Magnonic device and method

Abstract

To provide a magnonic device with higher applicability to quantum technology. A magnonic device comprising: a resonator; and a magnonic material disposed inside the resonator and configured to be magnetized, wherein the magnonic material is configured to generate magnons in a predetermined mode through nonlinear parametric coupling with a microwave present in the resonator.

Description

MAGNONIC DEVICE AND METHODThe present disclosure relates to a magnonic device and a method. The present application claims priority to Japanese Patent Application No. 2023-201089 filed on November 28, 2023, the entire contents of which are incorporated herein by reference.BackgroundNonlinear magnonics is an active area of research to generate novel magnonic states for the application of quantum metrology and information processing. Magnonic frequency comb generation, particularly those involving high-Q Yttrium Iron Garnet (YIG) materials, has been proposed utilizing the intrinsic magnon Kerr nonlinearity (NPL 1), or by employing nonlinearly coupled hybrid Opto-magnonic (NPL 2) or magnomechanical (NPLs 3-5) systems. Some recent studies have demonstrated magnonic frequency combs using nonlinear magnon scattering processes (NPLs 6-9).NPL1: [Sep. 2021] https: / / journals.aps.org / pra / abstract / 10.1103 / PhysRevA.104.033708.NPL 2: [Oct. 2022] https: / / opg.optica.org / prj / fulltext.cfm?uri=prj-10-12-2786&id=521908.NPL 3: [Jan. 2023] https: / / doi.org / 10.1016 / j.fmre.2022.08.017.NPL 4: [May 2023] https: / / doi.org / 10.1103 / PhysRevA.107.053708.NPL 5: [June 2023] https: / / arxiv.org / pdf / 2306.07985.pdf.NPL 6: [July 2021] https: / / doi.org / 10.1103 / PhysRevLett.127.037202.NPL 7: [Aug. 2022] https: / / doi.org / 10.1103 / PhysRevLett.129.107203.NPL 8: [Nov. 2005] http: / / dx.doi.org / 10.1103 / PhysRevLett.95.237202.NPL 9: [Sep. 2022] https: / / doi.org / 10.1063 / 5.0090033.SummaryConventional techniques face challenges due to weak nonlinearity and inabilities in imprinting and controlling quantum signature on the frequency comb. Most studies have primarily focused on the uniformly precessing fundamental Kittel magnon mode. Thus, these techniques have low applicability to quantum technology such as quantum metrology and information processing, and improvements are desired.Accordingly, an object of the present disclosure, which focuses on the above-mentioned points, is to provide a magnonic device and a method with higher applicability to quantum technology.(Solution to Problem)The gist of the present disclosure is as follows:[1] A magnonic device comprising:a resonator; anda magnonic material disposed inside the resonator and configured to be magnetized,wherein the magnonic material is configured to generate magnons in a predetermined mode through nonlinear parametric coupling with a microwave present in the resonator.[2] The magnonic device according to [1], wherein the magnonic device is configured to generate quantum frequency combs for both microwave and magnon modes using a monochromatic microwave input drive with a drive power greater than a first threshold.[3] The magnonic device according to [2], wherein the quantum frequency combs include squeezed frequency combs.[4] The magnonic device according to any one of [1] to [3], wherein the magnonic device is configured to lase for both microwave and magnon modes using a monochromatic microwave input drive with a drive power that is greater than a second threshold and less than a first threshold.[5] The magnonic device according to any one of [1] to [4], wherein the magnonic material has a shape that supports orbital angular momentum.[6] The magnonic device according to any one of [1] to [5], wherein the magnonic material has a shape that supports a noncircular precessing magnon mode.[7] The magnonic device according to [5] or [6], wherein the magnonic material is a spherical ferromagnetic insulator.[8] The magnonic device according to any one of [1] to [7], further comprising a magnetizer configured to generate a homogeneous bias magnetic field that uniformly magnetizes the magnonic material along one direction.[9] The magnonic device according to [8], wherein the magnetizer is configured to magnetize the magnonic material to saturation magnetization.

[0010] The magnonic device according to [8] or [9], wherein a component along the one direction of the magnetization is parametrically coupled to the microwave polarized along the one direction.

[0011] The magnonic device according to any one of [1] to

[0010] , wherein the magnonic device is configured to convert one photon of the microwave into two magnons and two magnons into one photon of the microwave by the nonlinear parametric coupling.

[0012] The magnonic device according to any one of [1] to

[0011] , wherein the magnonic material is disposed in a predetermined range that includes an antinode of the microwave.

[0013] The magnonic device according to any one of [1] to

[0012] , wherein the predetermined mode includes a hybrid orbital angular momentum mode or a noncircular precessing magnon mode.

