Important Elements of Spin-Exciton and Magnon-Exciton Coupling

The recent discovery of spin-exciton and magnon-exciton coupling in a layered antiferromagnetic semiconductor, CrSBr, is both fundamentally intriguing and technologically significant. This discovery unveils a unique capability to optically access and manipulate spin information using excitons, opening doors to applications in quantum interconnects, quantum photonics, and opto-spintronics. Despite their remarkable potential, materials exhibiting spin-exciton and magnon-exciton coupling remain limited. To broaden the library of such materials, we explore key parameters for achieving and tuning spin-exciton and magnon-exciton couplings. We begin by examining the mechanisms of couplings in CrSBr and drawing comparisons with other recently identified two-dimensional magnetic semiconductors. Furthermore, we propose various promising scenarios for spin-exciton coupling, laying the groundwork for future research endeavors.

Spin-wave dynamics in perpendicularly magnetized antidot multilayers

Using all-optical time-resolved magneto-optical Kerr effect measurements we demonstrate an efficient modulation of the spin-wave (SW) dynamics via the bias magnetic field orientation around nanoscale diamond shaped antidots that are arranged on a square lattice within a [Co(0.75 nm)/Pd(0.9 nm)]8multilayer with perpendicular magnetic anisotropy (PMA). Micromagnetic modeling of the experimental results reveals that the SW modes in the lower frequency regime are related to narrow shell regions around the antidots, where in-plane (IP) domain structures are formed due to the reduced PMA, caused by Ga+ion irradiation during the focused ion beam milling process of antidot fabrication. The IP direction of the shell magnetization undergoes a striking change with magnetic field orientation, leading to the sharp variation of the edge localized (shell) SW modes. Nevertheless, the coupling between such edge localized and bulk SWs for different orientations of bias field in PMA systems gives rise to interesting Physics and attests to new prospects for developing energy efficient and hybrid-system-based next-generation nanoscale magnonic devices.

The 2024 magnonics roadmap

Magnonicsis a research field that has gained an increasing interest in both the fundamental and applied sciences in recent years. This field aims to explore and functionalize collective spin excitations in magnetically ordered materials for modern information technologies, sensing applications and advanced computational schemes. Spin waves, also known as magnons, carry spin angular momenta that allow for the transmission, storage and processing of information without moving charges. In integrated circuits, magnons enable on-chip data processing at ultrahigh frequencies without the Joule heating, which currently limits clock frequencies in conventional data processors to a few GHz. Recent developments in the field indicate that functional magnonic building blocks for in-memory computation, neural networks and Ising machines are within reach. At the same time, the miniaturization of magnonic circuits advances continuously as the synergy of materials science, electrical engineering and nanotechnology allows for novel on-chip excitation and detection schemes. Such circuits can already enable magnon wavelengths of 50 nm at microwave frequencies in a 5G frequency band. Research into non-charge-based technologies is urgently needed in view of the rapid growth of machine learning and artificial intelligence applications, which consume substantial energy when implemented on conventional data processing units. In its first part, the 2024 Magnonics Roadmap provides an update on the recent developments and achievements in the field of nano-magnonics while defining its future avenues and challenges. In its second part, the Roadmap addresses the rapidly growing research endeavors on hybrid structures and magnonics-enabled quantum engineering. We anticipate that these directions will continue to attract researchers to the field and, in addition to showcasing intriguing science, will enable unprecedented functionalities that enhance the efficiency of alternative information technologies and computational schemes.

Magnon-Skyrmion Hybrid Quantum Systems: Tailoring Interactions via Magnons

Coherent and dissipative interactions between different quantum systems are essential for the construction of hybrid quantum systems and the investigation of novel quantum phenomena. Here, we propose and analyze a magnon-skyrmion hybrid quantum system, consisting of a micromagnet and nearby magnetic skyrmions. We predict a strong-coupling mechanism between the magnonic mode of the micromagnet and the quantized helicity degree of freedom of the skyrmion. We show that with this hybrid setup it is possible to induce magnon-mediated nonreciprocal interactions and responses between distant skyrmion qubits or between skyrmion qubits and other quantum systems like superconducting qubits. This work provides a quantum platform for the investigation of diverse quantum effects and quantum information processing with magnetic microstructures.

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.

Strong Photon-Magnon Coupling Using a Lithographically Defined Organic Ferrimagnet

A cavity-magnonic system composed of a superconducting microwave resonator coupled to a magnon mode hosted by the organic-based ferrimagnet vanadium tetracyanoethylene (V[TCNE]x) is demonstrated. This work is motivated by the challenge of scalably integrating a low-damping magnetic system with planar superconducting circuits. V[TCNE]x has ultra-low intrinsic damping, can be grown at low processing temperatures on arbitrary substrates, and can be patterned via electron beam lithography. The devices operate in the strong coupling regime, with a cooperativity exceeding 1000 for coupling between the Kittel mode and the resonator mode at T≈0.4 K, suitable for scalable quantum circuit integration. Higher-order magnon modes are also observed with much narrower linewidths than the Kittel mode. This work paves the way for high-cooperativity hybrid quantum devices in which magnonic circuits can be designed and fabricated as easily as electrical wires.

Parametric magnon transduction to spin qubits

The integration of heterogeneous modular units for building large-scale quantum networks requires engineering mechanisms that allow suitable transduction of quantum information. Magnon-based transducers are especially attractive due to their wide range of interactions and rich nonlinear dynamics, but most of the work to date has focused on linear magnon transduction in the traditional system composed of yttrium iron garnet and diamond, two materials with difficult integrability into wafer-scale quantum circuits. In this work, we present a different approach by using wafer-compatible materials to engineer a hybrid transducer that exploits magnon nonlinearities in a magnetic microdisc to address quantum spin defects in silicon carbide. The resulting interaction scheme points to the unique transduction behavior that can be obtained when complementing quantum systems with nonlinear magnonics.

