Magnon-Photon-Phonon Entanglement in Cavity Magnomechanics

Spin-Mechanical Coupling in 2D Antiferromagnet CrSBr

Spin-mechanical coupling is vital in diverse fields including spintronics, sensing, and quantum transduction. Two-dimensional (2D) magnetic materials provide a unique platform for investigating spin-mechanical coupling, attributed to their mechanical flexibility and novel spin orderings. However, studying their spin-mechanical coupling presents challenges in probing mechanical deformation and thermodynamic property changes at the nanoscale. Here we use nano-optoelectromechanical interferometry to mechanically detect the phase transition and magnetostriction effect in multilayer CrSBr, an air-stable antiferromagnet with large magnon-exciton coupling. The transitions among antiferromagnetism, spin-canted ferromagnetism, and paramagnetism are visualized. Nontrivial magnetostriction coefficient 2.3 × 10-5 and magnetoelastic coupling strength on the order of 106 J/m3 have been found. Moreover, we demonstrate the substantial tunability of the magnetoelastic constant by nearly 50% via gate-induced strain. Our findings demonstrate the strong spin-mechanical coupling in CrSBr and pave the way for developing sensitive magnetic sensing and efficient quantum transduction at the atomically thin limit.

Macroscopic entanglement between ferrimagnetic magnons and atoms via crossed optical cavities

We consider a two-dimensional opto-magnomechanical (OMM) system including two optical cavity modes, a magnon mode, a phonon mode, and a collection of two-level atoms. We show how the stationary entanglement between two-level atoms and magnons can be achieved. The presence of two optical cavities leads the atom-magnon entanglement to be achieved in a wide parameter regime. Furthermore, it is shown that one optical cavity can get entangled with magnons, phonons, and the other optical cavity. The entanglement is robust against thermal noise. The work may find applications in building hybrid quantum networks and quantum information processing.

Entanglement and quantum coherence of two YIG spheres in a hybrid Laguerre-Gaussian cavity optomechanics

We theoretically investigate continuous variable entanglement and macroscopic quantum coherence in the hybrid L-G rotational cavity optomechanical system containing two YIG spheres. In this system, a single L-G cavity mode and both magnon modes (which are due to the collective excitation of spins in two YIG spheres) are coupled through the magnetic dipole interaction whereas the L-G cavity mode can also exchange orbital angular momentum (OAM) with the rotating mirror (RM). We study in detail the effects of various physical parameters like cavity and both magnon detunings, environment temperature, optorotational and magnon coupling strengths on the bipartite entanglement and the macroscopic quantum coherence as well. We also explore parameter regimes to achieve maximum values for both of these quantum correlations. We also observed that the parameters regime for achieving maximum bipartite entanglement is completely different from macroscopic quantum coherence. So, our present study shall provide a method to control various nonclassical quantum correlations of macroscopic objects in the hybrid L-G rotational cavity optomechanical system and have potential applications in quantum sensing, quantum meteorology, and quantum information science.

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.

Magnomechanically induced transparency and tunable slow-fast light via a levitated micromagnet

In this paper, we theoretically investigate the magnomechanically induced transparency (MIT) phenomenon and slow-fast light propagation in a microwave cavity-magnomechanical system which includes a levitated ferromagnetic sphere. Magnetic dipole interaction determines the interaction between the photon, magnon, and center of mass motion of the cavity-magnomechanical system. As a result, we find that apart from coupling strength, which has an important role in MIT, the levitated ferromagnetic sphere's position provides us a parameter to manipulate the width of the transparency window. In addition, the control field's frequency has crucial influences on the MIT. Also this hybrid magnonic system allows us to demonstrate MIT in both the strong coupling and intermediate coupling regimes. More interestingly, we demonstrate tunable slow and fast light in this hybrid magnonic system. In other words, we show that the group delay can be adjusted by varying the control field's frequency, the sphere position, and the magnon-photon coupling strength. These parameters have an influence on the transformation from slow to fast light propagation and vice versa. Based on the recent experimental advancements, our results provide the possibility to engineer hybrid magnonic systems with levitated particles for the light propagation, and the quantum measurements and sensing of physical quantities.