[0014] The magnonic device according to

[0013] , wherein the predetermined mode includes mode (2, 0, 0) as the noncircular precessing magnon mode.

[0015] The magnonic device according to any one of [1] to

[0014] , further comprising a frequency filter to filter out a pump microwave including a direct output of the resonator.

[0016] The magnonic device according to

[0015] , wherein the frequency filter is a high-efficiency narrowband filter on the order of a linewidth of the resonator.

[0017] A method comprising:injecting a microwave into a resonator;magnetizing a magnonic material disposed inside the resonator; andgenerating, in the magnonic material, magnons in a predetermined mode through nonlinear parametric coupling with the microwave in the resonator.(Advantageous Effect)According to the present disclosure, a magnonic device and a method with higher applicability to quantum technology can be provided.In the accompanying drawings:FIG. 1 is a schematic diagram illustrating the configuration of a magnonic device according to an embodiment of the present disclosure.FIG. 2 is a first diagram for explaining an example of the operation of the magnonic device in FIG. 1.FIG. 3 is a second diagram for explaining an example of the operation of the magnonic device in FIG. 1.FIG. 4 is a third diagram for explaining an example of the operation of the magnonic device in FIG. 1.FIG. 5 is a fourth diagram for explaining an example of the operation of the magnonic device in FIG. 1.FIG. 6 is a flowchart for explaining an example of the operation of the magnonic device in FIG. 1.FIG. 7 is a schematic diagram illustrating the design of copper microwave cavity.FIG. 8 is a diagram illustrating the implementation of a cavity-magnon system.FIG. 9 is a schematic diagram illustrating a combined setup of an oxygen-free copper microwave cavity.FIG. 10 is a schematic diagram illustrating a coil-wrapped 3D-printed sleeve.FIG. 11 is a schematic diagram illustrating a FEMM simulation of coil sleeve.FIG. 12 is a schematic diagram illustrating an example implementation of YIG-cavity system.FIG. 13 is a schematic diagram illustrating the experimental setup for driving and measuring the cavity-magnon system.FIG. 14 is a schematic representation of a frequency filtering design for the cavity-magnon system.DETAILED DESCRIPTIONFirst, the background and problems associated with conventional magnonic technology are described in greater detail.(Introduction)Efficient transfer and fast operation of quantum information require coupling strengths larger than the intrinsic decay rates. Recently, cavity-magnonics [1‐3], in which the magnetostatic spin wave excitations (magnons) strongly couple to the cavity photon [4‐6], has emerged as a promising platform for quantum applications [7‐11]. High-fidelity quantum information processing requires nonclassical states [12, 13]. Typically, generating nonclassical states requires a high degree of nonlinearity and a parametric nonlinearity can be highly effective.Here, the present disclosure shows how to parametrically couple magnetostatic spin wave modes of a ferromagnetic sphere to cavity photons and use this to engineer a tunable microwave frequency comb. Such tunable microwave combs can play an important role in continuous-variable quantum computing, wavelength-multiplexed quantum networks in the microwave, and precision sensing and magnetic resonance imaging.Frequency combs (FC) are powerful high-precision metrology and spectroscopy tools that can be used in various applications such as telecommunications, quantum sensing, and information processing. They can be created by phase-locking many equally spaced frequency modes which then produces a spectrum of precisely defined frequencies. Since the frequency spacing can be experimentally controlled and tuned FC can be used as a ruler for measuring light frequencies with unprecedented accuracy.Several studies have explored the generation and manipulation of quantum optical frequency combs. Pinel et al. (2012)

[0021] , reported the first experimental evidence of a multimode non-classical optical FC, while others proposed a Raman quantum memory scheme for storing and retrieving highly entangled states using FC

[0011] . For a detailed review of FC’s historical backdrop, see (Fortier et al. 2019)

[0037] and (Diddams et al., 2020)

[0038] . More recently researchers have proposed a new kind of FC based on spin-waves