Slow-Wave Hybrid Magnonics

Cavity magnonics is an emerging research area focusing on the coupling between magnons and photons. Despite its great potential for coherent information processing, it has been long restricted by the narrow interaction bandwidth. In this Letter, we theoretically propose and experimentally demonstrate a novel approach to achieve broadband photon-magnon coupling by adopting slow waves on engineered microwave waveguides. To the best of our knowledge, this is the first time that slow wave is combined with hybrid magnonics. Its unique properties promise great potentials for both fundamental research and practical applications, for instance, by deepening our understanding of the light-matter interaction in the slow wave regime and providing high-efficiency spin wave transducers. The device concept can be extended to other systems such as optomagnonics and magnomechanics, opening up new directions for hybrid magnonics.

Reconfigurable spin current transmission and magnon-magnon coupling in hybrid ferrimagnetic insulators

Coherent spin waves possess immense potential in wave-based information computation, storage, and transmission with high fidelity and ultra-low energy consumption. However, despite their seminal importance for magnonic devices, there is a paucity of both structural prototypes and theoretical frameworks that regulate the spin current transmission and magnon hybridization mediated by coherent spin waves. Here, we demonstrate reconfigurable coherent spin current transmission, as well as magnon-magnon coupling, in a hybrid ferrimagnetic heterostructure comprising epitaxial Gd3Fe5O12 and Y3Fe5O12 insulators. By adjusting the compensated moment in Gd3Fe5O12, magnon-magnon coupling was achieved and engineered with pronounced anticrossings between two Kittel modes, accompanied by divergent dissipative coupling approaching the magnetic compensation temperature of Gd3Fe5O12 (TM,GdIG), which were modeled by coherent spin pumping. Remarkably, we further identified, both experimentally and theoretically, a drastic variation in the coherent spin wave-mediated spin current across TM,GdIG, which manifested as a strong dependence on the relative alignment of magnetic moments. Our findings provide significant fundamental insight into the reconfiguration of coherent spin waves and offer a new route towards constructing artificial magnonic architectures.

Ultrastrong to nearly deep-strong magnon-magnon coupling with a high degree of freedom in synthetic antiferromagnets

Ultrastrong and deep-strong coupling are two coupling regimes rich in intriguing physical phenomena. Recently, hybrid magnonic systems have emerged as promising candidates for exploring these regimes, owing to their unique advantages in quantum engineering. However, because of the relatively weak coupling between magnons and other quasiparticles, ultrastrong coupling is predominantly realized at cryogenic temperatures, while deep-strong coupling remains to be explored. In our work, we achieve both theoretical and experimental realization of room-temperature ultrastrong magnon-magnon coupling in synthetic antiferromagnets with intrinsic asymmetry of magnetic anisotropy. Unlike most ultrastrong coupling systems, where the counter-rotating coupling strength g2 is strictly equal to the co-rotating coupling strength g1, our systems allow for highly tunable g1 and g2. This high degree of freedom also enables the realization of normalized g1 or g2 larger than 0.5. Particularly, our experimental findings reveal that the maximum observed g1 is nearly identical to the bare frequency, with g1/ω0 = 0.963, indicating a close realization of deep-strong coupling within our hybrid magnonic systems. Our results highlight synthetic antiferromagnets as platforms for exploring unconventional ultrastrong and even deep-strong coupling regimes, facilitating the further exploration of quantum phenomena.

Nonreciprocal magnon blockade via the Barnett effect

We propose a scheme to achieve nonreciprocal magnon blockade via the Barnett effect in a magnon-based hybrid system. Due to the rotating yttrium iron garnet (YIG) sphere, the Barnett shift induced by the Barnett effect can be tuned from positive to negative via controlling magnetic field direction, leading to nonreciprocity. We show that a nonreciprocal unconventional magnon blockade (UMB) can emerge only from one magnetic field direction but not from the other side. Particularly, by further tuning system parameters, we simultaneously observe a nonreciprocal conventional magnon blockade (CMB) and a nonreciprocal UMB. This result achieves a switch between efficiency (UMB) and purity (CMB) of a single-magnon blockade. Interestingly, stronger UMB can be reached under stronger qubit-magnon coupling, even the strong coupling regime. Moreover, the nonreciprocity of the magnon blockade is sensitive to temperature. This work opens up a way for achieving quantum nonreciprocal magnetic devices and chiral magnon communications.

Magnon-mediated qubit coupling determined via dissipation measurements

Controlled interaction between localized and delocalized solid-state spin systems offers a compelling platform for on-chip quantum information processing with quantum spintronics. Hybrid quantum systems (HQSs) of localized nitrogen-vacancy (NV) centers in diamond and delocalized magnon modes in ferrimagnets-systems with naturally commensurate energies-have recently attracted significant attention, especially for interconnecting isolated spin qubits at length-scales far beyond those set by the dipolar coupling. However, despite extensive theoretical efforts, there is a lack of experimental characterization of the magnon-mediated interaction between NV centers, which is necessary to develop such hybrid quantum architectures. Here, we experimentally determine the magnon-mediated NV-NV coupling from the magnon-induced self-energy of NV centers. Our results are quantitatively consistent with a model in which the NV center is coupled to magnons by dipolar interactions. This work provides a versatile tool to characterize HQSs in the absence of strong coupling, informing future efforts to engineer entangled solid-state systems.

Optimized Protocols for Duplex Quantum Transduction

Quantum transducers convert quantum signals through hybrid interfaces of physical platforms in quantum networks. Modeled as quantum communication channels, performance of unidirectional quantum transduction can be measured by the quantum channel capacity. However, characterizing performance of quantum transducers used for duplex quantum transduction where signals are converted bidirectionally remains an open question. Here, we propose rate regions to characterize the performance of duplex quantum transduction. Using this tool, we find that quantum transducers optimized for simultaneous duplex transduction can outperform strategies based on the standard protocol of time-shared unidirectional transduction. Integrated over the frequency domain, we demonstrate that the rate region can also characterize quantum transducers with finite bandwidth.

