing the solution of the linear hydrodynamic equations to well-behaved one-dimensional integrals amenable to numerical computation. In our approach, the Brinkman flow problem is formulated as a mixed boundary value problem that is subsequently mapped in the form of dual integral equations on the domain boundaries. Thereupon, the solution of the equations of fluid motion is eventually reduced to the solution of two independent Fredholm integral equations of the first kind. The overall flow structure and emerging eddy patterns are found to strongly depend on the magnitude of the relevant geometrical and physical parameters of the system. Moreover, the effect of the confining plate on the dynamics of externally driven or force-free particles is assessed through the calculation of the relevant hydrodynamic reaction functions. The effect of the plate on the locomotory behavior of a self-propelling active dipole swimmer is shown to be maximum when the radius of the plate is comparable to the distance separating the swimmer from the plate. Our results may prove useful for characterizing transport processes in microfluidic devices and may pave the way toward understanding and controlling of small-scale flows in porous media.

The first principles of electromagnetism impose that the tangential electric field must be continuous at the interface between two media. The definition of the electric field depends on the frame of reference, leading to an ambiguity in the mathematical expression of the continuity condition when the two sides of the interface do not share the same rest frame. We briefly review the arguments supporting each choice of interface condition and illustrate how the most theoretically consistent choice leads to a paradox in induction experiments. We then present a model of sliding contact between two solids and between a fluid and a solid and show how this paradox can be lifted by taking into account the shear induced by the differential motion in a thin intermediate viscous layer at the interface, thereby also lifting the ambiguity in the electric interface condition. We present some guidelines regarding the appropriate interface condition to employ in magnetohydrodynamics applications, in particular for numerical simulations in which sliding contact is used as an approximation of the viscous interface between a conducting solid and a fluid of very low viscosity such as in planetary interior simulations.