[0039] . Despite the analogies between photons and magnons, generating magnonic combs has proved challenging, but some recent works have demonstrated magnonic FCs using nonlinearly coupled magnonic systems driven above a threshold amplitude [35, 36].The present disclosure introduces a new theoretical framework for nonlinear parametric cavity-magnon coupling. Using this parametric coupling and by driving the cavity with a strong coherent microwave field, the present disclosure shows the generation of squeezed microwave and magnonic frequency combs. The generated squeezing holds potential for improved metrology and quantum information applications.Microwave cavity magnonics is an attractive platform for continuous variables quantum computing and quantum information processing because magnons in a large ferromagnetic crystal can strongly couple to microwave cavity photons. Besides this strong interaction, controlling, manipulating, and generating nonclassical magnonic states are essential for further development. Here the present disclosure provides a magnonic device and method that demonstrate nonlinear parametric cavity-magnon coupling, an efficient way for generating and manipulating nonclassical states, and show the generation of squeezed microwave and magnonic frequency combs by driving the cavity with a strong coherent microwave field. The squeezing and the frequency spacing of the combs can be controlled by tuning a realistic set of experimental parameters, such as the power and frequency of the microwave drive as well as the external magnetic field. The squeezed frequency combs are powerful tools for high-precision metrology and spectroscopy. Furthermore, the present disclosure investigates the different regimes associated with generating such frequency combs, which includes the generation of squeezed magnon, squeezed coherent microwave, and squeezed magnon lasing. The magnonic device and method of the present disclosure open new possibilities for designing nonclassical microwave and magnonic states with potential applications in spintronics, precision quantum sensing, information processing and for constructing quantum networks.Hereinafter, embodiments of the present disclosure will be described with reference to the drawings.(Configurations)FIG. 1 is a schematic diagram illustrating the configuration of a magnonic device 1 according to an embodiment of the present disclosure. As shown in FIG. 1, the magnonic device 1 includes a resonator 11, a magnonic material 12, and magnetizer 13.The resonator 11 includes, for example, a cavity. The resonator 11 receives a microwave from the outside and repeatedly reflects the microwave inside the resonator 11. The microwave is emitted from any microwave source located outside the magnonic device 1 or included in the magnonic device 1 and is incident on the resonator 11. The resonator 11 realizes a nonlinear interaction between the microwave present in the resonator 11 and the magnonic material 12. The resonator 11 outputs a microwave in a predetermined state as a result of the nonlinear interaction. In the present disclosure, the “predetermined state” includes, for example, quantum frequency combs such as squeezed frequency combs or lasing.The magnonic material 12 is disposed inside the resonator 11 and is magnetized by the magnetizer 13. The magnonic material 12 generates magnons in a predetermined mode through nonlinear parametric coupling with the microwave present in the resonator 12. In the present disclosure, the “predetermined mode” includes at least one of a hybrid orbital angular momentum mode and a noncircular precessing magnon mode. For example, the predetermined mode is the noncircular precessing magnon mode and includes some orbital angular momentum modes. That is, the predetermined mode may also be defined as the noncircular precessing magnon mode and the modes in which the orbital angular momentum mode is not equal to zero. For example, the predetermined mode includes mode (2, 0, 0) as the noncircular precessing magnon mode.The magnonic material 12 is or contains, for example, a material of Yttrium Iron Garnet (YIG). YIG has a high unloaded Q factor which is an essential parameter for quantum applications as shown in Table 1.The magnonic material 12 has a shape that supports orbital angular momentum. Alternatively, the magnonic material 12 has a shape that supports a noncircular precessing magnon mode. The shape of the magnonic material 12 is, for example, a sphere. The magnonic material 12 is, for example, a spherical ferromagnetic insulator as shown in FIG. 1.The magnonic material 12 is disposed in a predetermined range that includes an antinode of the microwave present in the resonator 11. In the present disclosure, the “predetermined range” includes a range of the position of the magnonic material 12 in which sufficient coupling between photons of the microwave and the magnons can be achieved. The predetermined range may preferably include a range of less than ±1 / 4 λ, more preferably a range of less than ±1 / 8 λ, and still more preferably a range of less than ±1 / 10 λ, centered on an antinode of the microwave. For example, the magnonic material 12 may be disposed at the antinode of the microwave present in the resonator 11.The magnetizer 13 includes any magnetic field generator that generates a magnetic field. The magnetizer 13 generates a homogeneous bias magnetic field that uniformly magnetizes the magnonic material 12 disposed inside the resonator 11 along one direction. The magnetizer 13 magnetizes the magnonic material 12 to saturation magnetization. A component along the one direction of the magnetization is parametrically coupled to the microwave polarized along the one direction. For example, the one direction corresponds to z-direction as shown in FIG. 1.The magnonic device 1 converts one of one photon of the microwave and two magnons into the other by the nonlinear parametric coupling in the resonator 11. For example, the magnonic device 1 converts one photon of the microwave into two magnons and two magnons into one photon of the microwave by the nonlinear parametric coupling in the resonator 11. In the resonator 11, not only the conversion from one photon to two magnons, but also the reverse conversion from two magnons to one photon occur