Non-equilibrium dynamics of spin-lattice coupling

Quantifying the dynamics of normal modes and how they interact with other excitations is of central importance in condensed matter. Spin-lattice coupling is relevant to several sub-fields of condensed matter physics; examples include spintronics, high-Tc superconductivity, and topological materials. However, experimental approaches that can directly measure it are rare and incomplete. Here we use time-resolved X-ray diffraction to directly access the ultrafast motion of atoms and spins following the coherent excitation of an electromagnon in a multiferroic hexaferrite. One striking outcome is the different phase shifts relative to the driving field of the two different components. This phase shift provides insight into the excitation process of such a coupled mode. This direct observation of combined lattice and magnetization dynamics paves the way to access the mode-selective spin-lattice coupling strength, which remains a missing fundamental parameter for ultrafast control of magnetism and is relevant to a wide variety of materials.

Temperature-related single-photon transport in a waveguide QED

We propose a scheme to realize a novel, to the best of our knowledge, scenario that the single-photon transport in a one-dimensional waveguide can be affected by the temperature. The scheme is composed by a waveguide-atom interacting structure linked to a thermal bath. The single-photon reflection (or transmission) coefficient can be controlled by adjusting the temperature of the thermal bath. This provides a thermal control of the single-photon transport. Moreover, the scheme provides an approach for implementing the optical thermometer, in which the temperature of the thermal bath is estimated by measuring the photonic transport. The thermometer can accurately measure the temperature in the low-temperature region.

Resolving Nonclassical Magnon Composition of a Magnetic Ground State via a Qubit

Recently gained insights into equilibrium squeezing and entanglement harbored by magnets point toward exciting opportunities for quantum science and technology, while concrete protocols for exploiting these are needed. Here, we theoretically demonstrate that a direct dispersive coupling between a qubit and a noneigenmode magnon enables detecting the magnonic number states' quantum superposition that forms the ground state of the actual eigenmode-squeezed magnon-via qubit excitation spectroscopy. Furthermore, this unique coupling is found to enable control over the equilibrium magnon squeezing and a deterministic generation of squeezed even Fock states via the qubit state and its excitation. Our work demonstrates direct dispersive coupling to noneigenmodes, realizable in spin systems, as a general pathway to exploiting the equilibrium squeezing and related quantum properties thereby motivating a search for similar realizations in other platforms.

Controlling magnon-magnon entanglement and steering by atomic coherence

Here we show that it is possible to control magnon-magnon entanglement in a hybrid magnon-atom-cavity system based on atomic coherence. In a four-level V-type atomic system, two strong fields are applied to drive two dipole-allowed transitions and two microwave cavity modes are coupled with two dipole forbidden transitions as well as two magnon modes simultaneously. It is found that the stable magnon-magnon entanglement, one-way steering and two-way EPR steering can be generated and controlled by atomic coherence according to the following two points: (i) the coherent coupling between magnon and atoms is established via exchange of virtual photons; (ii) the dissipation of magnon mode is dominant over amplification since one of the atomic states mediated one-channel interaction always keeps empty. The coherent control of magnon-magnon correlations provides an effective approach to modify macroscopic quantum effects using the laser-driven atomic systems.

Bidirectional field-steering and atomic steering induced by a magnon mode in a qubit-photon system

This paper investigates the cavity-magnon steering and qubit-qubit steering of a hybrid quantum system consisting of a single-mode magnon, a two-qubit state, and a single-mode cavity field in the presence of their damping rates. The temporal wave vector of the system is obtained for the initial maximally entangled two-qubit state and initial vacuum state of the magnon and cavity modes. Additionally, the mathematical inequalities for obtaining the cavity-magnon steering and qubit-qubit steering are introduced. The findings reveal that steering between the magnon and cavity is asymmetric, while steering between the two qubits is symmetric in our system. Increasing the atom-field coupling improves steering from magnon to field, while reducing steering between the two qubits. Moreover, increasing magnon-field coupling enhances and elevates the lower bounds of qubit-qubit steering. Further, adding the damping rates causes deterioration of the cavity-magnon steering and qubit-qubit steering. However, the steering persistence is slightly greater when damping originates from the cavity field rather than the magnon modes based on the coupling parameters.

Meterscale Strong Coupling between Magnons and Photons

We experimentally realize a meterscale strong coupling effect between magnons and photons at room temperature, with a coherent coupling of ∼20  m and a dissipative coupling of ∼7.6  m. To this end, we integrate a saturable gain into a microwave cavity and then couple this active cavity to a magnon mode via a long coaxial cable. The gain compensates for the cavity dissipation, but preserves the cavity radiation that mediates the indirect photon-magnon coupling. It thus enables the long-range strong photon-magnon coupling. With full access to traveling waves, we demonstrate a remote control of photon-magnon coupling by modulating the phase and amplitude of traveling waves, rather than reconfiguring subsystems themselves. Our method for realizing long-range strong coupling in cavity magnonics provides a general idea for other physical systems. Our experimental achievements may promote the construction of information networks based on cavity magnonics.