Nonreciprocal magnon blockade based on nonlinear effects

We present an alternative scheme to achieve nonreciprocal unconventional magnon blockade (NUMB) in a hybrid system formed by two microwave cavities and one yttrium iron garnet (YIG) sphere, where the pump and signal cavities interact nonlinearly with each other and the signal cavity is coupled to the YIG sphere. It is found that the nonlinear coupling occurs between the pump cavity and magnon modes due to the dispersive interactions among three bosonic modes. Meanwhile, the Kerr nonlinearity is present in the pump cavity. Based on these nonlinear effects, a nonreciprocal magnon blockade could be achieved with the help of the weak parametric driving of the pump cavity. The present work provides an alternative method to prepare single magnon resource, which may be helpful for quantum information processing.

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.

Kerr nonlinearity assisted magnetically induced transparency in cavity magnon polaritons

We investigate optical transmission in cavity magnon polaritons and discover a complex multi-window magnetically induced transparency and a bistability with magnetic and optical characteristics. With the regulation of Kerr nonlinear effects and driven fields, a complex multi-window resonant transmission with fast and slow light effects appears, which includes transparency and absorption windows. The magnetically induced transparency and absorption can be explained by the destructive and constructive interference between different excitation pathways. Moreover, we demonstrate the bistability of magnons and photons with a hysteresis loop, where magnetic and optical bistabilities can induce and control each other. Our results pave a new way, to the best of our knowledge, for implementing a room-temperature multiband quantum memory.

Simultaneously enhanced magnomechanical cooling and entanglement assisted by an auxiliary microwave cavity

We propose a mechanism to simultaneously enhance quantum cooling and entanglement via coupling an auxiliary microwave cavity to a magnomechanical cavity. The auxiliary cavity acts as a dissipative cold reservoir that can efficiently cool multiple localized modes in the primary system via beam-splitter interactions, which enables us to obtain strong quantum cooling and entanglement. We analyze the stability of the system and determine the optimal parameter regime for cooling and entanglement under the auxiliary-microwave-cavity-assisted (AMCA) scheme. The maximum cooling enhancement rate of the magnon mode can reach 98.53%, which clearly reveals that the magnomechanical cooling is significantly improved in the presence of the AMCA. More importantly, the dual-mode entanglement of the system can also be significantly enhanced by AMCA in the full parameter region, where the initial magnon-phonon entanglement can be maximally enhanced by a factor of about 11. Another important result of the AMCA is that it also increases the robustness of the entanglement against temperature. Our approach provides a promising platform for the experimental realization of entanglement and quantum information processing based on cavity magnomechanics.

Quantum squeezing-induced quantum entanglement and EPR steering in a coupled optomechanical system

We propose a theoretical project in which quantum squeezing induces quantum entanglement and Einstein-Podolsky-Rosen steering in a coupled whispering-gallery-mode optomechanical system. Through pumping the χ(2)-nonlinear resonator with the phase matching condition, the generated squeezed resonator mode and the mechanical mode of the optomechanical resonator can generate strong quantum entanglement and EPR steering, where the squeezing of the nonlinear resonator plays the vital role. The transitions from zero entanglement to strong entanglement and one-way steering to two-way steering can be realized by adjusting the system parameters appropriately. The photon-photon entanglement and steering between the two resonators can also be obtained by deducing the amplitude of the driving laser. Our project does not need an extraordinarily squeezed field, and it is convenient to manipulate and provides a novel and flexible avenue for diverse applications in quantum technology dependent on both optomechanical and photon-photon entanglement and steering.

Parametrically amplified nonreciprocal magnon laser in a hybrid cavity optomagnonical system

We propose a scheme to achieve a tunable nonreciprocal magnon laser with parametric amplification in a hybrid cavity optomagnonical system, which consists a yttrium iron garnet (YIG) sphere and a spinning resonator. We demonstrate the control of magnon laser can be enhanced via parametric amplification, which make easier and more convenient to control the magnon laser. Moreover, we analyze and evaluate the effects of pump light input direction and amplification amplitude on the magnon gain and laser threshold power. The results indicate that we can obtian a higher magnon gain and a broader range of threshold power of the magnon laser. In our scheme both the nonreciprocity and magnon gain of the magnon laser can be increased significantly. Our proposal provides a way to obtain a novel nonreciprocal magnon laser and offers new possibilities for both nonreciprocal optics and spin-electronics applications.

