Method for generating frequency comb based on magnetor-magnetor superstrong coupling and application

Abstract

The invention discloses a method for generating a frequency comb based on magnetic vibrator-magnetic vibrator superstrong coupling and application, and belongs to the technical field of spintrons.In a system of two superstrong coupling magnetic vibrators, when a pumping magnetic field with the frequency close to the frequency of a high-frequency branch magnetic vibrator is applied, the system enters a non-linear state, and according to the amplitude of the pumping magnetic field, the frequency comb is generated according to the frequency of the high-frequency branch magnetic vibrator; the system presents a frequency comb, multiple period bifurcation and a chaotic frequency comb. The nonlinearity of the system is obviously enhanced along with the increase of the magnetic vibrator-magnetic vibrator coupling strength, so that the requirement on external power is reduced. Different from a traditional method which depends on weak nonlinearity of materials and needs high power density to exceed a starting threshold value, the super-strong coupling system provides an ideal platform for studying the chaos frequency comb. The chaotic system has high sensitivity and anti-noise characteristics, and plays an important role in signal detection. According to the invention, a brand new thought is provided for the application of a magnetic vibrator-magnetic vibrator coupling mechanism in the fields of high-precision frequency measurement, information processing, sensitive detection and the like.

Description

Technical Field

[0001] The present invention belongs to the technical field of spintronics, and particularly relates to a method for generating frequency comb and chaotic frequency comb based on magnon-magnon ultra-strong coupling and its application in signal recognition in noise. Background Art

[0002] A frequency comb is a spectrum composed of a series of discrete and equally spaced frequency components, which was first discovered in an optical system. After more than twenty years of development, it has become an important technology in fields such as atomic clocks, satellite navigation, molecular fingerprint recognition, metrology, and optical spectroscopy. Inspired by optical frequency combs, frequency combs have now been deeply studied in other physical systems. Among them, magnon frequency combs generated by the nonlinear coupling between different mode magnons have been reported both theoretically and experimentally. Currently, chaotic frequency combs originating from the nonlinear interaction within an optical microresonator have been proven to have important application potential in multiple fields such as metrology, spectroscopy, and coherent communication. However, in spin systems, chaotic frequency combs have not been realized yet. Summary of the Invention

[0003] The technical problem solved by the present invention is to provide a method for generating frequency comb, period-doubling bifurcation, and chaotic frequency comb in a spin system and to achieve signal recognition with high sensitivity and anti-noise characteristics.

[0004] Technical Solution: To solve the above technical problem, the technical solution adopted by the present invention is as follows:

[0005] The present invention proposes magnon frequency comb and chaotic frequency comb based on the magnon ultra-strong coupling mechanism in a spin system. By studying the nonlinear interaction between the upper and lower branches of magnon polaritons in a synthetic antiferromagnet (SAF) system, the present invention proves the feasibility of the proposed magnon chaotic frequency comb both theoretically and numerically. Through the period-doubling cascade bifurcation of the comb tooth spacing, the present invention observes the transition from frequency comb to chaos. The robustness of the chaotic frequency comb is demonstrated by the Poincaré section, bifurcation diagram, and maximum Lyapunov exponent. In addition, the significant advantage of the chaotic system lies in its high sensitivity to small perturbations and strong resistance to noise, and this characteristic is verified in the process of successfully recognizing periodic signals from background noise. The research results of the present invention provide a new example of a magnetic system for the potential application of nonlinear dynamics in fields such as metrology, sensing, information processing, and quantum spintronics.

[0006] A method for generating a frequency comb based on magnon-magnon ultrastrong coupling in the present invention. In a system of two ultrastrongly coupled magnons, when a pump magnetic field with a frequency close to that of the high-frequency branch magnon is applied, the system enters a nonlinear state. According to the amplitude of the pump magnetic field, the system exhibits typical nonlinear dynamic phenomena, including frequency comb, period-doubling bifurcation, and chaotic frequency comb.

[0007] Further, when the pump intensity is low, the frequency spectrum of the magnon frequency comb is:

[0008] ;

[0009] where, lf p represents the central frequency of the l-th comb tooth, and n and f d represent the n-th comb tooth and the comb tooth spacing.

[0010] Further, after the magnon polaritons in the high-frequency branch are excited by the pump field, they interact with the magnon polaritons in the low-frequency branch to generate sum-frequency (f p + f d ) and difference-frequency (f p - f d ) modes; as this cascading process continues, the system finally generates a frequency comb with a comb tooth spacing of f d .