Magnon-photon cross-correlations via optical nonlinearity in cavity magnonical system

We propose an alternative scheme to achieve the cross-correlations between magnon and photon in a hybrid nonlinear system including two microwave cavities and one yttrium iron garnet (YIG) sphere, where two cavities nonlinearly interact and meanwhile one of cavities couples to magnon representing the collective excitation in YIG sphere via magnetic dipole interaction. Based on dispersive couplings between two cavities and between one cavity and magnon with the larger detunings, the nonlinear interaction occurs between the other cavity and magnon, which plays a crucial role in generating quantum correlations. By analyzing the second-order correlation functions via numerical simulations and analytical calculations, the remarkable nonclassical correlations are existent in such a system, where the magnon blockade and photon antibunching could be obtainable on demand. The scheme we present is focused on the magnon-photon cross-correlations in the weak coupling regime and relaxes the requirements of experimental conditions, which may have potential applications in quantum information processing in the hybrid system.

Dissipative dynamics of optomagnonic nonclassical features via anti-Stokes optical pulses: squeezing, blockade, anti-correlation, and entanglement

We propose a feasible experimental model to investigate the generation and characterization of nonclassical states in a cavity optomagnonic system consisting of a ferromagnetic YIG sphere that simultaneously supports both the magnon mode and two whispering gallery modes of optical photons. The photons undergo the magnon-induced Brillouin light scattering, which is a well-established tool for the cavity-assisted manipulations of magnons as well as magnon spintronics. At first, we derive the desired interaction Hamiltonian under the influence of the anti-Stokes scattering process and then proceed to analyze the dynamical evolution of quantum statistics of photons and magnons as well as their intermodal entanglement. The results show that both photons and magnons generally acquire some nonclassical features, e.g., the strong antibunching and anti-correlation. Interestingly, the system may experience the perfect photon and magnon blockade phenomena, simultaneously. Besides, the nonclassical features may be protected against the unwanted environmental effects for a relatively long time, especially, in the weak driving field regime and when the system is initiated with a small number of particles. However, it should be noted that some fast quantum-classical transitions may occur in-between. Although the unwanted dissipative effects plague the nonclassical features, we show that this system can be adopted to prepare optomagnonic entangled states. The generation of entangled states depends on the initial state of the system and the interaction regime. The intermodal photon-magnon entanglement may be generated and pronounced, especially, if the system is initialized with low intensity even Schrödinger cat state in the strong coupling regime. The cavity-assisted manipulation of magnons is a unique and flexible mechanism that allows an interesting test bed for investigating the interdisciplinary contexts involving quantum optics and spintronics. Moreover, such a hybrid optomagnonic system may be used to design both on-demand single-photon and single-magnon sources and may find potential applications in quantum information processing.

Strong on-Chip Microwave Photon-Magnon Coupling Using Ultralow-Damping Epitaxial Y3Fe5O12 Films at 2 K

Y₃Fe₅O₁₂ is arguably the best magnetic material for magnonic quantum information science (QIS) because of its extremely low damping. We report ultralow damping at 2 K in epitaxial Y₃Fe₅O₁₂ thin films grown on a diamagnetic Y₃Sc₂Ga₃O₁₂ substrate that contains no rare-earth elements. Using these ultralow damping YIG films, we demonstrate for the first time strong coupling between magnons in patterned YIG thin films and microwave photons in a superconducting Nb resonator. This result paves the road toward scalable hybrid quantum systems that integrate superconducting microwave resonators, YIG film magnon conduits, and superconducting qubits into on-chip QIS devices.

Quantum Control of a Single Magnon in a Macroscopic Spin System

Nonclassical quantum states are the pivotal features of a quantum system that differs from its classical counterpart. However, the generation and coherent control of quantum states in a macroscopic spin system remain an outstanding challenge. Here we experimentally demonstrate the quantum control of a single magnon in a macroscopic spin system (i.e., 1 mm-diameter yttrium-iron-garnet sphere) coupled to a superconducting qubit via a microwave cavity. By tuning the qubit frequency in situ via the Autler-Townes effect, we manipulate this single magnon to generate its nonclassical quantum states, including the single-magnon state and the superposition of single-magnon state and vacuum (zero magnon) state. Moreover, we confirm the deterministic generation of these nonclassical states by Wigner tomography. Our experiment offers the first reported deterministic generation of the nonclassical quantum states in a macroscopic spin system and paves a way to explore its promising applications in quantum engineering.

Probing spin dynamics of ultra-thin van der Waals magnets via photon-magnon coupling

Layered van der Waals (vdW) magnets can maintain a magnetic order even down to the single-layer regime and hold promise for integrated spintronic devices. While the magnetic ground state of vdW magnets was extensively studied, key parameters of spin dynamics, like the Gilbert damping, crucial for designing ultra-fast spintronic devices, remains largely unexplored. Despite recent studies by optical excitation and detection, achieving spin wave control with microwaves is highly desirable, as modern integrated information technologies predominantly are operated with these. The intrinsically small numbers of spins, however, poses a major challenge to this. Here, we present a hybrid approach to detect spin dynamics mediated by photon-magnon coupling between high-Q superconducting resonators and ultra-thin flakes of Cr₂Ge₂Te₆ (CGT) as thin as 11 nm. We test and benchmark our technique with 23 individual CGT flakes and extract an upper limit for the Gilbert damping parameter. These results are crucial in designing on-chip integrated circuits using vdW magnets and offer prospects for probing spin dynamics of monolayer vdW magnets.

Hybrid magnonics in hybrid perovskite antiferromagnets

Hybrid magnonic systems are a newcomer for pursuing coherent information processing owing to their rich quantum engineering functionalities. One prototypical example is hybrid magnonics in antiferromagnets with an easy-plane anisotropy that resembles a quantum-mechanically mixed two-level spin system through the coupling of acoustic and optical magnons. Generally, the coupling between these orthogonal modes is forbidden due to their opposite parity. Here we show that the Dzyaloshinskii-Moriya-Interaction (DMI), a chiral antisymmetric interaction that occurs in magnetic systems with low symmetry, can lift this restriction. We report that layered hybrid perovskite antiferromagnets with an interlayer DMI can lead to a strong intrinsic magnon-magnon coupling strength up to 0.24 GHz, which is four times greater than the dissipation rates of the acoustic/optical modes. Our work shows that the DMI in these hybrid antiferromagnets holds promise for leveraging magnon-magnon coupling by harnessing symmetry breaking in a highly tunable, solution-processable layered magnetic platform.