Magnonic Frequency Comb in the Magnomechanical Resonator

An optical frequency comb is a spectrum of optical radiation which consists of evenly spaced and phase-coherent narrow spectral lines and is initially invented in a laser for frequency metrology purposes. A direct analog of frequency combs in the magnonic systems has not been demonstrated to date. In our experiment, we generate a new magnonic frequency comb in the resonator with giant mechanical oscillations through the magnomechanical interaction. We observe the magnonic frequency comb contains up to 20 comb lines, which are separated by the mechanical frequency of 10.08 MHz. The thermal effect based on the strong pump power induces the cyclic oscillation of the magnon frequency shift, which leads to a periodic oscillation of the magnonic frequency comb. Moreover, we demonstrate the stabilization and control of the frequency spacing of the magnonic frequency comb via injection locking. Our Letter lays the groundwork for magnonic frequency combs in the fields of sensing and metrology.

Feedback Control of Quantum Correlations in a Cavity Magnomechanical System with Magnon Squeezing

We suggest a method to improve quantum correlations in cavity magnomechanics, through the use of a coherent feedback loop and magnon squeezing. The entanglement of three bipartition subsystems: photon-phonon, photon-magnon, and phonon-magnon, is significantly improved by the coherent feedback-control method that has been proposed. In addition, we investigate Einstein-Podolsky-Rosen steering under thermal effects in each of the subsystems. We also evaluate the scheme's performance and sensitivity to magnon squeezing. Furthermore, we study the comparison between entanglement and Gaussian quantum discord in both steady and dynamical states.

Entanglement enhancement and EPR steering based on a PT-symmetric-like cavity-opto-magnomechanical hybrid system

We investigate the enhancement of entanglement and EPR steering in a parity-time(PT-) symmetric-like cavity-opto-magnomechanical system. The system consists of an optical cavity, a magnon mode in a ferromagnetic crystal, a phonon mode, and a microwave cavity. Our findings demonstrate that microwave-cavity gain significantly boosts distant quantum entanglement and greatly improves the robustness of bipartite entanglement against environment temperature. Additionally, we observe an enhancement of tripartite entanglement within the system and uncover the phenomenon of entanglement transfer. Notably, we also achieve one-way steering and two-way asymmetric steering in the system. This study offers insights into the integration of traditional optomechanics and cavity magnomechanics, presenting a novel approach to manipulate asymmetric quantum steering between two distant macroscopic objects. The implications of our research extend to the fields of quantum state preparation and quantum information.

Entanglement generation and steering implementation in a double-cavity-magnon hybrid system

We demonstrate a scheme for the generation of bipartite and tripartite entanglement, as well as he implementation of stable and controllable long-distance one-way and asymmetric two-way steering in a cavity-magnon hybrid system. This system consists of a magnon mode and two coupled microwave cavities. The first cavity is driven by a flux-driven Josephson parametric amplifier, which generates squeezed vacuum fields, and is coupled to the other cavity through optical tunneling interaction. The second cavity and magnon mode are coupled through magnetic dipole interaction. We find that under weak coupling between the two cavities, and strong coupling between the second cavity and magnon mode, remote controllable one-way steering and tripartite entanglement can be achieved. Our scheme may have potential applications in quantum information.

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.

High-efficiency entanglement of microwave fields in cavity opto-magnomechanical systems

We demonstrate a scheme to realize high-efficiency entanglement of two microwave fields in a dual opto-magnomechanical system. The magnon mode simultaneously couples with the microwave cavity mode and phonon mode via magnetic dipole interaction and magnetostrictive interaction, respectively. Meanwhile, the phonon mode couples with the optical cavity mode via radiation pressure. Each magnon mode and optical cavity mode adopts a strong red detuning driving field to activate the beam splitter interaction. Therefore, the entangled state generated by the injected two-mode squeezed light in optical cavities can be eventually transferred into two microwave cavities. A stationary entanglement E a 1 a 2 =0.54 is obtained when the input two-mode squeezed optical field has a squeezing parameter r = 1. The entanglement E a 1 a 2 increases as the squeezing parameter r increases, and it shows the flexible tunability of the system. Meanwhile, the entanglement survives up to an environmental temperature about 385 mK, which shows high robustness of the scheme. The proposed scheme provides a new mechanism to generate entangled microwave fields via magnons, which enables the degree of the prepared microwave entanglement to a more massive scale. Our result is useful for applications which require high entanglement of microwave fields like quantum radar, quantum navigation, quantum teleportation, quantum wireless fidelity (Wi-Fi) network, etc.

