Nonreciprocal Coupling Research Articles

Nonreciprocal and even Willis couplings in periodic thermoacoustic amplifiers

Thermoacoustic amplifiers are analyzed in the framework of nonreciprocal Willis coupling. The closed form expressions of the effective properties are derived, showing that an applied temperature gradient causes the appearance of a nonreciprocal Willis coupling. Even and nonreciprocal Willis couplings are exhibited already in the first-order Taylor expansion of the solution and are of equal modulus but opposite sign, thus suggesting that the even Willis coupling is a reaction to the nonreciprocity introduced by the temperature gradients. These Willis couplings cause a coalescence point in the $k$ space, which deviates from $\text{Re}(k)=0$ (with $k$ the wave number) and is thus a zero-group-velocity point, as well as the opening of an amplification gap at low frequency. Effective parameters and scattering properties are found in excellent agreement with experimental results. This article paves the way to further control the acoustic waves at very low frequencies with nonreciprocal systems.

Nonreciprocal exciton-polariton ring lattices

Recent experiments have shown the transfer of orbital angular momentum (OAM) from a non-resonant laser onto an exciton-polariton condensate, despite earlier views that the phase information of such a laser should be lost during the process of polariton condensation. We study with a phenomenological theory the interplay of a usual angular momentum independent gain and an angular momentum preserving gain. We find that even when the latter is much smaller, it is enough to favour condensation into a given orbital angular momentum state. This further allows a breaking of symmetry in the system, which further manifests in non-reciprocal one-way propagation in a lattice of coupled rings. Even though we consider only Hermitian reciprocal coupling between rings, the local non-Hermiticity generates an effective non-reciprocal coupling and supports a non-Hermitian topological invariant (winding number) associated to a non-Hermitian skin effect.

Two-dimensional anisotropic non-Hermitian Lieb lattice

We study an anisotropic two-dimensional non-Hermitian Lieb lattice, where the staggered gain and loss present in the horizontal and vertical directions, respectively. The intra-cell nonreciprocal coupling generates magnetic flux enclosed in the unit cell of the Lieb lattice and creates nontrivial topology. The active and dissipative topological edge states are along the horizontal and vertical directions, respectively. The two-dimensional non-Hermitian Lieb lattice also supports passive topological corner state. At appropriate magnetic flux, the non-Hermiticity can alter the corner state from one corner to the opposite corner as the non-Hermiticity increases. The gapless phase of the Lieb lattice is characterized by different configurations of exceptional points in the Brillouin zone. The topology of the anisotropic non-Hermitian Lieb lattices can be verified in many experimental platforms including the optical waveguide lattices, photonic crystals, and electronic circuits.

Robust exceptional point of arbitrary order in coupled spinning cylinders.

Exceptional points (EPs), i.e., non-Hermitian degeneracies at which eigenvalues and eigenvectors coalesce, can be realized by tuning the gain/loss contrast of different modes in non-Hermitian systems or by engineering the asymmetric coupling of modes. Here we demonstrate a mechanism that can achieve EPs of arbitrary order by employing the non-reciprocal coupling of spinning cylinders sitting on a dielectric waveguide. The spinning motion breaks the time-reversal symmetry and removes the degeneracy of opposite chiral modes of the cylinders. Under the excitation of a linearly polarized plane wave, the chiral mode of one cylinder can unidirectionally couple to the same mode of the other cylinder via the spin-orbit interaction associated with the evanescent wave of the waveguide. The structure can give rise to arbitrary-order EPs that are robust against spin-flipping perturbations, in contrast to conventional systems relying on spin-selective excitations. In addition, we show that higher-order EPs in the proposed system are accompanied by enhanced optical isolation, which may find applications in designing novel optical isolators, nonreciprocal optical devices, and topological photonics.

Localized states in coupled Cahn–Hilliard equations

Abstract The classical Cahn–Hilliard (CH) equation corresponds to a gradient dynamics model that describes phase decomposition in a binary mixture. In the spinodal region, an initially homogeneous state spontaneously decomposes via a large-scale instability into drop, hole or labyrinthine concentration patterns of a typical structure length followed by a continuously ongoing coarsening process. Here, we consider the coupled CH dynamics of two concentration fields and show that non-reciprocal (or active or non-variational) coupling may induce a small-scale (Turing) instability. At the corresponding primary bifurcation, a branch of periodically patterned steady states emerges. Furthermore, there exist localized states that consist of patterned patches coexisting with a homogeneous background. The branches of steady parity-symmetric and parity-asymmetric localized states form a slanted homoclinic snaking structure typical for systems with a conservation law. In contrast to snaking structures in systems with gradient dynamics, here, Hopf instabilities occur at a sufficiently large activity, which results in oscillating and travelling localized patterns.

