Nonreciprocal Interaction Research Articles

Nonreciprocal synchronization in embryonic oscillator ensembles

Synchronization of coupled oscillators is a universal phenomenon encountered across different scales and contexts, e.g., chemical wave patterns, superconductors, and the unison applause we witness in concert halls. The existence of common underlying coupling rules defines universality classes, revealing a fundamental sameness between seemingly distinct systems. Identifying rules of synchronization in any particular setting is hence of paramount relevance. Here, we address the coupling rules within an embryonic oscillator ensemble linked to vertebrate embryo body axis segmentation. In vertebrates, the periodic segmentation of the body axis involves synchronized signaling oscillations in cells within the presomitic mesoderm (PSM), from which somites, the prevertebrae, form. At the molecular level, it is known that intact Notch-signaling and cell-to-cell contact are required for synchronization between PSM cells. However, an understanding of the coupling rules is still lacking. To identify these, we develop an experimental assay that enables direct quantification of synchronization dynamics within mixtures of oscillating cell ensembles, for which the initial input frequency and phase distribution are known. Our results reveal a "winner-takes-it-all" synchronization outcome, i.e., the emerging collective rhythm matches one of the input rhythms. Using a combination of theory and experimental validation, we develop a coupling model, the "Rectified Kuramoto" (ReKu) model, characterized by a phase-dependent, nonreciprocal interaction in the coupling of oscillatory cells. Such nonreciprocal synchronization rules reveal fundamental similarities between embryonic oscillators and a class of collective behaviors seen in neurons and fireflies, where higher-level computations are performed and linked to nonreciprocal synchronization.

One-way optomechanical interaction between nanoparticles

Within a closed system, physical interactions are reciprocal. However, the effective interaction between two entities of an open system may not obey reciprocity. Here, we describe a non-reciprocal interaction between nanoparticles which is one-way, almost insensitive to the interparticle distance, and scalable to many particles. The interaction we propose is based on the non-conservative optical forces between two nanoparticles with highly directional scattering patterns. However, we elucidate that scattering patterns can in general be very misleading about the interparticle forces. We introduce zeroth- and first-order non-reciprocity factors to precisely quantify the merits of any optomechanical interaction between nanoparticles. Our proposed one-way interaction could constitute an important step in the realization of mesoscopic heat pumps and refrigerators, the study of non-equilibrium systems, and the simulation of non-Hermitian quantum models.

Dispersive nonreciprocity between a qubit and a cavity.

The dispersive interaction between a qubit and a cavity is ubiquitous in circuit and cavity quantum electrodynamics. It describes the frequency shift of one quantum mode in response to excitations in the other and, in closed systems, is necessarily bidirectional, i.e., reciprocal. Here, we present an experimental study of a nonreciprocal dispersive-type interaction between a transmon qubit and a superconducting cavity, arising from a common coupling to dissipative intermediary modes with broken time reversal symmetry. We characterize the qubit-cavity dynamics, including asymmetric frequency pulls and photon shot noise dephasing, under varying degrees of nonreciprocity by tuning the magnetic field bias of a ferrite component in situ. We introduce a general master equation model for nonreciprocal interactions in the dispersive regime, providing a compact description of the observed qubit-cavity dynamics agnostic to the intermediary system. Our result provides an example of quantum nonreciprocal phenomena beyond the typical paradigms of non-Hermitian Hamiltonians and cascaded systems.

Nonreciprocal interactions in crowd dynamics: Investigating the impact of moving threats on pedestrian speed preferences

Nonreciprocal interaction crowd systems, such as human–human, human–vehicle, and human–robot systems, often have serious impacts on pedestrian safety and social order. A more comprehensive understanding of these systems is needed to optimize system stability and efficiency. Despite the importance of these interactions, empirical research in this area remains limited. Thus, in our study we explore this underresearched area, focusing on scenarios where nonreciprocity plays a critical role, such as mass stabbings, which pose a substantial risk to public safety. We conducted the first experiments on this system and analysed high-accuracy data obtained from these experiments. Specifically, we conduct laboratory experiments on three scenarios: single exits, dual exits, and obscured chases. Then, we introduce an equation to describe the mechanism behind a direct threat zone, which significantly affects pedestrian behaviour. The extent of the direct threat zone is determined by the speed of the moving threat and the radius of danger occurrence. The equation can provide insights for different nonreciprocal interaction crowd systems, where the subjects of the nonreciprocal interactions can be a pedestrian, an autonomous robot or a vehicle. We further categorize potential threats into direct, adjacent, and rear-view zones, quantifying the level of threat for pedestrians. Our study revealed that a pedestrian’s desired velocity correlated positively with potential threat intensity, increasing until near the direct threat zone. An emerging steady state is observed when escape routes are blocked by moving threats. This deviation affects the density–velocity relationship, making it distinct from the general relationship. This deviation signifies unique pedestrian behaviour in the presence of moving threats. Additionally, the rate of change in the angle for pedestrian motion in various desired directions is synchronized. This indicates the emergence of collective intelligence in nonreciprocal interaction crowd systems. As a result, our study may constitute a pioneering step towards understanding nonreciprocal interactions in crowd systems through laboratory experiments. These findings may enhance pedestrian safety and inform not only government crowd management strategies but also individual self-protection measures.