Quantum illumination based on cavity-optomagnonics system with Kerr nonlinearity

Quantum illumination is a quantum optical sensing technique, which employs an entangled source to detect low-reflectivity object immersed in a bright thermal background. Hybrid cavity-optomagnonics system promises to work as quantum illumination because a yttrium iron garnet (YIG) sphere can couple to microwave field and optical field. In this paper, we propose a scheme to enhance the entanglement between the output fields of the microwave and optical cavities by considering the intrinsic Kerr nonlinearity of the YIG. We investigate the difference between intrinsic Kerr nonlinearity and optomagnonical parametric-type coupling on improving entanglement. Our result show that the large value optomagnonical parametric-type coupling does not mean the large entanglement, nevertheless, the large value of Kerr nonlinearity does monotonously improve the entanglement for our group of parameters. Consequently, under feasible parameters of current experiment, the signal-to-noise ratio and probability of detection error can be improved after considering the magnon Kerr nonlinearity.

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.

Enhancement of magnon-photon-phonon entanglement in a cavity magnomechanics with coherent feedback loop

In this paper, we present a coherent feedback loop scheme to enhance the magnon-photon-phonon entanglement in cavity magnomechanics. We provide a proof that the steady state and dynamical state of the system form a genuine tripartite entanglement state. To quantify the entanglement in the bipartite subsystem and the genuine tripartite entanglement, we use the logarithmic negativity and the minimum residual contangle, respectively, in both the steady and dynamical regimes. We demonstrate the feasibility of our proposal by implementing it with experimentally realizable parameters to achieve the tripartite entanglement. We also show that the entanglement can be significantly improved with coherent feedback by appropriately tuning the reflective parameter of the beam splitter and that it is resistant to environmental thermalization. Our findings pave the way for enhancing entanglement in magnon-photon-phonon systems and may have potential applications in quantum information.

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.

Enhanced Tripartite Interactions in Spin-Magnon-Mechanical Hybrid Systems

Coherent tripartite interactions among degrees of freedom of completely different nature are instrumental for quantum information and simulation technologies, but they are generally difficult to realize and remain largely unexplored. Here, we predict a tripartite coupling mechanism in a hybrid setup comprising a single nitrogen-vacancy (NV) center and a micromagnet. We propose to realize direct and strong tripartite interactions among single NV spins, magnons, and phonons via modulating the relative motion between the NV center and the micromagnet. Specifically, by introducing a parametric drive (two-phonon drive) to modulate the mechanical motion (such as the center-of-mass motion of a NV spin in diamond trapped in an electrical trap or a levitated micromagnet in a magnetic trap), we can obtain a tunable and strong spin-magnon-phonon coupling at the single quantum level, with up to 2 orders of magnitude enhancement for the tripartite coupling strength. This enables, for example, tripartite entanglement among solid-state spins, magnons, and mechanical motions in quantum spin-magnonics-mechanics with realistic experimental parameters. This protocol can be readily implemented with the well-developed techniques in ion traps or magnetic traps and could pave the way for general applications in quantum simulations and information processing based on directly and strongly coupled tripartite systems.

Nonlocal Detection of Interlayer Three-Magnon Coupling

A leading nonlinear effect in magnonics is the interaction that splits a high-frequency magnon into two low-frequency magnons with conserved linear momentum. Here, we report experimental observation of nonlocal three-magnon scattering between spatially separated magnetic systems, viz. a CoFeB nanowire and a yttrium iron garnet (YIG) thin film. Above a certain threshold power of an applied microwave field, a CoFeB Kittel magnon splits into a pair of counterpropagating YIG magnons that induce voltage signals in Pt electrodes on each side, in excellent agreement with model calculations based on the interlayer dipolar interaction. The excited YIG magnon pairs reside mainly in the first excited (n=1) perpendicular standing spin-wave mode. With increasing power, the n=1 magnons successively scatter into nodeless (n=0) magnons through a four-magnon process. Our results demonstrate nonlocal detection of two separately propagating magnons emerging from one common source that may enable quantum entanglement between distant magnons for quantum information applications.