Bound and subradiant multiatom excitations in an atomic array with nonreciprocal couplings

Collective decays of multiply-excited atoms become subradiant and bound in space when they are strongly coupled to the guided modes in an atom-waveguide interface. In this interface, we analyze their average density-density and modified third-order correlations via Kubo cumulant expansions, which can arise and sustain for long time. The shape-preserving dimers and trimers of atomic excitations emerge in the most subradiant coupling regime of light-induced dipole-dipole interactions. This leads to a potential application of quantum information processing and quantum storage in the encoded nonreciprocal spin diffusion, where its diffusion speed depends on the initial coherence between the excited atoms and is robust to their relative phase fluctuations. The state-dependent photon routing can be viable as well in this interface.

Nonreciprocal Polarization Coupling via Magneto-Optic Effect in Silicon Micro-Ring Resonator

The whispering gallery modes (WGMs) are studied theoretically in a proposed magneto-optic (MO) silicon micro-ring resonator with a radial magnetic field. The dispersion relations between both the frequency and polarization of the resonant mode and the gyration coefficient are achieved through Finite-Element Method (FEM). Nonreciprocal polarization coupling is observed between the intrinsic quasi-TM and quasi-TE modes, due to their different frequency shift coefficients originating from the magneto-optic effect. This polarization coupling results in the rapid changes of linear polarization degrees of the supermodes. The nonreciprocal mode coupling is universal and will be of practical value for the MO optical integration.

Nonreciprocal multimode and indirect couplings in cavity magnonics

We investigate the magnon-photon couplings by employing a small magnet within an irregular resonant cavity, which leads to a desirable nonreciprocity with a big isolation ratio. Moreover, the higher-order couplings between the spin wave modes with the polarized photon modes also exhibit the nonreciprocity. These couplings between polarized photon and spin waves could be regarded as an indirect multi-modes coupling between the ferromagnetic resonance (FMR) mode and spin wave mode magnons mediated by the cavity mode photons. We also derive a coupling matrix to predict the characteristics of this kind of indirect coupling. The existence of the indirect couplings broaden the field range of the nonreciprocity of the system. The achieved nonreciprocal multi-mode magnon-photon couplings in a single system offer a feasible method to improve the signal transmission quality.

Nonreciprocal Coupling Induced Self-Assembled Localized Structures.

Chains of coupled oscillators exhibit energy propagation by means of waves, pulses, and fronts. Nonreciprocal coupling radically modifies the wave dynamics of chains. Based on a prototype model of nonlinear chains with nonreciprocal coupling to nearest neighbors, we study nonlinear wave dynamics. Nonreciprocal coupling induces a convective instability between unstable and stable equilibrium. Increasing the coupling level, the chain presents a propagative pattern, a traveling wave. This emergent phenomenon corresponds to the self-assembly of localized structures. The pattern wavelength is characterized as a function of the coupling. Analytically, the phase diagram is determined and agrees with numerical simulations.

Acoustic Willis meta-atom beyond the bounds of passivity and reciprocity

Willis metamaterial enables exotic manipulations of acoustic waves with a precise combination of bulk modulus, mass density, and Willis parameters. While the realization of unrestricted and completely decoupled constitutive parameters would extend the horizon of future applications, the restriction of passivity and reciprocity dictate a hard bound in the values of achievable polarizabilities and correlations between them. Here, we break the bound of passivity and reciprocity by instituting a basis and independent kernel for each constitutive polarization in a virtualized metamaterial platform, active metamaterials realizing artificial polarization with the digital convolution. We demonstrate decoupled control of all four constitutive parameters in a nonreciprocal regime, at the same time achieving values of polarizabilities beyond the passivity limit. Broadband, flat-response nonreciprocal Willis coupling is also demonstrated with analytically designed causal frequency dispersion. Our approach will be useful for nonreciprocal wave manipulation and communication for broadband operation.

A Tunable Ferrite Isolator for 30 GHz Millimeter-Wave Applications

In this article, a tunable ferrite-loaded isolator working at millimeter-wave (mm-Wave) frequency for applications in multi-function systems is presented. The device is based on nonreciprocal coupling between a ferrite slab and a half-mode substrate-integrated waveguide (HMSIW). The HMSIW offers a compact design and, more important here, the ability of energy coupling to adjacent resonators. The ferrite slab is placed outside the HMSIW, close to the H-wall symmetry of the HMSIW, providing the possibility of movement for the ferrite slab and low insertion loss of the transmission mode. Any change in the position of the ferrite slab changes the propagation constant of the mode traveling across the ferrite-coupled HMSIW, which, consequently, results in different center frequencies of the isolation. To the best of our knowledge, the proposed design is one of the first tunable isolators for such a high frequency. Despite previously reported isolators that require a strong magnetic bias field for mm-Wave range applications, the proposed isolator requires a relatively low magnetic bias (less than 20 KA/m), which is provided by a small and lightweight permanent magnet. The 10 dB isolation bandwidth of the design is about 2 GHz varying from 34 to 37 GHz based on the position of the ferrite slab. The insertion loss of the device is measured between 2 and 3 dB.