[0011] Further, when the pump intensity increases, the system begins to exhibit a cascading bifurcation of period doubling, and the comb tooth spacing gradually evolves from f d to f d / 2, f d / 3, f d / 4; when the pump intensity h p increases above a certain critical value, the system enters a chaotic state, and the comb tooth spacing becomes irregular, forming a chaotic frequency comb.

[0012] Further, when the detuning is small, the path of the system to chaos starts from the frequency comb and gradually evolves through a series of bifurcations of tooth pitches. During this process, periodic oscillations and chaotic states alternate multiple times. When the detuning is large, the system will directly transition to the chaotic state without experiencing the process of period-doubling bifurcation.

[0013] Further, when f p is less than f u , the system is more likely to directly enter the chaotic state; while when f p is greater than f u , the system tends to enter chaos through the frequency comb. When f p is close to f u , the system will exhibit the phenomena of frequency comb and period-doubling cascade, ultimately leading to chaos.

[0014] Application of frequency comb in identifying signals in noise, applying a reference signal to make the system at the boundary between periodic oscillation and chaos h c , when there is a periodic signal with amplitude s 0 in the system, it will affect the total signal amplitude h 0 . When h 0 approaches h c -s 0 , the system exhibits periodic oscillation; when h 0 approaches h c +s 0 , the system transitions to chaotic oscillation; therefore, when there is a frequency difference between the periodic signal and the reference signal, h 0 is periodically greater than or less than h c , intermittent chaos will occur; this intermittent chaos is stable and has a fixed periodicity.

[0015] Further, the periodicity is given by the following formula:

[0016] .

[0017] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0018] (1) In the ultra-strongly coupled magnon-magnon system of the present invention, the generation mechanism of magnon chaotic frequency comb is explored. As the magnon-magnon coupling strength increases, the nonlinearity of the system is significantly enhanced, thereby reducing the demand for external power. Different from the traditional method that relies on the relatively weak nonlinearity of the material itself and requires high power density to exceed the starting threshold, the ultra-strongly coupled system provides an ideal platform for studying chaotic frequency comb.

[0019] (2) The chaotic system has high sensitivity and anti-noise characteristics and plays an important role in signal detection. The present invention demonstrates anti-noise signal recognition by utilizing the transition of the magnon chaotic comb from periodic oscillation to chaos (or from chaos to periodic oscillation). Even if the signal to be recognized is buried by Gaussian noise, the result is still the same as that without noise, which shows the robustness of the system and its immunity to noise interference.

[0020] (3) The present invention provides the possibility of realizing magnon chaotic frequency comb under ultra-strong coupling conditions, which provides a new idea for the application of magnon-magnon coupling mechanism in the fields of high-precision frequency metrology, information processing, and sensitive detection. Brief description of the drawings

[0021] Figure 1 is a schematic diagram of magnon chaotic frequency comb.

[0022] Figure 2Schematic diagram of a synthetic antiferromagnet in a spin-tilted state and its resonance spectrum.

[0023] Figure 3 is at f p = 8 GHz and h p = 2, 6, 8, 9, 11.2, 12 mT, the nonlinear characteristics of the SAF: m x time-domain variation of, m x and m z Poincaré section of, and the magnon spectrum of the synthetic antiferromagnet.

[0024] Figure 4 is for different detunings f p - f u = 0.05 GHz, f p - f u = -0.7 GHz, the relationship between the dispersion diagram and h p and the corresponding bifurcation diagram (blue dots) and LLE (green line).

[0025] Figure 5 is the magnon dispersion diagram as a function of f p variation, (a) and (b) h p = 6 mT, (c) and (d) h p = 8 mT, (e) and (f) h p = 12 mT. The right figures (b), (d), and (f) are magnified views of the corresponding dashed boxes in the left figures (a), (c), and (e). The appearance of the nonlinear phenomenon has thresholds on both sides of f u , and as h p increases, the distance between the thresholds also expands.

[0026] Figure 6 is the phase diagram showing the relationship between the system state and h p and f p .