simultaneously. The magnonic device 1 reaches a steady state in resonator 11 where the conversions in both directions are occurring simultaneously.As described below with reference to FIG. 2, the magnonic device 1 generates quantum frequency combs for both microwave and magnon modes using a monochromatic microwave input drive with a drive power greater than a first threshold Th1. The quantum frequency combs include squeezed frequency combs. On the other hand, the magnonic device 1 lases for both microwave and magnon modes using the monochromatic microwave input drive with a drive power that is greater than a second threshold Th2 and less than the first threshold Th1.In the present disclosure, the first threshold Th1 is a frequency comb threshold. The first threshold Th1 is an upper threshold at which the system exhibits a comb structure. On the other hand, the second threshold Th2 is a lasing threshold. The second threshold Th2 is a lower threshold at which the system enters the lasing phase.(Results)((Nonlinear Parametric Cavity-Magnon Interaction))((Mathematical Results))Now the present disclosure investigates the fluctuations in the frequency comb regime. Above the frequency comb threshold, the linearization fails. Hence the nonlinear Langevin equation is numerically solved to quantify the quadrature variances. The quadrature spectral density and the phase-space probability distribution in the different regimes are shown in FIG. 4. When the system is in the frequency comb regime, each stochastic realization of equation (6) exhibits limit cycles in the steady state with undefined phases. These random phases lead to a shift of individual trajectories, making the usual method of computing quadrature spectral densities not relevant.FIG. 5 is a fourth diagram for explaining an example of the operation of the magnonic device 1 in FIG. 1.FIG. 5 shows a phase locked phase-space distribution. In this figure, a dynamical representation of the squeezing is plotted at some definite coordinates of phase-space (x, p, t) for both cavity (a) and magnons (b). To do so, the different stochastic realizations of equations (6) were synchronized using the so-called phase-locking method, where one injects an additional weak drive into the system, which is close to one of the microwave comb frequencies. Here, the same parameters as in FIG. 2 were chosen and an input drive power P = 100 mW and an additional weak injection power of 1μW were used.The black line is the mean phase-space trajectory, which is a limit cycle. The dots on the limit cycle are the phase-locked response at different time coordinates. The gray areas are the magnified version of dots showing the probability distribution or the Q-function of the phase-space distribution of the (left) magnon, (right) microwave mode, at the corresponding time step.Observing the squeezing effects in both the cavity and magnon modes as shown in FIG. 5 gives us insights into these systems’ potential precision enhancement and control.(Brief Summary)The present disclosure contributes to the understanding of cavity magnonic systems and their potential applications in frequency comb generation. The present disclosure has shown that in principle, combs in both cavity and magnon modes are able to be output from a standard monochromatic input drive of the cavity. The obtained insights pave the way for further investigations and advancements in cavity magnonics, offering promising avenues for developing novel technologies in this field.(Flowchart)FIG. 6 is a flowchart for explaining an example of the operation of the magnonic device 1 in FIG. 1. The method according to an embodiment of the present disclosure is described with reference to FIG. 6.In step S101, the magnonic device 1 injects the microwave into the resonator 11.In step S102, the magnonic device 1 magnetizes, using the magnetizer 13, the magnonic material 12 disposed inside the resonator 11.In step S103, the magnonic device 1 generates, in the magnonic material 12, magnons in a predetermined mode through nonlinear parametric coupling with the microwave in the resonator 11.(Experimental Setup)This experimental setup demonstrates an example implementation of the cavity-magnon concept of the magnonic device 1 of the present disclosure ‐ and is a portable, cost-effective, cavity-magnon system integrating an oxygen-free copper cavity, permanent magnets, and a tunable coil-wrapped sleeve. The cavity is designed to operate in the TE101 mode, resonant at 10 GHz, and features a high quality factor (Q=3000). A 1 mm YIG sphere, placed at the magnetic field antinode inside the cavity, facilitates strong magnon-photon coupling. The permanent cylindrical disk magnets, mounted on precision translation stages, are spaced 33 mm apart to produce a uniform 0.3 T magnetic field. Additional magnetic field fine-tuning is achieved using a <500-turn coil wrapped around a 3D-printed sleeve enclosing the cavity, which can generate a tunable ±1 mT field using 200 mA of current, supplied by a stable current source such as the YOKOGAWA GS200.The cavity-magnon system is driven by a microwave synthesizer operating at 10.6 GHz, with the signal amplified to over 100 mW to meet the power requirements of the system. The amplified signal is directed into the cavity via a coaxial connector, and the reflected or transmitted signal is measured using a spectrum analyzer. FEMM simulations confirm the uniformity and strength of the magnetic field within the cavity and validate the feasibility of the coil-based fine-tuning. The simulation also highlights the effectiveness of the 3D-printed sleeve in maintaining precise alignment of the cavity and magnets while minimizing interference with the magnetic flux.Experimental data, including S11 parameter measurements obtained using a vector network analyzer (VNA), confirm the resonance properties of the system. The measured linewidth and quality factor align closely with the simulation results, verifying the cavity’s performance. This integrated system offers a robust platform for studying cavity-magnon coupling and related quantum phenomena, demonstrating precise control over the magnetic environment and high measurement sensitivity. The design balances structural stability, field tunability, and compactness, making it a versatile