Emergent Chirality and Hyperuniformity in an Active Mixture with Nonreciprocal Interactions.

We investigate collective dynamics in a binary mixture of programmable robots in experiments and simulations. While robots of the same species align their motion direction, interaction between species is distinctly nonreciprocal: species A aligns with B and species B antialigns with A. This nonreciprocal interaction gives rise to the emergence of collective chiral motion that can be stabilized by limiting the robot angular speed to be below a threshold. Within the chiral phase, increasing the robot density or extending the range of local repulsive interactions can drive the system through an absorbing-active transition. At the transition point, the robots exhibit a remarkable capacity for self-organization, forming disordered hyperuniform states.

Solvable non-Hermitian skin effects and real-space exceptional points: non-Hermitian generalized Bloch theorem

Non-Hermitian systems can exhibit extraordinary boundary behaviors, known as the non-Hermitian skin effects, where all the eigenstates are localized exponentially at one side of lattice model. To give a full understanding and control of non-Hermitian skin effects, we have developed the non-Hermitian generalized Bloch theorem to provide the analytical expression for all solvable eigenvalues and eigenstates, in which translation symmetry is broken due to the open boundary condition. By introducing the Vieta’s theorem for any polynomial equation with arbitrary degree, our approach is widely applicable for one-dimensional non-Hermitian tight-binding models. With the non-Hermitian generalized Bloch theorem, we can analyze the condition of existence or non-existence of the non-Hermitian skin effects at a mathematically rigorous level. Additionally, the non-Hermitian generalized Bloch theorem allows us to explore the real-space exceptional points. We also establish the connection between our approach and the generalized Brillouin zone method. To illustrate our main results, we examine two concrete examples including the Su–Schrieffer–Heeger chain model with long-range couplings, and the ladder model with non-reciprocal interaction. Our non-Hermitian generalized Bloch theorem provides an efficient way to analytically study various non-Hermitian phenomena in more general cases.

Structure formation induced by non-reciprocal cell-cell interactions in a multicellular system.

Collective cellular behavior plays a crucial role in various biological processes, ranging from developmental morphogenesis to pathological processes such as cancer metastasis. Our previous research has revealed that a mutant cell of Dictyostelium discoideum exhibits collective cell migration, including chain migration and traveling band formation, driven by a unique tail-following behavior at contact sites, which we term "contact following locomotion" (CFL). Here, we uncover an imbalance of forces between the front and rear cells within cell chains, leading to an additional propulsion force in the rear cells. Drawing inspiration from this observation, we introduce a theoretical model that incorporates non-reciprocal cell-cell interactions. Our findings highlight that the non-reciprocal interaction, in conjunction with self-alignment interactions, significantly contributes to the emergence of the observed collective cell migrations. Furthermore, we present a comprehensive phase diagram, showing distinct phases at both low and intermediate cell densities. This phase diagram elucidates a specific regime that corresponds to the experimental system.

Method of spectral response to stochastic processes for measuring the nonreciprocal effective interactions.

The theoretical background of the nonperturbative method of spectral response to stochastic processes (SRSP) for measuring the nonreciprocal interparticle effective interactions in strongly coupled underdamped systems is described. Analytical expressions for vibrational spectral density of confined Brownian particles with a nonreciprocal effective interaction are presented. The changes in the vibrational spectral density with varying different parameters of the system (nonreciprocity, viscosity, ratios of particle sizes, and intensities of random processes acting on each particle) are discussed using the example of a pair of nonidentical particles in a harmonic trap. The SRSP method is compared to three other nonperturbative methods. The SRSP method demonstrates an undeniable advantage when processing particle trajectories with errors in particle tracking.

Emergence of chimeras: An impetus by exceptional points.

A nonconservative system with nonreciprocal interaction has been found to reveal exotic features where sudden phase transitions can occur. In this paper, the emanation of a chimera in a network of Stuart-Landau oscillators with nonreciprocal interaction is reported. Note that the spins follow the random discrete distribution. In other words, we pick a random oscillator to rotate clockwise or anticlockwise. At the transition points, we find the spectral singularities in the eigenplane, where eigenvalues coalesce, commonly known as exceptional points. We find that the counterrotational symmetry breaking induced by exceptional points antecedents the occurrence of the chimera. We numerically attest to the findings for two cases of initial conditions, namely, bipartite and random. We also extend our study to a two-dimensional array of nonreciprocally interacting, distributed spins. The findings could have pragmatic implications in the areas of active matter, networks, and photonics.