Correlation functions of non-Markovian systems out of equilibrium: analytical expressions beyond single-exponential memory

This paper is concerned with correlation functions of stochastic systems with memory, a prominent example being a molecule or colloid moving through a complex (e.g. viscoelastic) fluid environment. Analytical investigations of such systems based on non-Markovian stochastic equations are notoriously difficult. A common approximation is that of a single-exponential memory, corresponding to the introduction of one auxiliary variable coupled to the Markovian dynamics of the main variable. As a generalization, we here investigate a class of ‘toy’ models with altogether three degrees of freedom, giving rise to more complex forms of memory. Specifically, we consider, mainly on an analytical basis, the under- and overdamped motion of a colloidal particle coupled linearly to two auxiliary variables, where the coupling between variables can be either reciprocal or non-reciprocal. Projecting out the auxiliary variables, we obtain non-Markovian Langevin equations with friction kernels and colored noise, whose structure is similar to that of a generalized Langevin equation. For the present systems, however, the non-Markovian equations may violate the fluctuation–dissipation relation as well as detailed balance, indicating that the systems are out of equilibrium. We then study systematically the connection between the coupling topology of the underlying Markovian system and various autocorrelation functions. We demonstrate that already two auxiliary variables can generate surprisingly complex (e.g. non-monotonic or oscillatory) memory and correlation functions. Finally, we show that a minimal overdamped model with two auxiliary variables and suitable non-reciprocal coupling yields correlation functions resembling those describing hydrodynamic backflow in an optical trap.

Unconventional time-bandwidth performance of resonant cavities with nonreciprocal coupling

The time-bandwidth limit is a mathematical tenet that affects all reciprocal resonators, stating that the product of the spectral bandwidth that can couple into a resonant system and its characteristic energy decay time is always equal to 1. Here, we develop an analytical and numerical model to show that introducing nonreciprocal coupling to a generalized resonator changes the power balance between the reflected and intracavity fields, which consequently overcomes the time-bandwidth limit of the resonant system. By performing a full evaluation of the time-bandwidth product (TBP) of the modeled resonator, we show that it represents a measure of the increased delay imparted to a light wave, with respect to what the bandwidth of the reciprocal resonant structure would allow to the same amount of in-coupled power. No longer restricted to the value 1, we show that the TBP can instead be used as a figure of merit of the improvement in intracavity power enhancement due to the nonreciprocal coupling.

Two-dimensional non-Hermitian Skin Effect in a Synthetic Photonic Lattice

Non-Hermitian skin effect (NHSE) has led to interesting physics and sophisticated applications beyond the conventional framework. However, NHSE studies have been limited to an individual dimension due to the difficulty of constructing nonreciprocal coupling in higher-dimensional systems. With the concept of synthetic dimension, we realize two-dimensional (2D) NHSE in a synthetic photonic lattice. The synthetic photonic lattice is composed of a spatial dimension and a synthetic frequency dimension, which is constructed by introducing gain and loss and dynamically modulating the complex refractive index in a one-dimensional ring-resonator array. In the synthetic 2D NHSE system, we can manipulate the spatial position and frequency mode of the light in real time, thus enabling programmable light propagation and frequency conversion. Specifically, the incident light can be localized in the spatial dimension and the frequency dimension simultaneously, leading to second-order corner modes in the synthetic 2D NHSE lattice. Besides, the 2D NHSE system exhibits an excellent robustness for the disorder and point defect in the lattice. This work generalizes the non-Hermitian skin effect in synthetic dimension to control the light in different dimensions, which shows great promise for potential applications in on-chip light manipulation, frequency synthesis, and information processing.

Real-time steering of curved sound beams in a feedback-based topological acoustic metamaterial

We present the concept of a feedback-based topological acoustic metamaterial as a tool for realizing autonomous and active guiding of sound beams along arbitrary curved paths in free two-dimensional space. The metamaterial building blocks are acoustic transducers, embedded in a slab waveguide. The transducers generate a desired dispersion profile in closed-loop by processing real-time pressure field measurements through preprogrammed controllers. In particular, the metamaterial can be programmed to exhibit analogies of quantum topological wave phenomena, which enables unconventional and exceptionally robust sound beam guiding. As an example, we realize the quantum valley Hall effect by creating, using a collocated pressure feedback, an alternating acoustic impedance pattern across the waveguide. The pattern is traversed by artificial trajectories of different shapes, which are reconfigurable in real-time. Due to topological protection, the sound waves between the plates remain localized on the trajectories, and do not back-scatter by the sharp corners or imperfections in the design. The feedback-based design can be used to realize arbitrary physical interactions in the metamaterial, including non-local, nonlinear, time-dependent, or non-reciprocal couplings, paving the way to unconventional acoustic wave guiding on the same reprogrammable platform. We then present a non-collocated control algorithm, which mimics another quantum effect, rendering the sound beams uni-directional.