tool for advanced microwave and quantum experiments.FIG. 7 is a schematic diagram illustrating the design of copper microwave cavity. This figure depicts an oxygen-free copper cavity designed for microwave applications, operating at approximately 10 GHz. The cavity has a rectangular geometry with internal dimensions of 22 mm (length) × 3 mm (height) × 18 mm (width). The external dimensions are slightly larger, with the overall structure extending to 29 mm in length. A coaxial connector is mounted on top of the cavity to enable microwave signal coupling, with the feedline entering into the cavity through a small aperture. The cavity is constructed using oxygen-free copper to minimize electrical resistance and improve performance at high frequencies. The illustration includes an inset showing a detailed view of the coaxial connector used for coupling, and arrows are included to indicate the internal cavity dimensions.FIG. 8 is a diagram illustrating the implementation of a cavity-magnon system using a 1 mm YIG sphere placed at the antinode of the magnetic field inside an oxygen-free copper cavity. The cavity operates in the TE101 mode and is resonant at 10 GHz, with a measured quality factor Q=3000. The top image shows the physical cavity setup, while the inset illustrates the simulated magnetic field intensity distribution within the cavity. The bottom plot presents the measured S11 parameters as a function of frequency, obtained using a vector network analyzer (VNA), with both measured data points and the fitted curve indicating the linewidth and resonance behavior of the system.FIG. 9 is a schematic diagram illustrating a combined setup of an oxygen-free copper microwave cavity placed between two permanent cylindrical disk magnets. The magnets are mounted with a separation of 33 mm and are designed to produce a uniform magnetic field of 0.3 T in the cavity’s region. The left panel regarding the combined setup shows the cavity positioned centrally between the two magnets. The cavity retains its internal dimensions of 22 mm (length) × 3 mm (height), with the magnets symmetrically aligned on either side of the cavity. The right panel regarding the side view displays a side perspective of the setup, highlighting the cylindrical disk magnets and their placement relative to the cavity. The magnet separation is explicitly labeled as 32 mm, while the height dimension is marked as “arbitrary,” indicating variability in the vertical alignment. This configuration has been simulated to ensure uniformity in the magnetic field across the cavity, optimizing it for high-frequency microwave applications.FIG. 10 is a schematic diagram illustrating a coil-wrapped 3D-printed sleeve, designed to securely hold the oxygen-free copper cavity between two permanent cylindrical disk magnets. The sleeve ensures precise alignment of the cavity within the uniform 0.3 T magnetic field produced by the magnets, which are positioned 33 mm apart.FIG. 11 is a schematic diagram illustrating a FEMM simulation of coil sleeve. This was used to evaluate the feasibility of generating a tunable magnetic field by wrapping a coil around the physical cavity. The simulation confirms that a field in the range of ~.1 mT can be achieved with approximately <500 turns of 30 AWG wire, driven by a current of 200 mA. The setup can be stably controlled using a high-precision current source such as the YOKOGAWA GS200. The field uniformity and strength are validated by the simulation data, which displays a field magnitude of approximately 0.301 T produced by the permanent magnets, demonstrating that the added coil can effectively tune the field with high precision.FIG. 12 is a schematic diagram illustrating an example implementation of YIG-cavity system. FIG. 12 shows a 3D model of the complete experimental setup of the magnonic device 1 of the present disclosure, combining the high-Q oxygen-free copper cavity, permanent magnets, and a coil-wrapped 3D-printed sleeve. The permanent magnets, mounted on precision translation stages, are positioned to produce a uniform magnetic field around the cavity. The cavity is housed within the 3D-printed sleeve, which includes a coil for additional field control or tuning. The translation stages allow for precise adjustment of the magnet spacing, optimizing the uniformity and strength of the magnetic field for microwave experiments. The overall design integrates all components into a compact and functional configuration.FIG. 13 is a schematic diagram illustrating the experimental setup for driving and measuring the cavity-magnon system. A microwave synthesizer operating at 10.6 GHz provides the input signal, which is amplified by a high-power amplifier to achieve an output power of greater than 100 mW, as calculated to drive the system effectively. The amplified signal is then directed into the cavity, and the reflected or transmitted signal is analyzed using a spectrum analyzer to characterize the system’s response and resonance behavior.The direct output of the resonator 11 included in this cavity-magnon system includes both the strong pump and the weaker frequency comb system generated by the nonlinearity. Here the present disclosure describes using a frequency filter to filter out this strong pump microwave. While any high-efficiency narrowband filter on the order of the linewidth of the cavity is sufficient, one potential implementation is the use of an identical RF cavity as used in the cavity-magnon system. This frequency filter will then be matched to the linewidth of the cavity, with slight tuning of the microwave antenna for exact matching, and the high q of the cavity will reduce the strong pump input.FIG. 14 is a schematic representation of a frequency filtering design for the cavity-magnon system. An RF source at 10 GHz is amplified and coupled to the cavity-magnon system, where output frequencies are processed by a frequency filter to selectively suppress unwanted components due the central frequency of the strong pump, driving the nonlinear process. The spectral outputs before and after filtering are shown, highlighting the effectiveness of the filtering process.