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.

Mechanical Bistability in Kerr-modified Cavity Magnomechanics

Bistable mechanical vibration is observed in a cavity magnomechanical system, which consists of a microwave cavity mode, a magnon mode, and a mechanical vibration mode of a ferrimagnetic yttrium-iron-garnet sphere. The bistability manifests itself in both the mechanical frequency and linewidth under a strong microwave drive field, which simultaneously activates three different kinds of nonlinearities, namely, magnetostriction, magnon self-Kerr, and magnon-phonon cross-Kerr nonlinearities. The magnon-phonon cross-Kerr nonlinearity is first predicted and measured in magnomechanics. The system enters a regime where Kerr-type nonlinearities strongly modify the conventional cavity magnomechanics that possesses only a radiation-pressure-like magnomechanical coupling. Three different kinds of nonlinearities are identified and distinguished in the experiment. Our Letter demonstrates a new mechanism for achieving mechanical bistability by combining magnetostriction and Kerr-type nonlinearities, and indicates that such Kerr-modified cavity magnomechanics provides a unique platform for studying many distinct nonlinearities in a single experiment.

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.

Noise-Tolerant Optomechanical Entanglement via Synthetic Magnetism

Entanglement of light and multiple vibrations is a key resource for multichannel quantum information processing and memory. However, entanglement generation is generally suppressed, or even fully destroyed, by the dark-mode (DM) effect induced by the coupling of multiple degenerate or near-degenerate vibrational modes to a common optical mode. Here we propose how to generate optomechanical entanglement via DM breaking induced by synthetic magnetism. We find that at nonzero temperature, light and vibrations are separable in the DM-unbreaking regime but entangled in the DM-breaking regime. Remarkably, the threshold thermal phonon number for preserving entanglement in our simulations has been observed to be up to 3 orders of magnitude stronger than that in the DM-unbreaking regime. The application of the DM-breaking mechanism to optomechanical networks can make noise-tolerant entanglement networks feasible. These results are quite general and can initiate advances in quantum resources with immunity against both dark modes and thermal noise.

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.

Quantum entanglement and one-way steering in a cavity magnomechanical system via a squeezed vacuum field

We propose a simple scheme to generate quantum entanglement and one-way steering between distinct mode pairs in a generic cavity magnomechanical system, which is composed of a microwave cavity and a yttrium iron garnet sphere supporting magnon and phonon modes. The microwave cavity is pumped by a weak squeezed vacuum field, which plays an important role for establishing quantum entanglement and steering. It is found that when the magnon mode is driven by the red-detuned laser, the maximum entanglement between cavity mode and phonon mode and the maximum phonon-to-photon one-way steering can be effectively generated via adjusting the ratio of two coupling rates. While under the much weaker magnomechanical coupling, the quantum entanglement and one-way steering between cavity mode and magnon mode can be achieved, where the steering direction is determined merely by the relative dissipation strength of the cavity to the magnon mode. More interestingly, we reveal that the robustness to the temperature for entanglement and steering between any mode pairs can be evidently enhanced by selecting the squeezing parameter appropriately.

Nonreciprocal optical-microwave entanglement in a spinning magnetic resonator

We propose a nonreciprocal optical-microwave entanglement in a hybrid system composed of a spinning magnetic resonator and a microwave resonator. The optical Sagnac effect caused by the spinning of the magnetic resonator leads to a significant difference in the quantum entanglement for driving the magnetic resonator from opposite directions, which results in the nonreciprocal optical-microwave entanglement. Remarkably, the nonreciprocal optical-microwave entanglement determined by the spinning speed, driving direction, and driving frequency has a high tunability, so it can be turned on or off on demand. Our work opens up a new, to the best of our knowledge, route to achieve nonreciprocal entanglement between microwave and optical domains, which may have potential applications in chiral quantum networking.

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.