Analysis of the Irreplaceability of Offline Relationship

During covid 19, traditional offline social interaction becomes difficult. Benefiting from the availability of social media, people are increasingly relying on social media to socialize. Can social media interaction replace real-life interaction? Is a social media-based relationship a sufficient substitution for a real relationship? This article divides social media interaction into reciprocal and non-reciprocal and compares two different social media interactions with real-life interactions. For the reciprocal social media interaction, The first research question distinguishes computer-mediated communication (CMC) from face-to-face (FtF) and discusses the possibility of CMC replacing FtF. Because the absence of social cues cannot be made up, CMC is not a sufficient substitute for FtF. For the non-reciprocal social media interaction, the second research question focuses on parasocial interaction-induced parasocial relationships. Because of non-reciprocality and lack of authenticity, the parasocial relationship is not a good substitute for a real relationship. In conclusion, social media relationship is not a sufficient substitute for a real relationship, but they can be used as a good supplement to a real relationship. The difference between reciprocal social media relationships and non-reciprocal social media relationships is also discussed. Reciprocal social media relationships and real relationships are interchangeable, while non-reciprocal social media relationships cannot transform into real relationships.

Non-reciprocal interactions spatially propagate fluctuations in a 2D Ising model

Motivated by the anisotropic interactions between fish, we implement spatially anisotropic and therefore non-reciprocal interactions in the 2D Ising model. First, we show that the model with non-reciprocal interactions alters the system critical temperature away from that of the traditional 2D Ising model. Further, local perturbations to the magnetization in this out-of-equilibrium system manifest themselves as traveling waves of spin states along the lattice, also seen in a mean-field model of our system. The speed and directionality of these traveling waves are controllable by the orientation and magnitude of the non-reciprocal interaction kernel as well as the proximity of the system to the critical temperature.

Non-reciprocal interaction for living matter

Non-reciprocal interaction for living matter

Enhancement of quantum excitation transport by photonic nonreciprocity

Enhanced interaction between two two-level emitters (e.g., atoms) by nonreciprocal photonic media can be of benefit to broad areas, from quantum information science to biological detection. Here we provide a detailed analysis on why nonreciprocal photon-mediated interaction enhances interatomic excitation transport efficiency. We investigate a system consisting of two two-level emitters embedded in a generic photonic environment. By comparing symmetric and asymmetric photon exchange, we analytically show that breaking electromagnetic reciprocity makes it possible for the cooperative decay rate to exceed the spontaneous decay rate, even in a translation-invariant homogeneous system. This means that the excitation of an emitter must decay mostly into the other emitter rather than leaking and dissipating into the reservoir photonic modes. We also provide an example where a chain of two-level emitters dominantly interacts via the reciprocal modes of a plasmonic waveguide. We then show that breaking reciprocity in such a system via driving a dc current through the plasmonic material can drastically increase the probability of photon emission from one emitter to another, leading to an order-of-magnitude enhancement in quantum energy-transport efficiency.

Self-sustained non-equilibrium co-existence of fluid and solid states in a strongly coupled complex plasma system

A complex (dusty) plasma system is well known as a paradigmatic model for studying the kinetics of solid-liquid phase transitions in inactive condensed matter. At the same time, under certain conditions a complex plasma system can also display characteristics of an active medium with the micron-sized particles converting energy of the ambient environment into motility and thereby becoming active. We present a detailed analysis of the experimental complex plasmas system that shows evidence of a non-equilibrium stationary coexistence between a cold crystalline and a hot fluid state in the structure due to the conversion of plasma energy into the motion energy of microparticles in the central region of the system. The plasma mediated non-reciprocal interaction between the dust particles is the underlying mechanism for the enormous heating of the central subsystem, and it acts as a micro-scale energy source that keeps the central subsystem in the molten state. Accurate multiscale simulations of the system based on combined molecular dynamics and particle-in-cell approaches show that strong structural nonuniformity of the system under the action of electostatic trap makes development of instabilities a local process. We present both experimental tests conducted with a complex plasmas system in a DC glow discharge plasma and a detailed theoretical analysis.

Droplets in underlying chemical communication recreate cell interaction behaviors

The sensory-motor interaction is a hallmark of living systems. However, developing inanimate systems with “recognize and attack” abilities remains challenging. On the other hand, controlling the inter-droplet dynamics on surfaces is key in microengineering and biomedical applications. We show here that a pair of droplets can become intelligently interactive (chemospecific stimulus-response inter-droplet autonomous operation) when placed on a nanoporous thin film surface. We find an attacker-victim-like non-reciprocal interaction between spatially separated droplets leading to an only-in-one shape instability that triggers a drop projection to selectively couple, resembling cellular phenomenologies such as pseudopod emission and phagocytic-like functions. The nanopore-driven underlying communication and associated chemical activity are the main physical ingredients behind the observed behavior. Our results reveal that basic features found in many living cell types can emerge from a simple two-droplet framework. This work is a promising step towards the design of microfluidic smart robotics and for origin-of-life protocell models.