(Effect)The magnonic device 1 according to the embodiment described above improves applicability to quantum technology. The present disclosure is intrinsically related to the burgeoning domain of quantum information science, specifically the subfield of magnonics ‐ the study of quantized spin wave dynamics in a magnetically ordered material. It presents a pioneering solution for generating and controlling squeezed microwave and magnonic frequency combs from a simple monochromatic microwave input mode. Practically, frequency combs, known for their precise and evenly spaced frequency lines, are crucial in various applications, such as precision timekeeping, optical to microwave frequency synthesis, high-speed communications, and spectroscopy. However, traditional methods of generating these combs suffer from many limitations, such as weak nonlinearity, tunability of frequency comb, inefficiencies and the inability to squeeze the modes.The present disclosure proposes, on the one hand, a unique and innovative solution to generate microwave and magnonic frequency combs by identifying a way to parametrically excite the magnon with a microwave. While on the other hand, the nonlinear parametric coupling allows an experimental control of the quadrature variances of the microwave and magnon modes through the so-called quantum squeezing‐ a quantum property enhancing the precision measurement below the Heisenberg limit. This significant enhancement could pave the way for more reliable quantum computing, high-speed and high-precision signal processing.Therefore, the present disclosure could spark advancements in various unexpected quantum technologies, impacting numerous sectors. As an example, this could include everything from developing faster and more efficient telecommunications networks to enabling new forms of secure communications or could be used as a tool for future magnonic-based quantum computers.The magnonic device 1 generates quantum frequency combs for both microwave and magnon modes using the monochromatic microwave input drive with a drive power greater than the first threshold Th1. Therefore, the magnonic device 1 can output a microwave in quantum frequency combs state from the resonator 11. The magnonic device 1 can provide a commercial product capable of producing microwave frequency combs. While optical frequency combs have seen successful commercialization, the microwave domain still lacks such solutions. The present disclosure can solve such problem. The magnonic device 1 can achieve precise and stable measurements of microwave signals by using frequency combs as accurate references. The magnonic device 1 can harness the power of frequency combs for efficient qubit manipulation and entanglement generation, advancing quantum computing applications.The quantum frequency combs include squeezed frequency combs. Therefore, the magnonic device 1 can also function as controlled squeezed light sources, which are essential for reducing noise and enhancing sensitivity in various quantum applications. This further improves the applicability to quantum technology.The present disclosure represents a groundbreaking advancement in the field of microwave cavity-magnonics. While conventional technology has laid the foundation, significant limitations in preparing and controlling quantum states have posed major challenges. The present disclosure aims to overcome these obstacles by introducing novel techniques that incorporate quantum signatures into magnonic combs.At the core of the present disclosure lies the concept of parametric cavity-magnon coupling. Unlike conventional technology that relies on intrinsic magnon nonlinearity, nonlinear hybrid magnonic systems, or nonlinear magnon scattering processes to generate magnonic frequency combs, the framework of the present disclosure enables the generation of squeezed magnonic combs. The present disclosure has demonstrated the ability to output quantum frequency comb structures for both microwave and magnon modes using a simple monochromatic microwave input drive.Another advantage of the present disclosure is that it eliminates the need for two-tone driving to tune the frequency comb spacing. Instead, the frequency combs are self-generated once a threshold value of input power is reached. This allows for complete experimental control over the properties of the combs by merely adjusting the properties of the microwave input, such as its power and frequency detuning. Therefore, the configuration of the magnonic device 1 can be simplified.The magnonic device 1 lases for both microwave and magnon modes using the monochromatic microwave input drive with a drive power that is greater than the second threshold Th2 and less than the first threshold Th1. Therefore, the magnonic device 1 can output a microwave in a lasing state from the resonator 11. The magnonic device 1 can provide a commercial MASER (Microwave Amplification by Stimulated Emission of Radiation) product.The magnonic material 12 has a shape that supports orbital angular momentum. Therefore, the magnonic device 1 can generate magnons based on the orbital angular momentum mode through the above-mentioned nonlinear parametric coupling.The magnonic material 12 has a shape that supports a noncircular precessing magnon mode. Therefore, the magnonic device 1 can generate magnons based on the noncircular precessing magnon mode through the above-mentioned nonlinear parametric coupling.The magnonic material 12 is a spherical ferromagnetic insulator. Therefore, the magnonic device 1 can more easily achieve at least one of the hybrid orbital angular momentum mode or the noncircular precessing magnon mode.The magnonic device 1 includes a magnetizer 13 that generates a homogeneous bias magnetic field that uniformly magnetizes the magnonic material 12 along one direction. Therefore, the magnonic device 1 can realize a resonance condition in the magnonic material 12 between one photon of the microwave and a plurality of magnons by the bias magnetic field generated by the magnetizer 13. This allows the magnonic device 1 to enhance the nonlinear parametric coupling.The magnetizer 13 magnetizes the magnonic material 12 to saturation magnetization. Therefore, the magnonic device 1 can further enhance the nonlinear parametric coupling.The component along the one direction of the magnetization is parametrically coupled to the microwave polarized along the one direction. Therefore, the magnonic device 1 can further enhance the nonlinear parametric coupling.The magnonic device 1 converts one of one photon of the microwave and two magnons into the other by the nonlinear parametric coupling. The magnonic device 1 can realize the generation of the quantum frequency combs or the lasing through such nonlinear parametric coupling.The magnonic material 12 is disposed in a predetermined range that includes the antinode of the microwave. Therefore, the magnonic device 1 can enhance the coupling between the magnonic material 12 and the microwave. Sufficient coupling between photons of the microwave and the magnons can be achieved.The predetermined mode includes the hybrid orbital angular momentum mode or the noncircular precessing magnon mode. Therefore, the magnonic device 1 can generate magnons based on the hybrid orbital angular momentum mode or the noncircular precessing magnon mode through the above-mentioned nonlinear parametric coupling.