Generation of robust optical entanglement in cavity optomagnonics

We propose a scheme to realize robust optical entanglement in cavity optomagnonics, where two optical whispering gallery modes (WGMs) couple to a magnon mode in a yttrium iron garnet (YIG) sphere. The beam-splitter-like and two-mode squeezing magnon-photon interactions can be realized simultaneously when the two optical WGMs are driven by external fields. Entanglement between the two optical modes is then generated via their coupling with magnons. By exploiting the destructive quantum interference between the bright modes of the interface, the effects of initial thermal occupations of magnons can be eliminated. Moreover, the excitation of the Bogoliubov dark mode is capable of protecting the optical entanglement from thermal heating effects. Therefore, the generated optical entanglement is robust against thermal noise and the requirement of cooling the magnon mode is relaxed. Our scheme may find applications in the study of magnon-based quantum information processing.

Nonreciprocal sideband responses in a spinning microwave magnomechanical system

Nonreciprocal sideband responses in a spinning microwave magnomechanical system consists of a spinning resonator coupled with a yttrium iron garnet sphere are proposed. We show that the efficiency of sideband generation can be enhanced in one driving direction but restrained in the opposite. This nonreciprocity results from Sagnac effect induced by the spinning resonator, leading to asymmetric magnonic responses in two different driving directions. Beyond the conventional linearized description, the properties of nonreciprocal two-color second-order sideband are demonstrated. By adjusting Sagnac-Fizeau shift and the power of control field, the degree of asymmetric magnonic responses can be strengthened, therefore causing stronger nonreciprocity of sideband. Especially, for the case of strong Sagnac-Fizeau shift and the control field, high level of efficiency and isolation ratio of sideband are achieved simultaneously and the operational bandwidth of strong nonreciprocity can be expanded. Our proposal provides an effective avenue for the manipulation of the nonreciprocity of sideband and has potentially practical applications in on-chip microwave isolation devices and magnon-based precision measurement.

P T symmetry in a superconducting hybrid quantum system with longitudinal coupling

We propose a scheme consisting of coupled nanomechanical cantilever resonators and superconducting flux qubits to engineer a parity-time- (P T-) symmetric phononic system formed by active and passive modes. The effective gain (loss) of the phonon mode is achieved by the longitudinal coupling of the resonator and the fast dissipative superconducting qubit with a blue-sideband driving (red-sideband driving). A P T-symmetric to broken-P T-symmetric phase transition can be observed in both balanced gain-to-loss and unbalanced gain-to-loss cases. Applying a resonant weak probe field to the dissipative resonator, we find that (i) for balanced gain and loss, the acoustic signal absorption to amplification can be tuned by changing the coupling strength between resonators; (ii) for unbalanced gain and loss, both acoustically induced transparency and anomalous dispersion can be observed around Δ = 0, where the maximum group delay is also located at this point. Our work provides an experimentally feasible scheme to design P T-symmetric phononic systems and a powerful platform for controllable acoustic signal transmission in a hybrid quantum system.

Unveiling a Pump-Induced Magnon Mode via Its Strong Interaction with Walker Modes

We observe a power-dependent anticrossing of Walker spin-wave modes under microwave pumping when a ferrimagnet is placed in a microwave waveguide that does not support any discrete photon mode. We interpret this unexpected anticrossing as the generation of a pump-induced magnon mode that couples strongly to the Walker modes of the ferrimagnet. This anticrossing inherits an excellent tunability from the pump, which allows us to control the anticrossing via the pump power, frequency, and waveform. Further, we realize a remarkable functionality of this anticrossing, namely, a microwave frequency comb, in terms of the nonlinear interaction that mixes the pump and probe frequencies. Such a frequency comb originates from the magnetic dynamics and thereby does not suffer from the charge noise. The unveiled hybrid magnonics driven away from its equilibrium enriches the utilization of anticrossing for coherent information processing.

Bias field orientation driven reconfigurable magnonics and magnon-magnon coupling in triangular shaped Ni80Fe20nanodot arrays

Reconfigurable magnonics have attracted intense interest due to their myriad advantages including energy efficiency, easy tunability and miniaturization of on-chip data communication and processing devices. Here, we demonstrate efficient reconfigurability of spin-wave (SW) dynamics as well as SW avoided crossing by varying bias magnetic field orientation in triangular shaped Ni₈₀Fe₂₀nanodot arrays. In particular, for a range of in-plane angles of bias field, we achieve mutual coherence between two lower frequency modes leading to a drastic modification in the ferromagnetic resonance frequency. Significant modification in magnetic stray field distribution is observed at the avoided crossing regime due to anisotropic dipolar interaction between two neighbouring dots. Furthermore, using micromagnetic simulations we demonstrate that the hybrid SW modes propagate longer through an array as opposed to the non-interacting modes present in this system, indicating the possibility of coherent energy transfer of hybrid magnon modes. This result paves the way for the development of integrated on-chip magnonic devices operating in the gigahertz frequency regime.

Enhancement of the microwave photon-magnon coupling strength for a planar fabricated resonator

Planar resonators have a wide usage in modern microwave technologies and perspectives in novel quantum technologies development. As was demonstrated earlier, their utilization allows to achieve high values of microwave photon-magnon coupling strength-an important parameter in technologies of information coherent transfer from electromagnetic GHz range to the optical range. In the present work, the achievement of the high value of the microwave photon-magnon coupling strength by exploiting the increase of the spatial concentration of the magnetic component of the planar resonator electromagnetic field is reported. Starting from the conventional planar split-ring resonator design we increased the coupling strength up to 40% by modifying the resonator shape. The numerical simulation and experimental verification showed a predicted increase in the spatial concentration of the microwave magnetic component and showed the increased value of the microwave photon-magnon coupling strength as a sequence.