[0027] Figure 7 is a proof-of-concept demonstration of noise signal recognition. (a) Schematic diagrams of three different input cases: only the reference signal, the reference signal and the signal to be recognized, the reference signal and the signal to be recognized buried by Gaussian noise. m x and the time variation of the short-time Fourier transform are shown as follows: (b) only the reference signal, the response of m shows periodic oscillations. (c) The reference signal and the periodic signal to be recognized exist simultaneously, resulting in intermittent chaos. (d) The reference signal, the signal to be recognized and noise exist simultaneously, and the intermittent chaos persists. The frequency difference between the reference signal and the signal to be recognized is Δf = 0.01 GHz. The dashed box indicates the occurrence of intermittent chaos. Detailed implementation manners

[0028] The following further elaborates the present invention in conjunction with specific embodiments. The embodiments are implemented on the premise of the technical solution of the present invention. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention.

[0029] Embodiment 1

[0030] This embodiment provides a method for generating a frequency comb based on the ultra-strong coupling of magnons-magnons, which can generate frequency combs, period-doubling bifurcations, and chaotic frequency combs.

[0031] In a system of ultra-strongly coupled magnons, their eigenfrequencies are f u and f d . When a pump magnetic field with a frequency close to the frequency f p ≈f u of the high-frequency branch magnons is applied, the system enters a non-linear state. According to the amplitude h p of the pump magnetic field, the system exhibits typical non-linear dynamic phenomena, including frequency combs, period-doubling bifurcations, and chaotic behaviors.

[0032] When the pump intensity is low (usually less than 10 mT), the spectrum of the magnon frequency comb is as follows:

[0033] .

[0034] Among them, lf p represents the central frequency of the l-th comb tooth, and n and f d represent the n-th comb tooth and the comb tooth spacing. In this case, the formation of the frequency comb can be attributed to the three-magnon process. After the magnon polaritons of the high-frequency branch are excited by the pump field, they interact with the magnon polaritons of the low-frequency branch to generate sum-frequency (f p +f d ) and difference-frequency (f p -f d ) modes. As this cascading process continues, the system finally generates a frequency comb with a comb tooth spacing of f d . When the pump intensity increases, the system begins to exhibit a cascading bifurcation of period doubling, and the comb tooth spacing gradually evolves from f d to f d / 2, f d / 3, f d / 4, etc. When the pump intensity h p increases above a certain critical value, the system enters a chaotic state, and the comb tooth spacing becomes irregular, forming a chaotic frequency comb.

[0035] These nonlinear dynamical phenomena can be characterized by the Poincaré section in the phase space. On the selected section, the trajectories of the magnetic moments exhibit different patterns: a single closed curve corresponds to a single quasi-periodic oscillation, three closed curves correspond to a triple quasi-periodic oscillation, and a chaotic trajectory corresponds to a chaotic frequency comb. These phenomena comprehensively demonstrate the nonlinear evolution characteristics of the system.

[0036] The dynamics of ferromagnetic, antiferromagnetic, and SAF systems can be described by two coupled Landau-Lifshitz-Gilbert (LLG) equations:

[0037] ; ;

[0038] where, m i (i = 1, 2) represents two normalized magnetic moments, γ and α i are the gyromagnetic ratio and the Gilbert damping respectively, and the effective magnetic field includes the external magnetic field H ext , the anisotropy field H k,1(2) = H k,1(2) m 1(2) and the exchange field H ex,1(2) = H ex m 2(1) . Here, H k and H ex are the total anisotropy field and the interlayer coupling field respectively. Due to the system containing high-order nonlinear terms, significant nonlinear interactions will be excited between the upper and lower branches of magnon polaritons under the action of a pump close to resonance.

[0039] To further analyze the nonlinear behavior and coupling strength of the system, the present invention uses the generalized Hopfield Hamiltonian to describe the magnon-magnon coupling system:

[0040]

[0041] where, is the reduced Planck constant, ω + and ω - correspond to the angular frequencies of two kinds of magnons respectively, and i is the imaginary unit. ( ) corresponds to the annihilation operator of the +(-) magnon mode, ( ) corresponds to the creation operator of the +(-) magnon mode. Here, the "+ magnon mode" and the "- magnon mode" refer to different magnon modes. g 1 and g 2Corresponding to the co-rotating coupling strength and the counter-rotating coupling strength respectively. When the coupling strength enters the ultrastrong state, the nonlinear effect between the upper and lower branches of magnon polaritons will be enhanced, and the three-magnon process will be strengthened, thus generating various nonlinear phenomena.

[0042] Currently, experimental reports of magnon-magnon ultrastrong coupling in compensated ferromagnets and SAF systems already exist. To realize the magnon analogue of chaotic frequency combs, the present invention takes SAF as the research object and analyzes its nonlinear dynamic behavior. SAF is a three-layer structure composed of two ferromagnetic layers separated by an intermediate non-magnetic layer, and its interlayer exchange coupling is dominated by the RKKY (Ruderman-Kittel-Kasuya-Yosida) interaction.