Thermodynamics of Reduced State of the Field

Recent years have seen the flourishing of research devoted to quantum effects on mesoscopic and macroscopic scales. In this context, in Entropy 2019, 21, 705, a formalism aiming at describing macroscopic quantum fields, dubbed Reduced State of the Field (RSF), was envisaged. While, in the original work, a proper notion of entropy for macroscopic fields, together with their dynamical equations, was derived, here, we expand thermodynamic analysis of the RSF, discussing the notion of heat, solving dynamical equations in various regimes of interest, and showing the thermodynamic implications of these solutions.

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.

Landscape-Flux Framework for Nonequilibrium Dynamics and Thermodynamics of Open Hamiltonian Systems Coupled to Multiple Heat Baths

We establish a nonequilibrium dynamic and thermodynamic formalism in the landscape-flux framework for open Hamiltonian systems in contact with multiple heat baths governed by stochastic dynamics. To systematically characterize nonequilibrium steady states, the nonequilibrium trinity construct is developed, which consists of detailed balance breaking, nonequilibrium potential landscape, and irreversible probability flux. We demonstrate that the temperature difference of the heat baths is the physical origin of detailed balance breaking, which generates the nonequilibrium potential landscape characterizing the nonequilibrium statistics and creates the irreversible probability flux signifying time irreversibility, with the latter two aspects closely connected. It is shown that the stochastic dynamics of the system can be formulated in the landscape-flux form, where the reversible force drives the conservative Hamiltonian dynamics, the irreversible force consisting of a landscape gradient force and an irreversible flux force drives the dissipative dynamics, and the stochastic force adds random fluctuations to the dynamics. The possible connection of the nonequilibrium trinity construct to nonequilibrium phase transitions is also suggested. A set of nonequilibrium thermodynamic equations, applicable to both nonequilibrium steady states and transient relaxation processes, is constructed. We find that an additional thermodynamic quantity, named the mixing entropy production rate, enters the nonequilibrium thermodynamic equations. It arises from the interplay between detailed balance breaking and transient relaxation, and it also relies on the conservative dynamics. At the nonequilibrium steady state, the heat flow, entropy flow, and entropy production are demonstrated to be thermodynamic manifestations of the nonequilibrium trinity construct. The general nonequilibrium formalism is applied to a class of solvable systems consisting of coupled harmonic oscillators. A more specific example of two harmonic oscillators coupled to two heat baths is worked out in detail. The example may facilitate connection with experiments.

Interferometric control of magnon-induced nearly perfect absorption in cavity magnonics

The perfect absorption of electromagnetic waves has promoted many applications, including photovoltaics, radar cloaking, and molecular detection. Unlike conventional methods of critical coupling that require asymmetric boundaries or coherent perfect absorption that require multiple coherent incident beams, here we demonstrate single-beam perfect absorption in an on-chip cavity magnonic device without breaking its boundary symmetry. By exploiting magnon-mediated interference between two internal channels, both reflection and transmission of our device can be suppressed to zero, resulting in magnon-induced nearly perfect absorption (MIPA). Such interference can be tuned by the strength and direction of an external magnetic field, thus showing versatile controllability. Furthermore, the same multi-channel interference responsible for MIPA also produces level attraction (LA)-like hybridization between a cavity magnon polariton mode and a cavity photon mode, demonstrating that LA-like hybridization can be surprisingly realized in a coherently coupled system.

Nonlocal magnon entanglement generation in coupled hybrid cavity systems

We investigate dynamical generation of macroscopic nonlocal entanglements between two remote massive magnon-superconducting-circuit hybrid systems. Two fiber-coupled microwave cavities are employed to serve as an interaction channel connecting two sets of macroscopic hybrid units, each containing a magnon (hosted by an yttrium-iron-garnet sphere) and a superconducting-circuit qubit. Surprisingly, it is found that stronger coupling does not necessarily mean faster entanglement generation. The proposed hybrid system allows the existence of an optimal fiber coupling strength that requires the shortest amount of time to generate a systematic maximal entanglement. Our theoretical results are shown to be within the scope of specific parameters that can be achieved with current technology. The noise effects on the implementation of systems are also treated in a general environment, suggesting the robustness of entanglement generation. Our discrete-variable qubit-like entanglement theory of magnons may lead to direct applications in various quantum information tasks.

