Nonreciprocal Coupling Research Articles

Observation of Topological Transition in Floquet Non-Hermitian Skin Effects in Silicon Photonics.

Non-Hermitian physics has greatly enriched our understanding of nonequilibrium phenomena and uncovered novel effects such as the non-Hermitian skin effect (NHSE) that has profoundly revolutionized the field. NHSE has been predicted in systems with nonreciprocal couplings which, however, are challenging to realize in experiments. Without nonreciprocal couplings, the NHSE can also emerge in systems with coexisting gauge fields and loss or gain (e.g., in Floquet non-Hermitian systems). However, such Floquet NHSE remains largely unexplored in experiments. Here, we realize the Floquet NHSEs in periodically modulated optical waveguides integrated on a silicon photonic platform. By engineering the artificial gauge fields induced by the periodical modulation, we observe various Floquet NHSE phases and unveil their rich topological transitions. Remarkably, we discover the transitions between the unipolar NHSE phases and an unconventional bipolar NHSE phase, which is accompanied by the directional reversal of the NHSEs. The underlying physics is revealed by the band winding in complex quasienergy space which undergoes a topology change from isolated loops with the same winding to linked loops with opposite windings. Our work unfolds a new route toward Floquet NHSEs originating from the interplay between gauge fields and dissipation effects, and thus offers fundamentally new ways for steering light and other waves.

Ultra-sensitivity in reconstructed exceptional systems

ABSTRACT Sensors are of fundamental importance and widely used in modern society, such as in industry and environmental monitoring, biomedical sample ingredient analysis and wireless networks. Although numerous sensors have been developed, there is a continuous demand for sensors with increased sensitivity, to detect signals that were previously undetectable. Recently, non-Hermitian degeneracies, also known as exceptional points (EPs), have attracted attention as a way of improving the responsiveness of sensors. In contrast to previous investigations, here we present a new approach to achieving ultra-sensitivity by reconstructing exceptional systems. In the reconstruction process, some eigenstates near the previous EPs are utilized, and non-reciprocal long-range couplings are introduced. The sensitivities of our reconstructed systems have improved by several orders of magnitude compared to those based on EPs. Furthermore, we design and fabricate corresponding integrated circuit sensors to demonstrate the scheme. Our work paves the way for the development of highly sensitive sensors, which have a wide range of applications in various fields.

Exceptional points in SSH-like models with a hopping amplitude gradient

The Su–Schrieffer–Heeger (SSH) system is a popular model for exploring topological insulators and topological phases in one dimension. Recent interest in exceptional points has led to re-examination of non-Hermitian generalizations of many physical models, including the SSH model. In such non-Hermitian systems, singular points called exceptional points (EPs) appear that are of interest for applications in super-resolution sensing systems and topological lasers. Here, a non-Hermitian and non-PT-symmetric variation of the SSH model is introduced, in which the hopping amplitudes are nonreciprocal and vary monotonically along the chain. It is found that, while the existence of the EPs is due to the nonreciprocal couplings, the number, position, and order of the EPs can all be altered by the addition of the hopping amplitude gradient, adding a new, to the best of our knowledge, tool for tailoring the spectrum of a non-Hermitian system.

Two-dimensional Su-Schrieffer-Heeger model with imaginary potentials and nonreciprocal couplings

We examine the 2D-SSH model and focus on its topological states and skin effects resulting from imaginary potentials and nonreciprocal couplings. Our calculations demonstrate that inducing topological edge and corner states allows for different topological phase transitions in the 2D-SSH model. The topological phase transition is achieved by adjusting the ratio of the intercell electron hopping to the intracell electron hopping. The PT symmetry of the system is destroyed when an imaginary potential is present. If non-reciprocal effects are introduced, then skin effects will be seen. This work contributes to understanding how the interplay between imaginary potentials and nonreciprocal couplings modulates the skin effects and topological states in 2D-SSH model.

Efficiency of an autonomous, dynamic information engine operating on a single active particle.