[0043] The SAF system has two intrinsic homogeneous magnon modes: an acoustic mode (AM) with in-phase precession and an optical mode (OM) with anti-phase precession. The dynamics of the two magnetic moments in the system are determined by formula (1) (including (1a) and (1b)). By introducing an asymmetry in magnetic anisotropy between the two ferromagnetic layers, magnon-magnon ultrastrong coupling is achieved, and the magnon polaritons in the f u and f d branches are generated by the coupling of AM and OM. As Figure 2 shows a schematic diagram of SAF, an external in-plane magnetic field H x is applied along the x-axis to keep the static magnetic moment in a spin-tilted state. Here, the present invention mainly studies the characteristics of the net magnetization m = (m 1 + m 2 ) / 2 to discuss the case of g 1 / ω 0 = g 2 / ω 0 = 0.495, H x = 120 mT as an example. In this case, the high-frequency branch f u = 8 GHz, and the low-frequency branch f d = 0.5 GHz. At the same time, in different frequency branches, the chirality of the magnetic moment precession also exchanges: at f d , the precession direction of the magnetic moment m 1 is right-handed, while the precession direction of m 2 is left-handed; however, at f u , the chirality of m 1 and m 2 exchanges. When the frequency of the applied pump magnetic field is close to 45° in the x-y plane of f u , as the amplitude h p increases, behaviors including periodic oscillation, frequency comb, period-doubling bifurcation, and chaos appear. From m xIn the time-domain variation, the present invention finds that the waveform evolves continuously with the increase of h p . In Figure 3 , except for the lack of clear periodicity in chaotic behavior, other behaviors are shown as the time variation of one period of m x .

[0044] To understand the evolution of the dynamics, the present invention describes the Poincaré section of the system. Here, the present invention records the trajectory points each time m x reaches its local maximum. Initially, the graph has only one point, indicating periodic oscillation. When h p increases to 6 mT, the Poincaré section changes from a single point to a closed curve, indicating the transition from periodic behavior to quasi-periodic behavior. Subsequently, period-doubling, period-quadrupling, and period-tripling bifurcations occur, represented by two, four, and three closed curves respectively. At approximately h p = 12 mT, the closed curve turns into a chaotic graph. In the frequency domain, when h p is small, there is only the pump frequency f p = 8 GHz. At h p = 6 mT, three main peaks centered at f d = 0.5, f p = 8, and 2f p = 16 GHz appear in the spectrum, and a clear frequency comb with a tooth pitch of the low frequency f d = 0.5 GHz appears. As h p increases, the tooth pitch of the comb becomes 0.25, 0.17, and 0.125 GHz, representing period-doubling, period-tripling, and period-quadrupling bifurcations respectively. Finally, at approximately h p = 12 mT, the spectrum becomes disordered and enters the chaotic state.

[0045] To study the route to chaos in the system, the present invention characterizes the dynamics under different detuning conditions by analyzing the dispersion diagram, bifurcation diagram, and maximum Lyapunov exponents (LLEs). First, focus on the case of small detuning (f p - f u = 0.05 GHz). Figure 4 shows the variation of the dispersion diagram with the pump field intensity h p . Near h p = 4.2 mT, the system first appears a frequency comb; as h pWith the increase of [parameter], the system experiences a period-doubling bifurcation near 7.1 mT and further a period-four bifurcation near 8.7 mT. The chaotic phenomenon is first observed at 9.2 mT, where the trajectories start to diverge significantly. Subsequently, a period-tripling bifurcation occurs near 9.8 mT, and finally, above 11.7 mT, the system enters a persistent chaotic state. The research shows that the path of the system leading to chaos starts from a frequency comb and evolves gradually through a series of bifurcations of tooth pitches. During this process, the periodic oscillation and the chaotic state alternate multiple times.

[0046] To further reveal the transition between periodic and chaotic behaviors, the present invention extracts the local maxima of the wave packet and plots the bifurcation diagram, which shows three main transition stages from periodic oscillation to chaos. The chaotic behavior is quantitatively characterized by LLE, and the definition of LLE is:

[0047]

[0048] where δm represents the difference between two initially close magnetization trajectories, that is , and J is the Jacobian matrix derived from the LLG equation, which depends on the magnetization vector m(t) and time t.