Tunable interaction between excitons and hybridized magnons in a layered semiconductor

The interaction between distinct excitations in solids is of both fundamental interest and technological importance. One such interaction is the coupling between an exciton, a Coulomb bound electron-hole pair, and a magnon, a collective spin excitation. The recent emergence of van der Waals magnetic semiconductors¹ provides a platform to explore these exciton-magnon interactions and their fundamental properties, such as strong correlation², as well as their photospintronic and quantum transduction³ applications. Here we demonstrate the precise control of coherent exciton-magnon interactions in the layered magnetic semiconductor CrSBr. We varied the direction of an applied magnetic field relative to the crystal axes, and thus the rotational symmetry of the magnetic system⁴. Thereby, we tuned not only the exciton coupling to the bright magnon, but also to an optically dark mode via magnon-magnon hybridization. We further modulated the exciton-magnon coupling and the associated magnon dispersion curves through the application of uniaxial strain. At a critical strain, a dispersionless dark magnon band emerged. Our results demonstrate an unprecedented level of control of the opto-mechanical-magnonic coupling, and a step towards the predictable and controllable implementation of hybrid quantum magnonics^5-11.

Ringing spectroscopy in the magnomechanical system

The ringing phenomenon has been studied in optical whispering gallery mode (WGM) resonators and can be used to sense the ultrafast process in spectroscopy. Here we observe the ringing phenomenon in a magnomechanical system for the first time, which is induced by the interference between the microwave photons converted from the damped phonons and the probing microwave photons. This interference eventually appears as a transparency window even along with the ringing phenomenon in the measured microwave reflection spectrum, which is influenced by the scanning speed and the input power. Then, the ringing spectroscopy is used to measure the coupling strength between the magnon and phonon modes, and outline the displacement profile of S 1 , 2 , 2 mechanical mode in a YIG microsphere, demonstrating the theoretical analysis. In addition, the ring-up spectroscopy is developed in our magnomechanical system, laying the foundation for fast sensing based on mechanical motion.

Giant spin ensembles in waveguide magnonics

The dipole approximation is usually employed to describe light-matter interactions under ordinary conditions. With the development of artificial atomic systems, 'giant atom' physics is possible, where the scale of atoms is comparable to or even greater than the wavelength of the light they interact with, and the dipole approximation is no longer valid. It reveals interesting physics impossible in small atoms and may offer useful applications. Here, we experimentally demonstrate the giant spin ensemble (GSE), where a ferromagnetic spin ensemble interacts twice with the meandering waveguide, and the coupling strength between them can be continuously tuned from finite (coupled) to zero (decoupled) by varying the frequency. In the nested configuration, we investigate the collective behavior of two GSEs and find extraordinary phenomena that cannot be observed in conventional systems. Our experiment offers a new platform for 'giant atom' physics.

The Classicality and Quantumness of the Driven Qubit–Photon–Magnon System

The hybrid architecture of the driven qubit–photon–magnon system has recently emerged as a promising candidate for novel quantum technologies. In this paper, we introduce the effective wave-function of a superconducting single qubit and a magnon mode contained within a cavity resonator and an external field. The non-classicality of the magnon and resonator modes are investigated by using the negative values of the Wigner function. Additionally, we discuss the non-classicality of the qubit state via the Wigner–Yanase skew information. We find that the mixture angle of the qubit–resonator plays a controllable role in non-classicality. However, the strength of the magnon–photon increases the non-classical behaviour of the system.

Magnon-atom-optical photon entanglement via the microwave photon-mediated Raman interaction

We show that it is possible to generate magnon-atom-optical photon tripartite entanglement via the microwave photon-mediated Raman interaction. Magnons in a macroscopic ferromagnet and optical photons in a cavity are induced into a Raman interaction with an atomic spin ensemble when a microwave field couples the magnons to one Raman wing. The controllable magnon-atom entanglement, magnon-optical photon entanglement, and even genuine magnon-atom-optical photon tripartite entanglement can be generated simultaneously. In addition, these bipartite and tripartite entanglements are robust against the environment temperature. Our scheme paves the way for exploring a quantum interface bridging the microwave and optical domains, and may provide a promising building block for hybrid quantum networks.

Exciton-coupled coherent magnons in a 2D semiconductor

The recent discoveries of two-dimensional (2D) magnets^1-6 and their stacking into van der Waals structures^7-11 have expanded the horizon of 2D phenomena. One exciting application is to exploit coherent magnons¹² as energy-efficient information carriers in spintronics and magnonics^13,14 or as interconnects in hybrid quantum systems^15-17. A particular opportunity arises when a 2D magnet is also a semiconductor, as reported recently for CrSBr (refs. ^18-20) and NiPS₃ (refs. ^21-23) that feature both tightly bound excitons with a large oscillator strength and potentially long-lived coherent magnons owing to the bandgap and spatial confinement. Although magnons and excitons are energetically mismatched by orders of magnitude, their coupling can lead to efficient optical access to spin information. Here we report strong magnon-exciton coupling in the 2D A-type antiferromagnetic semiconductor CrSBr. Coherent magnons launched by above-gap excitation modulate the exciton energies. Time-resolved exciton sensing reveals magnons that can coherently travel beyond seven micrometres, with a coherence time of above five nanoseconds. We observe these exciton-coupled coherent magnons in both even and odd numbers of layers, with and without compensated magnetization, down to the bilayer limit. Given the versatility of van der Waals heterostructures, these coherent 2D magnons may be a basis for optically accessible spintronics, magnonics and quantum interconnects.