The Szilard engine stands as a compelling illustration of the intricate interplay between information and thermodynamics. While at thermodynamic equilibrium, the apparent breach of the second law of thermodynamics was reconciled by Landauer and Bennett's insights into memory writing and erasure, recent extensions of these concepts into regimes featuring active fluctuations have unveiled the prospect of exceeding Landauer's bound, capitalizing on information to divert free energy from dissipation towards useful work. To explore this question further, we investigate an autonomous dynamic information engine, addressing the thermodynamic consistency of work extraction and measurement costs by extending the phase space to incorporate an auxiliary system, which plays the role of an explicit measurement device. The nonreciprocal coupling between active particle and measurement device introduces a feedback control loop, and the cost of measurement is quantified through a suitably defined auxiliary entropy production. The study considers different measurement scenarios, highlighting the role of measurement precision in determining engine efficiency.

Nonlinear wave propagation in a bistable optical chain with nonreciprocal coupling

The propagation of nonlinear waves, such as fires, weather fronts, and disease spread, has drawn attention since the dawn of time. A well-known example of nonlinear wave–fronts–in our daily lives is the domino waves, which propagate equally toward the left or right flank due to their reciprocal coupling. However, there are other situations where front propagation is not fully understood, such as bistable fronts with nonreciprocal coupling. These couplings are characterised by the fact that the energy emitter and receiver are not interchangeable. Here, we study the propagation of nonlinear waves in a bistable optical chain forced by nonreciprocal optical feedback. The spatiotemporal evolution and the front speeds are characterised as a function of the nonreciprocal coupling. We derive an equation to describe the interacting optical elements in a liquid crystal light valve with nonreciprocal optical feedback and compare the experimental results with numerical simulations of the coupled bistable systems.

Steady-state phases and interaction-induced depletion in a driven-dissipative chirally-coupled dissimilar atomic array

A nanophotonic waveguide coupled with an atomic array forms one of the strongly coupled quantum interfaces to showcase many fascinating collective features of quantum dynamics. In particular, for a dissimilar array of two different interparticle spacings with competing photon-mediated dipole-dipole interactions and directionality of couplings, we study the steady-state phases of atomic excitations under a weakly driven condition of laser field. We identify a partial set of steady-state phases of the driven system composed of combinations of steady-state solutions in a homogeneous array. We also reveal the intricate role of the atom at the interface of the dissimilar array in determining the steady-state phases and find an alteration in the dichotomy of the phases strongly associated with steady-state distributions with crystalline orders. We further investigate in detail the interaction-induced depletion in half of the dissimilar array, where the blockaded region results from two contrasting interparticle spacings near the reciprocal coupling regime. This can be further evidenced from the analytical solutions under the reciprocal coupling. Our results can provide insights in the driven-dissipative quantum phases of atomic excitations with nonreciprocal couplings and pave the avenues toward quantum simulations of exotic many-body states essential for quantum information applications. Published by the American Physical Society 2024

Nonreciprocal field transformation with active acoustic metasurfaces.

Field transformation, as an extension of the transformation optics, provides a unique means for nonreciprocal wave manipulation, while the experimental realization remains a substantial challenge as it requires stringent material parameters of the metamaterials, e.g., purely nonreciprocal bianisotropic parameters. Here, we develop and demonstrate a nonreciprocal field transformation in a two-dimensional acoustic system, using an active metasurface that can independently control all constitutive parameters and achieve purely nonreciprocal Willis coupling. The field-transforming metasurface enables tailor-made field distribution manipulation, achieving localized field amplification by a predetermined ratio. The metasurface demonstrates the self-adaptive capability to various excitation conditions and can be extended to other geometric shapes. The metasurface also achieves nonreciprocal wave propagation for internal and external excitations, demonstrating a one-way acoustic device. The nonreciprocal field transformation not only extends the framework of the transformation theory for nonreciprocal wave manipulation but also holds great potential in applications such as ultrasensitive sensors and nonreciprocal communication.

Nonequilibrium dynamics and entropy production of a trapped colloidal particle in a complex nonreciprocal medium.

We discuss the two-dimensional motion of a Brownian particle that is confined to a harmonic trap and driven by a shear flow. The surrounding medium induces memory effects modeled by a linear, typically nonreciprocal coupling of the particle coordinates to an auxiliary (hidden) variable. The system's behavior resulting from the microscopic Langevin equationsfor the three variables is analyzed by means of exact moment equationsderived from the Fokker-Planck representation, and numerical Brownian dynamics simulations. Increasing the shear rate beyond a critical value we observe, for suitable coupling scenarios with nonreciprocal elements, a transition from a stationary to a nonstationary state, corresponding to an escape from the trap. We analyze this behavior, analytically and numerically, in terms of the associated moments of the probability distribution, and from the perspective of nonequilibrium thermodynamics. Intriguingly, the entropy production rate remains finite when crossing the stability threshold.