Low-Loss Ferrite Circulator as a Tunable Chiral Quantum System

Microwave circulators are usually treated as auxiliary, classical components in superconducting quantum computing. This study integrates the cavity-magnon polariton modes of a custom-built circulator with superconducting microwave cavities to implement a tunable nonreciprocal interaction. The apparatus is well described by a non-Hermitian Hamiltonian, yielding a theoretical framework to model other nonreciprocally coupled circuit elements on the same platform in the future. The experiment also showcases an experimental probe of the left and right eigenvectors associated with the non-Hermitian Hamiltonian.

Are These Cats Playing? A Closer Look at Social Play in Cats and Proposal for a Psychobiological Approach and Standard Terminology.

Play in domestic cats has been largely studied using a contextual approach, i.e., with a focus on what the cat is playing with, such as an object, itself or another cat. Such classification may be superficially attractive scientifically but it limits the ability to investigate function. We propose consideration of a psychobiological approach, which increases attention on hypotheses about the motivational and emotional state of the actors, may be more valuable. This may be particularly important in the case of intercat exchanges that might involve play, for example when one cat may chase another which does not want to be chased, the general interaction should not be considered playful. Key to improving the scientific study of such interactions is the need to adopt a common terminology, thus we synthesise a common ethogram from the published literature. Secondly at the heart of a psychobiological approach is a consideration of both the affective state and motivational goal of each actor in an interaction, since they may not be congruent, and recognition of the hypothetical nature of any such functional classification. However, this bottom up approach provides valuable insights that can be tested. We argue that when one cat treats another as an object or prey, such activity relates to the former cat seeking to learn about its own skills in relation to manipulating its physical environment (prey are not considered part of the complex social relationships and thus social environment of an individual). However, when interaction between cats is reciprocal it may function to facilitate social learning and may be best described as mutual social play. It needs to be recognised that interactions are dynamic and thus our classification of a situation needs to be flexible. So mutual social play may turn into a form of non-reciprocal interaction. We conclude by outlining priorities for future research to help us improve our ability to answer the question “Are these cats playing?” in a wider range of contexts.

Asymmetric acoustic wave scattering by a nonreciprocal and position-dependent mass defect

We investigate the asymmetric wave scattering in a phononic one-dimensional lattice with a nonreciprocal defect and position dependent masses coupled by the defect spring. The nonreciprocal interaction is characterized by a single parameter Δ while the nonlinear contribution due to position-dependent masses are controlled by a parameter χ. The transmission and reflection coefficients are analytically computed and the effects of the nonreciprocity and nonlinearity are detailed. We show that, in opposite with the linear case, the rectification factor has a frequency dependence, which leads to a more efficient diode-like action at large wavevectors. Further, the nonlinearity leads to an asymmetry of the reflected component, absent in the linear regime. We extend our analysis to a system with frictional forces which suppresses the multistability window promoted by the nonlinear mass contribution without compromising the rectification action.

Ion-exchange enabled synthetic swarm.

Active matters are out-of-equilibrium systems that convert energy from the environment to mechanical motion. Non-reciprocal interaction between active matters may lead to collective intelligence beyond the capability of individuals. In nature, such emergent behaviours are ubiquitously observed in animal colonies, giving these species remarkable adaptive capability. In artificial systems, however, the emergence of non-trivial collective intelligent dynamics remains undiscovered. Here we show that a simple ion-exchange reaction can couple self-propelled ZnO nanorods and sulfonated polystyrene microbeads together. Chemical communication is established that enhances the reactivity and motion of both nanorods and the microbeads, resulting in the formation of an active swarm of nanorod-microbead complexes. We demonstrate that the swarm is capable of macroscopic phase segregation and intelligent consensus decision-making.

Nonreciprocal surface magnetoelastic dynamics

Motivated by recent experiments, we investigate the nonreciprocal magnetoelastic interaction between the surface acoustic phonons of dielectric non-magnetic substrates and magnons of proximity nanomagnets. The magnetization dynamics exerts rotating forces at the edges of the nanomagnet that causes the nonreciprocal interaction with surface phonons due to its rotation-momentum locking. This coupling induces the nonreciprocity of the surface phonon transmission and a nearly complete phonon diode effect by several (tens of) magnetic nanowires of high (ordinary) magnetic quality. Phase-sensitive microwave transmission is also nonreciprocal that can pick up clear signals of the coherent phonons excited by magnetization dynamics. Nonreciprocal pumping of phonons by precessing magnetization is predicted using Landauer-B\"uttiker formalism.