Structural, Optical, and Magnetic Properties of Erbium-Substituted Yttrium Iron Garnets

We synthesized a series of slightly erbium-substituted yttrium iron garnets (Er:YIG), Y_3-x Er _x Fe₅O₁₂ at different Er concentrations (x = 0, 0.01, 0.05, 0.10, and 0.20) using a solid-state reaction and investigated their structural, magnetic, and optical properties as a function of Er concentration. The volume of the unit cell slightly increased with Er concentration and Er atoms predominately replaced Y atoms in the dodecahedrons of YIG. The optical properties exhibited certain decreases in reflectance in the 1500-1600 nm wavelength range due to the presence of Er³⁺. Despite the many unpaired 4f electrons in Er³⁺, the total magnetic moments of Er:YIG showed similar trends with temperatures and magnetic fields above 30 K. An X-ray magnetic circular dichroism study confirmed the robust Fe 3d magnetic moments. However, the magnetic moments suddenly decreased to below 30 K with Er substitution, and the residual magnetism (M _R) and coercive field (H _C) in the magnetic hysteresis loops decreased to below 30 K with Er substitution. This implies that Er substitution in YIG has a negligible effect on magnetic properties over a wide temperature range except below 30 K where the Er 4f spins are coupled antiparallel to the majority Fe 3d spins. Our studies demonstrated that above 30 K the magnetic properties of YIG are retained even with Er substitution, which is evidence that the Er doping scheme is applicable for YIG-based magneto-optical devices in the mid-infrared regime.

Analog Quantum Control of Magnonic Cat States on a Chip by a Superconducting Qubit

We propose to directly and quantum-coherently couple a superconducting transmon qubit to magnons-the quanta of the collective spin excitations, in a nearby magnetic particle. The magnet's stray field couples to the qubit via a superconducting quantum interference device. We predict a resonant magnon-qubit exchange and a nonlinear radiation-pressure interaction that are both stronger than dissipation rates and tunable by an external flux bias. We additionally demonstrate a quantum control scheme that generates magnon-qubit entanglement and magnonic Schrödinger cat states with high fidelity.

Parametric-amplification-induced nonreciprocal magnon laser

We theoretically propose a scheme to achieve all-optical nonreciprocal magnon lasing action in a composite cavity optomagnonical system considering of a yttrium iron garnet sphere coupled to a parametric resonator. The magnon lasing behavior can be engendered via the magnon-induced Brillouin scattering process in the cavity optomagnonical system. By unidirectionally driving the χ⁽²⁾-nonlinear resonator with a classical coherent field, the squeezed effect occurs only in the selected direction due to the phase-matching condition, resulting in asymmetric detuning between the two resonators, which is the physical mechanism to generate a nonreciprocal magnon laser. We further examine the gain factor and power threshold of the magnon laser. Moreover, the isolation rate can reach 21 dB by adjusting the amplitude of the parametric amplification. Our work shows a path to obtain an all-optical nonreciprocal magnon laser, which provides a means for the preparation of a coherent magnon laser and laser protection.

Laser induced enhanced coupling between photons and squeezed magnons in antiferromagnets

In this paper we consider a honeycomb antiferromagnet subject to an external laser field. Obtaining a time-independent effective Hamiltonian, we find that the external laser renormalizes the exchange interaction between the in-plane components of the spin-operators, and induces a synthetic Dzyaloshinskii-Moria interaction (DMI) between second neighbors. The former allows the control of the magnon dispersion's bandwidth and the latter breaks time-reversal symmetry inducing non-reciprocity in momentum space. The eigen-excitations of the system correspond to squeezed magnons whose squeezing parameters depend on the properties of the laser. When studying how these spin excitations couple with cavity photons, we obtain a coupling strength which can be enhanced by an order of magnitude via careful tuning of the laser's intensity, when compared to the case where the laser is absent. The transmission plots through the cavity are presented, allowing the mapping of the magnons' dispersion relation.

Control of a qubit state by a soliton propagating through a Heisenberg spin chain

We demonstrate that nonlinear magnetic solitary excitations (solitons) traveling through a Heisenberg spin chain may be used as a robust tool capable of coherent control of the qubit's state. The physical problem is described by a Hamiltonian involving the interaction between the soliton and the qubit. We show that under certain conditions the generic Hamiltonian may be mapped on that of a qubit two-level system with matrix elements depending on the soliton parameters. We considered the action of a bright and a dark soliton depending on the driving nonlinear wave function. We considered a local interaction restricted the closest to the qubit spin in the chain. We computed the expressions of the physical quantities of interest for all cases and analyzed their behavior in some special limits.

Coherent Coupling of Two Remote Magnonic Resonators Mediated by Superconducting Circuits

We demonstrate microwave-mediated distant magnon-magnon coupling on a superconducting circuit platform, incorporating chip-mounted single-crystal Y_{3}Fe_{5}O_{12} (YIG) spheres. Coherent level repulsion and dissipative level attraction between the magnon modes of the two YIG spheres are demonstrated. The former is mediated by cavity photons of a superconducting resonator, and the latter is mediated by propagating photons of a coplanar waveguide. Our results open new avenues toward exploring integrated hybrid magnonic networks for coherent information processing on a quantum-compatible superconducting platform.

Magnon-phonon hybridization in 2D antiferromagnet MnPSe3

Magnetic excitations in van der Waals (vdW) materials, especially in the two-dimensional (2D) limit, are an exciting research topic from both the fundamental and applied perspectives. Using temperature-dependent, magneto-Raman spectroscopy, we identify the hybridization of two-magnon excitations with two phonons in manganese phosphorus triselenide (MnPSe₃), a magnetic vdW material that hosts in-plane antiferromagnetism. Results from first-principles calculations of the phonon and magnon spectra further support our identification. The Raman spectra’s rich temperature dependence through the magnetic transition displays an avoided crossing behavior in the phonons’ frequency and a concurrent decrease in their lifetimes. We construct a model based on the interaction between a discrete level and a continuum that reproduces these observations. Our results imply a strong hybridization between each phonon and a two-magnon continuum. This work demonstrates that the magnon-phonon interactions can be observed directly in Raman scattering and provides deep insight into these interactions in 2D magnetic materials.