Entanglement enhanced by Kerr nonlinearity in a cavity-optomagnonics system

We present a method to enhance steady-state bipartite and tripartite entanglement in a cavity-optomagnonics system by utilizing the Kerr nonlinearity originating from the magnetocrystalline anisotropy. The system comprises two microwave cavities and a magnon and represents the collective motion of several spins in a macroscopic ferrimagnet. We prove that Kerr nonlinearity is reliable for the enhancement of entanglement and produces a small frequency shift in the optimal detuning. Our system is more robust against the environment-induced decoherence than traditional optomechanical systems. Finally, we briefly analyze the validity of the system and demonstrate its feasibility for detecting the generated entanglement.

Nonreciprocal Optomechanical Entanglement against Backscattering Losses

We propose how to achieve nonreciprocal quantum entanglement of light and motion and reveal its counterintuitive robustness against random losses. We find that by splitting the counterpropagating lights of a spinning resonator via the Sagnac effect, photons and phonons can be entangled strongly in a chosen direction but fully uncorrelated in the other. This makes it possible both to realize quantum nonreciprocity even in the absence of any classical nonreciprocity and also to achieve significant entanglement revival against backscattering losses in practical devices. Our work provides a way to protect and engineer quantum resources by utilizing diverse nonreciprocal devices, for building noise-tolerant quantum processors, realizing chiral networks, and backaction-immune quantum sensors.

Magnon laser based on Brillouin light scattering

An analogous laser action of magnons has become a subject of interest, and it is crucial for the study of nonlinear magnons spintronics. In this Letter, we demonstrate the magnon laser behavior based on Brillouin light scattering in a ferrimagnetic insulator sphere, which supports optical whispering gallery modes and magnon resonances. We show that the excited magnon plays what has traditionally been the role of the Stokes wave and is coherently amplified during the Brillouin scattering process, making the magnon laser possible. Furthermore, the stimulating excited magnon number increasing exponentially with the input light power can be manipulated by adjusting the external magnetic field. In addition to providing insight into magneto-optical interaction, the study of the magnon laser action will help to develop novel, to the best of our knowledge, technologies for handling spin-wave excitations, and it could affect scientific fields beyond magnonics. Potential applications range from preparing coherent magnon sources to operating on-chip functional magnetic devices.

Probing magnon-magnon coupling in exchange coupled Y[Formula: see text]Fe[Formula: see text]O[Formula: see text]/Permalloy bilayers with magneto-optical effects

We demonstrate the magnetically-induced transparency (MIT) effect in Y[Formula: see text]Fe[Formula: see text]O[Formula: see text](YIG)/Permalloy (Py) coupled bilayers. The measurement is achieved via a heterodyne detection of the coupled magnetization dynamics using a single wavelength that probes the magneto-optical Kerr and Faraday effects of Py and YIG, respectively. Clear features of the MIT effect are evident from the deeply modulated ferromagnetic resonance of Py due to the perpendicular-standing-spin-wave of YIG. We develop a phenomenological model that nicely reproduces the experimental results including the induced amplitude and phase evolution caused by the magnon-magnon coupling. Our work offers a new route towards studying phase-resolved spin dynamics and hybrid magnonic systems.

Magnetostrictively Induced Stationary Entanglement between Two Microwave Fields

We present a scheme to entangle two microwave fields by using the nonlinear magnetostrictive interaction in a ferrimagnet. The magnetostrictive interaction enables the coupling between a magnon mode (spin wave) and a mechanical mode in the ferrimagnet, and the magnon mode simultaneously couples to two microwave cavity fields via the magnetic dipole interaction. The magnon-phonon coupling is enhanced by directly driving the ferrimagnet with a strong red-detuned microwave field, and the driving photons are scattered onto two sidebands induced by the mechanical motion. We show that two cavity fields can be prepared in a stationary entangled state if they are, respectively, resonant with two mechanical sidebands. The present scheme illustrates a new mechanism for creating entangled states of optical fields and enables potential applications in quantum information science and quantum tasks that require entangled microwave fields.