(Variations)Although the present disclosure has been described based on the drawings and embodiments, it should be noted that a person skilled in the art may easily make variations and modifications based on the present disclosure. Therefore, it should be noted that such variations and modifications are included within the scope of the present disclosure. For example, functions and the like included in each structure and step may be rearranged, and multiple structures and steps may be combined into one or divided, as long as no logical inconsistency results.In the embodiment described above, the magnonic device 1 is described as generating quantum frequency combs with the drive power greater than the first threshold Th1 and lasing with the drive power that is greater than the second threshold Th2 and less than the first threshold Th1, but the magnonic device 1 is not limited to this. The magnonic device 1 may generate frequency combs and / or lase in any range of the drive power. Also, the magnonic device 1 may generate quantum frequency combs for either microwave or magnon modes. The magnonic device 1 may lase for either microwave or magnon modes.In the embodiment described above, the quantum frequency combs are described as including squeezed frequency combs, but the quantum frequency combs are not limited to this. The quantum frequency combs may not be squeezed frequency combs.In the embodiment described above, the magnonic material 12 is described as having the shape that supports orbital angular momentum, but the magnonic material 12 is not limited to this. The magnonic material 12 may have the shape that does not support orbital angular momentum as long as the magnons are generated in the predetermined mode through the nonlinear parametric coupling.In the embodiment described above, the magnonic material 12 is described as having the shape that supports the noncircular precessing magnon mode, but the magnonic material 12 is not limited to this. The magnonic material 12 may have the shape that does not support the noncircular precessing magnon mode as long as the magnons are generated in the predetermined mode through the nonlinear parametric coupling.In the embodiment described above, the magnonic material 12 is described as being the spherical ferromagnetic insulator, but the magnonic material 12 is not limited to this. The magnonic material 12 may have a shape other than the sphere.In the embodiment described above, the magnonic device 1 is described as including the magnetizer 13, but the magnonic device 1 is not limited to this. The magnonic device 1 may not include the magnetizer 13. Also, the magnetizer 13 may generate an inhomogeneous bias magnetic field as long as the magnons are generated in the predetermined mode through the nonlinear parametric coupling. The magnetizer 13 may non-uniformly magnetize the magnonic material 12 along one direction as long as the magnons are generated in the predetermined mode through the nonlinear parametric coupling.In the embodiment described above, the magnetizer 13 is described as magnetizing the magnonic material 12 to saturation magnetization, but the magnetizer 13 is not limited to this. The magnetizer 13 is not limited to such 100 % magnetization, but may magnetize the magnonic material 12 at a predetermined rate other than 100 % as long as the magnons are generated in the predetermined mode through the nonlinear parametric coupling. For example, the predetermined rate may be preferably 80 %, more preferably 85 %, more preferably 90 %, more preferably 95 %, and still more preferably 99 %.In the embodiment described above, the component along the one direction of the magnetization is described as being parametrically coupled to the microwave polarized along the one direction, but the component is not limited to this. The direction of the component of the magnetization and the polarization direction of the microwave may not be parallel to each other.In the embodiment described above, the magnonic device 1 is described as converting one of one photon of the microwave and two magnons into the other by the nonlinear parametric coupling, but the magnonic device 1 is not limited to this. The magnonic device 1 may convert one of any number of photons of the microwave and any number of magnons into the other by the nonlinear parametric coupling. Also, the magnonic device 1 may reach a non-equilibrium state in resonator 11 where only one of the conversions in both directions is occurring.In the embodiment described above, the predetermined mode is described as including mode (2, 0, 0) as the noncircular precessing magnon mode, but the predetermined mode is not limited to this. The predetermined mode may include a mode other than mode (2, 0, 0) as long as the nonlinear parametric coupling can be achieved.In the embodiment described above, the magnonic material 12 is described as containing the material of Yttrium Iron Garnet (YIG), but the magnonic material 12 is not limited to this. Besides YIG other materials may be used to implement the magnonic frequency combs using the above-mentioned methods.REFERENCESThe following references are hereby incorporated herein by reference in their entirety for all purposes:[1] Zare Rameshti, B. et al. Cavity magnonics. Phys. Rep. 979, 1‐61 (2022). 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Claims