Control of non-Hermitian skin effect by staggered synthetic gauge fields

Synthetic gauge fields introduce an unconventional degree of freedom for studying many fundamental phenomena in different branches of physics. Here, we propose a scheme to use staggered synthetic gauge fields for control of the non-Hermitian skin effect (NHSE). A modified Su–Schrieffer–Heeger model is employed, where two dimer chains with non-reciprocal coupling phases are coupled, exhibiting non-trivial point-gap topology and the NHSE. In contrast to previous studies, the skin modes in our model are solely determined by the coupling phase terms associated with the staggered synthetic gauge fields. By manipulating such gauge fields, we can achieve maneuvering of skin modes as well as the bipolar NHSE. As a typical example, we set up a domain wall by imposing different synthetic gauge fields on two sides of the wall, thereby demonstrating flexible control of the non-Hermitian skin modes at the domain wall. Our scheme opens a new avenue for the creation and manipulation of NHSE by synthetic gauge fields, which may find applications in beam shaping and non-Hermitian topological devices.

Topological properties and skin effects modulated by different-density nonreciprocal couplings in the Su-Schrieffer-Heeger structure

We pay attention to the topological properties and skin effects in the one-dimensional Su-Schrieffer-Heeger (SSH) structure, by considering the presence of different-density non-reciprocal couplings. We find that when only one single non-reciprocal coupling term is introduced, e.g., in the middle of the SSH structure, edge states can be induced around the sites suffering from the non-reciprocal coupling. As one non-reciprocal coupling term is introduced in each two cells, the topological phase transition is modified. Besides, new topological edge states and skin effects appear at the ends of the SSH structure, and the edge states can be differentiated by their localities, localization degrees, and the imaginary part of energy. Furthermore, if two neighboring cells of the SSH structure are coupled by the non-reciprocal coupling, the topological edge states and skin effect more well-defined, accompanied by the further change of the topological phase transition condition. These results suggest that the non-reciprocal coupling plays a unique and important role in modulating the topological properties and the skin effects of the one-dimensional SSH structure.

Nonreciprocal Pattern Formation of Conserved Fields

In recent years, nonreciprocally coupled systems have received growing attention. Previous work has shown that the interplay of nonreciprocal coupling and Goldstone modes can drive the emergence of temporal order such as traveling waves. We show that these phenomena are generically found in a broad class of pattern-forming systems, including mass-conserving reaction-diffusion systems and viscoelastic active gels. All these systems share a characteristic dispersion relation that acquires a nonzero imaginary part at the edge of the band of unstable modes and exhibit a regime of propagating structures (traveling wave bands or droplets). We show that models for these systems can be mapped to a common “normal form” that can be seen as a spatially extended generalization of the FitzHugh-Nagumo model, providing a unifying dynamical-systems perspective. We show that the minimal nonreciprocal Cahn-Hilliard equations exhibit a surprisingly rich set of behaviors, including interrupted coarsening of traveling waves without selection of a preferred wavelength and transversal undulations of wave fronts in two dimensions. We show that the emergence of traveling waves and their speed are precisely predicted from the dispersion relation at interfaces far away from the homogeneous steady state. Our work, thus, generalizes previously studied nonreciprocal phase transitions and shows that interfaces are the relevant collective excitations governing the rich dynamical patterns of conserved fields. Published by the American Physical Society 2024

Discontinuous phase transition from ferromagnetic to oscillating states in a nonequilibrium mean-field spin model.

We study a nonequilibrium ferromagnetic mean-field spin model exhibiting a phase with spontaneous temporal oscillations of the magnetization, on top of the usual paramagnetic and ferromagnetic phases. This behavior is obtained by introducing dynamic field variables coupled to the spins through nonreciprocal couplings. We determine a nonequilibrium generalization of the Landau free energy in terms of the large deviation function of the magnetization and of an appropriately defined smoothed stochastic time derivative of the magnetization. While the transition between paramagnetic and oscillating phase is continuous, the transition between ferromagnetic and oscillating phases is found to be discontinuous, with a coexistence of both phases, one being stable and the other one metastable. Depending on parameter values, the ferromagnetic points may either be inside or outside the limit cycle, leading to different transition scenarios. The stability of these steady states is determined from the large deviation function. We also show that in the coexistence region, the entropy production has a pronounced maximum as a function of system size.