Long-Time Memory and Ternary Logic Gate Using a Multistable Cavity Magnonic System

Multistability is an extraordinary nonlinear property of dynamical systems and can be explored to implement memory and switches. Here we experimentally realize the tristability in a three-mode cavity magnonic system with Kerr nonlinearity. The three stable states in the tristable region correspond to the stable solutions of the frequency shift of the cavity magnon polariton under specific driving conditions. We find that the system staying in which stable state depends on the history experienced by the system, and this state can be harnessed to store the history information. In our experiment, the memory time can reach as long as 5.11 s. Moreover, we demonstrate the ternary logic gate with good on-off characteristics using this multistable hybrid system. Our new findings pave a way towards cavity magnonics-based information storage and processing.

Remote Generation of Magnon Schrödinger Cat State via Magnon-Photon Entanglement

The magnon cat state represents a macroscopic quantum superposition of collective magnetic excitations of large number spins that not only provides fundamental tests of macroscopic quantum effects but also finds applications in quantum metrology and quantum computation. In particular, remote generation and manipulation of Schrödinger cat states are particularly interesting for the development of long-distance and large-scale quantum information processing. Here, we propose an approach to remotely prepare magnon even or odd cat states by performing local non-Gaussian operations on the optical mode that is entangled with the magnon mode through pulsed optomagnonic interaction. By evaluating key properties of the resulting cat states, we show that for experimentally feasible parameters, they are generated with both high fidelity and nonclassicality, as well as with a size large enough to be useful for quantum technologies. Furthermore, the effects of experimental imperfections such as the error of projective measurements and dark count when performing single-photon operations have been discussed, where the lifetime of the created magnon cat states is expected to be t∼1  μs.

Magnon-mediated nonreciprocal microwave transmission based on quantum interference

Nonreciprocity has always been a subject of interest and plays a key role in a variety of applications like signal processing and noise isolation. In this work, we propose a simple and feasible scheme to implement nonreciprocal microwave transmission in a high-quality-factor superconducting cavity with ferrimagnetic materials. We derive necessary requirements to create nonreciprocity in our system where a magnon mode and two microwave modes are coupled to each other, highlighting the adjustability of a static magnetic field controlled nonreciprocal transmission based on quantum interference between different transmission paths, which breaks time-reversal symmetry of the three-mode cavity magnonics system. The high light isolation adjusted within a range of different magnetic fields can be obtained by modulating the photon-magnon coupling strength. Due to the simplicity of the device and the system tunability, our results may facilitate potential applications for light magnetic sensing and coherent information processing.

Voltage-Controlled Reconfigurable Magnonic Crystal at the Sub-micrometer Scale

Multiferroics offer an elegant means to implement voltage control and on the fly reconfigurability in microscopic, nanoscaled systems based on ferromagnetic materials. These properties are particularly interesting for the field of magnonics, where spin waves are used to perform advanced logical or analogue functions. Recently, the emergence of nanomagnonics is expected to eventually lead to the large-scale integration of magnonic devices. However, a compact voltage-controlled, on demand reconfigurable magnonic system has yet to be shown. Here, we introduce the combination of multiferroics with ferromagnets in a fully epitaxial heterostructure to achieve such voltage-controlled and reconfigurable magnonic systems. Imprinting a remnant electrical polarization in thin multiferroic BiFeO₃ with a periodicity of 500 nm yields a modulation of the effective magnetic field in the micrometer-scale, ferromagnetic La_2/3Sr_1/3MnO₃ magnonic waveguide. We evidence the magnetoelectric coupling by characterizing the spin wave propagation spectrum in this artificial, voltage induced, magnonic crystal and demonstrate the occurrence of a robust magnonic band gap with >20 dB rejection.

Resonant amplification of intrinsic magnon modes and generation of new extrinsic modes in a two-dimensional array of interacting multiferroic nanomagnets by surface acoustic waves

Using time-resolved magneto-optical Kerr effect (TR-MOKE) microscopy, we demonstrate surface-acoustic-wave (SAW) induced resonant amplification of intrinsic spin-wave (SW) modes, as well as generation of new extrinsic or driven modes at the SAW frequency, in a densely packed two-dimensional array of elliptical Co nanomagnets fabricated on a piezoelectric LiNbO₃ substrate. This system can efficiently serve as a magnonic crystal (MC), where the intrinsic shape anisotropy and the strong inter-element magnetostatic interaction trigger the incoherent precession of the nanomagnets' magnetization in the absence of any bias magnetic field, giving rise to the 'intrinsic' SW modes. The magnetoelastic coupling leads to a rich variety of SW phenomena when the SAW is launched along the major axis of the nanomagnets, such as 4-7 times amplification of intrinsic modes (at 3, 4, 7 and 10 GHz) when the applied SAW frequencies are resonant with these frequencies, and the generation of new extrinsic modes at non-resonant SAW frequencies. However, when the SAW is launched along the minor axis, a dominant driven mode appears at the applied SAW frequency. This reveals that the magnetoelastic coupling between SW and SAW is anisotropic in nature. Micromagnetic simulation results are in qualitative agreement with the experimental observations and elucidate the underlying dynamics. Our findings lay the groundwork for bias-field free magnonics, where the SW behavior is efficiently tuned by SAWs. It has important applications in the design of energy efficient on-chip microwave devices, SW logic, and extreme sub-wavelength ultra-miniaturized microwave antennas for embedded applications.