1. A magnonic device comprising: a resonator; and a magnonic material disposed inside the resonator and configured to be magnetized, wherein the magnonic material is configured to generate magnons in a predetermined mode through nonlinear parametric coupling with a microwave present in the resonator.

2. The magnonic device according to claim 1, wherein the magnonic device is configured to generate quantum frequency combs for both microwave and magnon modes using a monochromatic microwave input drive with a drive power greater than a first threshold.

3. The magnonic device according to claim 2, wherein the quantum frequency combs include squeezed frequency combs.

4. The magnonic device according to any one of claims 1 to 3, wherein the magnonic device is configured to lase for both microwave and magnon modes using a monochromatic microwave input drive with a drive power that is greater than a second threshold and less than a first threshold.

5. The magnonic device according to any one of claims 1 to 3, wherein the magnonic material has a shape that supports orbital angular momentum.

6. The magnonic device according to any one of claims 1 to 3, wherein the magnonic material has a shape that supports a noncircular precessing magnon mode.

7. The magnonic device according to claim 5, wherein the magnonic material is a spherical ferromagnetic insulator.

8. The magnonic device according to any one of claims 1 to 3, further comprising a magnetizer configured to generate a homogeneous bias magnetic field that uniformly magnetizes the magnonic material along one direction.

9. The magnonic device according to claim 8, wherein the magnetizer is configured to magnetize the magnonic material to saturation magnetization.

10. The magnonic device according to claim 8, wherein a component along the one direction of the magnetization is parametrically coupled to the microwave polarized along the one direction.

11. The magnonic device according to any one of claims 1 to 3, wherein the magnonic device is configured to convert one photon of the microwave into two magnons and two magnons into one photon of the microwave by the nonlinear parametric coupling.

12. The magnonic device according to any one of claims 1 to 3, wherein the magnonic material is disposed in a predetermined range that includes an antinode of the microwave.

13. The magnonic device according to any one of claims 1 to 3, wherein the predetermined mode includes a hybrid orbital angular momentum mode or a noncircular precessing magnon mode.

14. The magnonic device according to claim 13, wherein the predetermined mode includes mode (2, 0, 0) as the noncircular precessing magnon mode.

15. The magnonic device according to any one of claims 1 to 3, further comprising a frequency filter to filter out a pump microwave including a direct output of the resonator.

16. The magnonic device according to claim 15, wherein the frequency filter is a high-efficiency narrowband filter on the order of a linewidth of the resonator.

17. A method comprising: injecting a microwave into a resonator; magnetizing a magnonic material disposed inside the resonator; and generating, in the magnonic material, magnons in a predetermined mode through nonlinear parametric coupling with the microwave in the resonator.

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