Atomic excitation trapping in dissimilar chirally coupled atomic arrays

An atomic array coupled to a one-dimensional nanophotonic waveguide allows photon-mediated dipole-dipole interactions and nonreciprocal decay channels. Such an array possesses many intriguing quantum phenomena due to its distinctive and emergent quantum correlations. In this atom-waveguide quantum system, we theoretically investigate the atomic excitation dynamics and its transport property, specifically at an interface of dissimilar atomic arrays with different interparticle distances. We find that the atomic excitation dynamics is highly dependent on the interparticle distances of dissimilar arrays and the directionality of nonreciprocal couplings. By tuning these parameters, a dominant excitation reflection can be achieved at the interface of the arrays in the single excitation case. We further study two effects on the transport property—of external drive and of single excitation delocalization over multiple atoms—where we manifest a rich interplay between multisite excitation and the relative phase in determining the transport properties. Finally, we present an intriguing trapping effect of atomic excitation by designing multiple zones of dissimilar arrays. Similar to the single excitations, multiple excitations are reflected from the array interfaces and trapped as well, although complete trapping of many excitations together is relatively challenging at long time due to a faster combined decay rate. Our results can provide insights into nonequilibrium quantum dynamics in dissimilar arrays, and they can shed light on confining and controlling quantum registers useful for quantum information processing. Published by the American Physical Society 2024

Higher-order Non-Hermitian skin effect in an acoustic lattice

Non-Hermitian physical systems offer a distinct band topology that gives rise to the interesting phenomenon known as the non-Hermitian skin effect (NHSE). However, the exploration of higher-order NHSE in classical wave systems by leveraging non-reciprocity has been largely unexplored. In this study, we introduce a novel approach to experimentally realize the higher-order NHSE in a two-dimensional non-reciprocal breathing acoustic Kagome lattice. This lattice is composed of acoustic cavities with non-reciprocal coupling achieved through electrically controlled active acoustic elements. We successfully observed second-order corner modes using a 3 × 3 lattice, which manifest as localized pressure distributions at specific frequencies in both parallelogram and triangular topological acoustic lattices. We delve into the underlying mechanisms and their implications, thereby paving the way for a deeper understanding of higher-order NHSE and potentially innovative applications rooted in the acoustic non-reciprocity.

The size effect and analogous boundary states in a circular non-Hermitian chain

We investigate the size effect and boundary states based on a circular non-Hermitian chain under the nonreciprocal intra-cell coupling and inter-cell coupling regimes. We find that the circular non-Hermitian chain exhibits an even–odd effect on the unit cell corresponding to a large chain, which is different from the open non-Hermitian chain only exhibiting the same effect for a small chain. Moreover, we find that the originally localized bulk states become totally extended via designing the boundary coupling strength appropriately. The extended bulk states reveal the fact of the disappearance of the non-Hermitian skin effect. In particular, we show that the circular non-Hermitian chain also possesses the analogous edge states under some parameter regimes, which is pretty counterintuitive since the circular chain usually cannot define a boundary. Our investigations supply the different non-Hermitian phenomena in a circular non-Hermitian chain.

Steering non-Hermitian skin states by engineering interface in 1D nonreciprocal acoustic crystal