Nonreciprocal coherent coupling of nanomagnets by exchange spin waves

Nanomagnets are widely used to store information in non-volatile spintronic devices. Spin waves can transfer information with low-power consumption as their propagations are independent of charge transport. However, to dynamically couple two distant nanomagnets via spin waves remains a major challenge for magnonics. Here we experimentally demonstrate coherent coupling of two distant Co nanowires by fast propagating spin waves in an yttrium iron garnet thin film with sub-50 nm wavelengths. Magnons in two nanomagnets are unidirectionally phase-locked with phase shifts controlled by magnon spin torque and spin-wave propagation. The coupled system is finally formulated by an analytical theory in terms of an effective non-Hermitian Hamiltonian. Our results are attractive for analog neuromorphic computing that requires unidirectional information transmission.

Irreversibility, heat and information flows induced by non-reciprocal interactions

We study the thermodynamic properties induced by non-reciprocal interactions between stochastic degrees of freedom in time- and space-continuous systems. We show that, under fairly general conditions, non-reciprocal coupling alone implies a steady energy flow through the system, i.e., non-equilibrium. Projecting out the non-reciprocally coupled degrees of freedom renders non-Markovian, one-variable Langevin descriptions with complex types of memory, for which we find a generalized second law involving information flow. We demonstrate that non-reciprocal linear interactions can be used to engineer non-monotonic memory, which is typical for, e.g., time-delayed feedback control, and is automatically accompanied with a nonzero information flow through the system. Furthermore, already a single non-reciprocally coupled degree of freedom can extract energy from a single heat bath (at isothermal conditions), and can thus be viewed as a minimal version of a time-continuous, autonomous ‘Maxwell demon’. We also show that for appropriate parameter settings, the non-reciprocal system has characteristic features of active matter, such as a positive energy input on the level of the fluctuating trajectories without global particle transport.

Localized photonic states and dynamic process in nonreciprocal coupled Su-Schrieffer-Heeger chain.

We investigate the localized photonic states and dynamic process in one-dimensional nonreciprocal coupled Su-Schrieffer-Heeger chain. Through numerical calculation of energy eigenvalue spectrum and state distributions of the system, we find that different localized photonic states with special energy eigenvalues can be induced by the nonreciprocal coupling, such as zero-energy edge states, interface states and bound states with pure imaginary energy eigenvalues. Moreover, we analyze the dynamic process of photonic states in such non-Hermitian system. Interestingly, it is shown that the nonreciprocal coupling has an evident gathering effect on the photons, which also break the trapping effect of topologically protected edge states. In addition, we consider the impacts of on-site defect potentials on the dynamic process of photonic states for the system. It is indicated that the photons go around the defect lattice site and still present the gathering effect, and different forms of laser pulses can be induced with the on-site defect potentials in different lattice sites. Furthermore, we present the method for the quantum simulation of current model based on the circuit quantum electrodynamic lattice.

Design and verification of a broadband highly-efficient plasmonic circulator* *Project supported by the Six-Talent-Peaks Project in Jiangsu Province of China (Grant No. XYDXX-072) and the National Natural Science Foundation of China (Grant No. 61372048).

Circulators play a significant role in radar and microwave communication systems. This paper proposes a broadband and highly efficient plasmonic circulator, which consists of spoof surface plasmon polaritons (SSPPs) waveguides and ferrite disks to support non-reciprocal mode coupling. The simulated performance of symmetrically designed circulator shows that it has an insertion loss of roughly 0.5 dB while the isolation and return loss is more than 12 dB in the frequency range of 6.0 GHz–10.0 GHz (relative bandwidth of 50%). Equivalent circuit model has been proposed to explain the operating mechanism of the plasmonic circulator. The equivalent circuit model, numerical simulations, and experimental results are consistent with each other, which demonstrates the good performance of the proposed plasmonic circulator.

Single active particle engine utilizing a nonreciprocal coupling between particle position and self-propulsion.

We recently argued that a self-propelled particle is formally equivalent to a system consisting of two subsystems coupled by a nonreciprocal interaction [Phys. Rev. E 100, 050603(R) (2019)2470-004510.1103/PhysRevE.100.050603]. Here, we show that this nonreciprocal coupling allows us to extract useful work from a single self-propelled particle maintained at constant temperature, by using an aligning interaction to control correlations between the particle's position and self-propulsion.