[0049] The Jacobian matrix describes the evolution rate between adjacent orbits. A positive LLE indicates a faster divergence rate between adjacent orbits, which further indicates that the system is in a chaotic state. The green dotted line plot in the figure shows the calculated LLEs, which is consistent with the results of the bifurcation diagram. Through these calculations, the present invention can further confirm whether the system enters a chaotic state and the transition process of its dynamic behavior.

[0050] Different from the above situation, when the detuning is large, the path of the system leading to chaos shows different characteristics. Figure 4 In [reference], the dispersion diagram, bifurcation diagram, and LLEs at a detuning of (f p -f u =-0.7 GHz) show that the frequency comb and the period-doubling bifurcation phenomenon disappear, and the system directly transitions from periodic oscillation at about 10.2 mT to chaotic behavior. At the same time, at about 10.2 mT of h p , the LLE becomes positive, indicating that the system enters a chaotic state. This phenomenon shows that the change of detuning significantly affects the dynamic behavior of the system, resulting in a direct transition from periodic behavior to chaos without experiencing the stage of period-doubling bifurcation.

[0051] Figure 5 Describes the magnon dispersion diagram when the pump field is detuned near f u , including different h p=Overall images and partial enlarged images at 6, 8, and 12 mT. From the perspective of the overall images, two thresholds are shown on both sides of the high frequency f u . When h p = 6 mT, only the frequency comb phenomenon appears, and f p and 2f p can be observed, and the intensity is the highest at f u and f d . The interval frequency of the comb teeth is about 0.5 GHz, and the threshold is between 7.5 GHz and 8.75 GHz. As h p increases to 8 mT, the system exhibits frequency comb, period-doubling bifurcation, and chaos phenomena. In addition, at f p = 16 GHz, the phenomenon of 1 / 2f p can be observed, and the threshold changes to 7.4 GHz and 9.1 GHz. When 7.4 ≤ f p ≤ 8.2 GHz, the system shows period-doubling bifurcation; when 8.2 ≤ f p ≤ 8.75 GHz, the system presents a frequency comb; and when 8.75 ≤ f p ≤ 9.1 GHz, the system enters a chaotic state. Finally, when h p increases to 12 mT, chaotic behavior becomes the main phenomenon, and the mode of 3f p can be observed. At this time, the threshold changes again to 7.25 GHz and 9.25 GHz. From these results, it can be found that as h p increases, the threshold distance gradually increases, and it is easier to excite the nf p frequency mode.

[0052] To gain an in-depth understanding of the influence of these behaviors, the present invention studies the state of the system when changing the amplitude h p and the frequency f p . Figure 6 summarizes the different states of the system, and the colored regions represent the non-linear response of the system. The non-linear regions include the magnon frequency comb region, the period-doubling bifurcation region, and the chaotic region, which are marked by different colors. The results show that when f p is less than f u , the system is more likely to directly enter the chaotic state; while when f p is greater than f u , the system tends to enter chaos through the frequency comb. When f p is close to f u , the system will exhibit the phenomena of frequency comb and period-doubling cascade, ultimately leading to chaos.

[0053] Example 2

[0054] This embodiment provides an application of the frequency comb generated in Embodiment 1 in identifying signals in noise. The chaotic system has high sensitivity and noise immunity characteristics and plays an important role in signal detection. Here, the present invention demonstrates the identification of noise-immune signals by utilizing the transition of the magnon chaotic comb from periodic oscillation to chaos (or from chaos to periodic oscillation). In the application, the pump magnetic field is referred to as the reference signal. At the critical amplitude of the reference signal h c , the system transitions from periodic oscillation to chaos.

[0055] The present invention assumes that the oscillation of m is periodic under the action of only the reference signal h(t) = h p sin(2πf p t + φ). If there is a periodic signal s = s 0 sin(2πf s t + β) in the system, then the total signal is expressed as h t = h + s = h 0 sin(2πf 0 t + φ + ε), where the amplitude h 0 and the phase ε are respectively:

[0056]

[0057]

[0058] where t represents time, φ and β are the phases of the reference signal and the periodic signal respectively, and s 0 is the amplitude of the periodic signal. Since h p >> s 0 , the phase change ε becomes negligible (i.e., ε ~ 0), so the phase change can be ignored in the analysis. It can be found from Equation (4) that the periodic signal will affect the amplitude h 0 . When h 0 is close to h c - s 0 , the system exhibits periodic oscillation; when h 0 is close to h c + s 0 , the system transitions to chaotic oscillation. Therefore, in the case where there is a frequency difference f p - f s = Δf, h 0 is periodically greater than or less than h c , and intermittent chaos will occur. This intermittent chaos is stable and has a fixed periodicity, and its periodicity is given by the following formula:

[0059]

[0060] To verify the above theory, the present invention calculated the oscillation of m under three input conditions, asFigure 7 As shown in (a): (i) only the reference signal, h p = 8.3 mT, f p = 7.49 GHz; (ii) the reference signal is combined with the signal to be identified (s 0 = 0.5 mT); (iii) the reference signal and the signal to be identified are buried in Gaussian noise with a standard deviation of σ = s 0 = 0.5 mT. At h c = 8.5 mT, f p = 7.5 GHz, the system transitions from periodic oscillation to chaotic behavior. When the reference signal and the periodic signal to be identified coexist, intermittent chaos occurs. From the period of intermittent chaos T ≈ 100 ns, according to formula (6), the frequency difference Δf is approximately 0.01 GHz. Given that the frequency of the reference signal is f p = 7.49 GHz, the frequency of the signal to be identified f s is 7.5 GHz. In the case of f p = f s = 7.5 GHz, the intermittent chaos disappears. In addition, even when the signal to be identified is buried in Gaussian noise, the results are still consistent with those without noise, indicating the robustness of the model and its immunity to noise interference.

[0061] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A method for generating a frequency comb based on magnon-magnon superstrong coupling, characterized in that: In a system of two ultrastrongly coupled magnons, when a pump magnetic field with a frequency close to the frequency of the high-frequency branch magnon is applied, the system enters a nonlinear state. Depending on the amplitude of the pump magnetic field, the system exhibits typical nonlinear dynamic phenomena, including frequency combs, period-doubling bifurcations, and chaotic frequency combs.

2. The method for generating a frequency comb based on magnon-magnon superstrong coupling according to claim 1, characterized in that: When the pump intensity is low, the spectrum of the magnon frequency comb is: ； Among them, lf p represents the center frequency of the lth comb tooth, n and f d Indicates the distance between the nth comb teeth.

3. The method for generating a frequency comb based on magnon-magnon superstrong coupling according to claim 2, characterized in that: After being excited by the pump field, the high-frequency magnon polaritons interact with the low-frequency magnon polaritons to generate a sum frequency (f p +f d ) and difference frequency (f p -f d ) mode; as this cascade process continues, the system eventually generates a comb spacing of f d frequency comb.

4. The method for generating a frequency comb based on magnon-magnon superstrong coupling according to claim 3, characterized in that: When the pump intensity increases, the system begins to show a period-doubling cascade bifurcation, and the comb tooth spacing increases from f d Gradually evolved into f d / 2, f d / 3, f d / 4; when the pump intensity h p When it increases above a certain critical value, the system enters a chaotic state, the spacing between the comb teeth becomes irregular, and a chaotic frequency comb is formed.

5. The method for generating a frequency comb based on magnon-magnon superstrong coupling according to claim 1, characterized in that: When the detuning is small, the path to chaos starts from the frequency comb and gradually evolves through a series of pitch bifurcations. During this process, periodic oscillations and chaotic states alternate many times. When the detuning is large, the system will directly transition to a chaotic state without going through the process of period-doubling bifurcations.

6. The method for generating a frequency comb based on magnon-magnon superstrong coupling according to claim 1, characterized in that: When f p Less than f u When f p Greater than f u When f p Close to f u When , the system will show the phenomenon of frequency comb and period doubling cascade, which eventually leads to the generation of chaos.

7. Application of the frequency comb according to any one of claims 1 to 6 in identifying signals in noise, characterized in that: The reference signal makes the system at the boundary between periodic oscillation and chaos. c , when there is a periodic signal with amplitude s0 in the system, it will affect the total signal amplitude h0. When h0 is close to h c -s0, the system exhibits periodic oscillations; when h0 is close to h c +s0, the system transitions to chaotic oscillation; therefore, when there is a frequency difference between the periodic signal and the reference signal In the case of h0, h0 is periodically greater than or less than h c , intermittent chaos will occur; this intermittent chaos is stable, has a fixed periodicity, and is not affected by noise.

8. The use of a frequency comb in identifying signals in noise according to claim 7, characterized in that: The periodicity of the occurrence of intermittent chaos is given by the following formula: 。

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