Topological insulators, which possess robust topologically protected properties for manipulating the wave propagation against the disorder and defects, have grown into a large research field in photonic and phononic crystals. However, the conventional topological band theory is used to describe a closed photonic/phononic crystal that is assumed to be Hermitian system. In fact, practical physical systems often couple with outside environment, and induce non-Hermitian Hamiltonian with complex eigenvalues. Recently, many novel topological properties have been induced by the interacting between non-Hermitian and topological phases, a prominent example is non-Hermitian skin effect that all eigenstates are localized to the boundary in open system, which different from the conventional topological edge states. The unique physical phenomenon has stimulated various applications, such as wave funneling, enhanced sensing, and topological lasing. In this work, we describe the non-Hermitian skin effect using winding numbers. The sign of the winding number determines the rotation direction of the loops in the complex frequency plane, which the sign can be controlled by the nonreciprocal coupling direction. In this context, we designed different topological skin interface between different domains with opposite winding numbers to manipulate the energy focusing to middle or two-end of non-Hermitian 1D acoustic cavity chain. In experiment, we used an electroacoustic coupling method, employing a unidirectional coupler composed of microphones, speakers, phase shifters, and amplifiers, to introduce positive and negative non-reciprocal couplings between the two acoustic cavities and studied the characteristics of these non-reciprocal couplings. Then, the non-reciprocal coupling cavities were extended into a chain structure, and the magnitude and sign of the non-reciprocal couplings were flexibly controlled using phase shifters and amplifiers. Through this method, we successfully constructed interfaces between different winding numbers, achieving a one-dimensional non-Hermitian skin effect at various interfaces. The experimental results indicate that the sound can be focused at middle interface or two-end interfaces for different nonreciprocal coupling distributions, and the skin interface can also be switched from middle to two-end by exchanging the nonreciprocal coupling direction of the domains. Our research results offer greater flexibility in the design of acoustic devices and may provide a new platform for exploring advanced topological acoustic systems for controlling sound propagation.

Engineering of energy band and its impact on the light transmission in a non-reciprocal Hermitian hourglass lattice.

We study a quasi-one-dimensional non-reciprocal Hermitian hourglass photonic lattice that can accomplish multiple functions. Under the effect of non-reciprocal coupling, this lattice can produce an energy isolation effect, two kinds of flatbands, and energy band inversion. The excitation and propagation of a single energy band and multiple energy bands can be realized; in the flatband condition, the system has compact localized states, and the flatbands can be excited by a straightforward method. Our findings advance the theory of energy band regulation in artificial photonic lattices.

Vorticity wave interaction, Krein collision, and exceptional points in shear flow instabilities.

We relate the model of vorticity wave interaction to Krein collision, PT-symmetry breaking, and the formation of exceptional points in shear flow instabilities. We show that the dynamical system of coupled vorticity waves is a pseudo-Hermitian system with nonreciprocal coupling terms. Krein signatures of the eigenvalues are illustrated as the signs of the action of the vorticity waves. Interaction between positive-action and negative-action vorticity waves then corresponds to the Krein collision between eigenvalues with opposite Krein signatures, the spontaneous breaking of PT symmetry, and the formation of exceptional points. The control parameter of the PT-symmetry-breaking bifurcation is the ratio between frequency detuning and coupling strength of the vorticity waves. The critical behavior near the exceptional points is described as a transition between phase-locking and phase-slip dynamics of the vorticity waves. The phase-slip dynamics correspond to nonmodal, transient growth of perturbations in the regime of unbroken PT symmetry, and the phase-slip frequency Ω∝|k-k_{c}|^{1/2} shares the same critical exponent with the phase rigidity of system eigenvectors.

Entropy production in the nonreciprocal Cahn-Hilliard model.

We study the nonreciprocal Cahn-Hilliard model with thermal noise as a prototypical example of a generic class of non-Hermitian stochastic field theories, analyzed in two companion papers [Suchanek, Kroy, and Loos, Phys. Rev. Lett. 131, 258302 (2023)10.1103/PhysRevLett.131.258302; Phys. Rev. E 108, 064123 (2023)10.1103/PhysRevE.108.064123]. Due to the nonreciprocal coupling between two field components, the model is inherently out of equilibrium and can be regarded as an active field theory. Beyond the conventional homogeneous and static-demixed phases, it exhibits a traveling-wave phase, which can be entered via either an oscillatory instability or a critical exceptional point. By means of a Fourier decomposition of the entropy production rate, we quantify the associated scale-resolved time-reversal symmetry breaking, in all phases and across the transitions, in the low-noise regime. Our perturbative calculation reveals its dependence on the strength of the nonreciprocal coupling. Surging entropy production near the static-dynamic transitions can be attributed to entropy-generating fluctuations in the longest wavelength Fourier mode and heralds the emerging traveling wave. Its translational dynamics can be mapped on the dissipative ballistic motion of an active (quasi)particle.