Magnon Accumulation in Chirally Coupled Magnets

We report strong chiral coupling between magnons and photons in microwave waveguides that contain chains of small magnets on special lines. Large magnon accumulations at one edge of the chain emerge when exciting the magnets by a phased antenna array. This mechanism holds the promise of new functionalities in nonlinear and quantum magnonics.

Steady Bell State Generation via Magnon-Photon Coupling

We show that parity-time (PT) symmetry can be spontaneously broken in the recently reported energy level attraction of magnons and cavity photons. In the PT-broken phase, the magnon and photon form a high-fidelity Bell state with maximum entanglement. This entanglement is steady and robust against the perturbation of the environment, which is in contrast to the general wisdom that expects instability of the hybridized state when the symmetry is broken. This anomaly is further understood by the compete of non-Hermitian evolution and particle number conservation of the hybrid system. As a comparison, neither PT-symmetry breaking nor steady magnon-photon entanglement is observed inside the normal level repulsion case. Our results may open an exciting window to utilize magnon-photon entanglement as a resource for quantum information science.

Nonreciprocal interference and coherent photon routing in a three-port optomechanical system

We study the interference between different weak signals in a three-port optomechanical system, which is achieved by coupling three cavity modes to the same mechanical mode. If one cavity serves as a control port and is perturbed continuously by a control signal, nonreciprocal interference can be observed when another signal is injected upon different target ports. In particular, we exhibit frequency-independent perfect blockade induced by the completely destructive interference over the full frequency domain. Moreover, coherent photon routing can be realized by perturbing all ports simultaneously, with which the synthetic signal only outputs from the desired port. We also reveal that the routing scheme can be extended to more-port optomechanical systems. The results in this paper may have potential applications for controlling light transport and quantum information processing.

Improving macroscopic entanglement with nonlocal mechanical squeezing

We report an efficient mechanism to generate mechanical entanglement in a two-cascaded cavity optomechanical system with optical parametric amplifiers (OPAs) inside the two coupled cavities. We use the especially tuned OPAs to squeeze the hybrid mode composed of two mechanical modes, leading to strong macroscopic entanglement between the two movable mirrors. The squeezing parameter as well as the effective mechanical damping are both modulated by the OPA gains. The optimal degree of mechanical entanglement therefore depends on the balanced process between coherent hybrid mode squeezing and dissipation engineering. The mechanical entanglement is robust to strong cavity decay, going beyond simply resolved sideband regime, and is resistant to reasonable high thermal noise. The scheme provides an alternative way for generating strong macroscopic entanglement in cascaded optomechanical systems.

Generation and characterization of position-momentum entangled photon pairs in a hot atomic gas cell

Continuous-variable position-momentum entanglement (or Einstein-Podolsky-Rosen entanglement) of two particles has played important roles in the fundamental study of quantum physics as well as in the progress of quantum information. In this paper, we propose a scheme to generate Einstein-Podolsky-Rosen (EPR) position-momentum entangled photon pairs efficiently via spontaneous four-wave mixing (SFWM) process in a hot rubidium gas cell. The EPR entanglement between the photon pair is measured and characterized by using the ghost interference and the ghost imaging method. Due to the simplicity of the experimental setup and the high photon pair generation rate, our EPR entangled photon source may has potential applications in quantum imaging, hyperentanglement preparation and atomic ensemble based quantum information processing and quantum communication protocols.

Phonon laser in a cavity magnomechanical system

Using phonons to simulate an optical two-level laser action has been the focus of research. We theoretically study phonon laser in a cavity magnomechanical system, which consist of a microwave cavity, a sphere of magnetic material and a uniform external bias magnetic field. This system can realize the phonon-magnon coupling and the cavity photon-magnon coupling via magnetostrictive interaction and magnetic dipole interaction respectively, the magnons are driven directly by a strong microwave field simultaneously. Frist, the intensity of driving magnetic field which can reach the threshold condition of phonon laser is given. Then, we demonstrate that the adjustable external magnetic field can be used as a good control method to the phonon laser. Compared with phonon laser in optomechanical systems, our scheme brings a new degree of freedom of manipulation. Finally, with the experimentally feasible parameters, threshold power in our scheme is close to the case of optomechanical systems. Our study may inspire the field of magnetically controlled phonon lasers.