Narrow linewidth non-Hermite sensing system based on anti-PT symmetry and application thereof

Abstract

The invention relates to a narrow-linewidth non-Hermite sensing system based on anti-PT symmetry and application thereof. The system comprises a resonator circuit formed by connecting a resistor, an inductor and a capacitor; the voltage source is connected with the resistor and the inductor in the resonator circuit, and the voltage source is connected with the capacitor in parallel; the adjusting source is connected in parallel with the capacitor in the resonator circuit and is arranged at the other end of the resistor and the other end of the inductor; wherein the non-Hermite sensing system is in anti-PT symmetry, and the dynamic regulation and control of the anti-PT symmetry can be realized by adjusting the generalized coupling coefficient of the non-Hermite sensing system. According to the invention, the anti-PT symmetry theory is applied to the single-resonator sensing system for the first time, so that the loss and coupling between resonant modes are dynamically regulated and controlled, and the system performance is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the field of sensing technology, and particularly to a narrow-linewidth non-Hermitian sensing system based on anti-parity-time (PT) symmetry and its applications. Background Art

[0002] Non-Hermitian physics has shown great application potential in high-precision detection fields such as quantum sensing, optics, acoustics, and electromagnetics. Therefore, how to achieve narrow linewidth and high sensitivity through resonators has become an important direction in scientific research and industrial design. These resonators can be used to detect weak magnetic fields in quantum sensing, for laser frequency stabilization and precise frequency control in optics, and for detecting weak vibrations and signals in acoustics and electromagnetics. However, in real non-Hermitian systems, the quality factor (Q-factor) decreases due to energy loss caused by intrinsic losses, which in turn leads to an increase in linewidth and a decrease in system sensitivity. These problems significantly limit the application of non-Hermitian systems in precision measurement. With the development of non-Hermitian physics related to parity-time (PT) symmetry, the sensor sensitivity and system stability have been improved, providing new possibilities for solving these problems.

[0003] Exceptional Points (EPs) have extremely high sensitivity to external perturbations through their unique eigenvalue splitting characteristics. This enhanced sensitivity stems from the topological structure of the eigenvalue surface in the parameter space, which can convert small perturbations into significant dynamic changes. However, while the EP-based sensing system enhances sensitivity, it also amplifies the system's sensitivity to noise, affecting its robustness in practical applications. To address these limitations, researchers have proposed various schemes to enhance robustness, including using topologically protected edge states to reduce internal interference and constructing special surface synthetic spaces to reduce the impact of structural perturbations. However, the designs of these schemes are highly complex, which limits their application in practical scenarios. An easy-to-implement sensing technology that simultaneously achieves high sensitivity and robustness remains a key research direction. Summary of the Invention

[0004] The purpose of the present invention is to overcome the defects of the prior art, and provide a narrow-linewidth non-Hermitian sensing system based on anti-PT symmetry and its applications, so as to solve the problem of the lack of robustness in the practical application of existing non-Hermitian systems by introducing exceptional points, and the problem that the application of using topologically protected edge states to reduce internal interference is limited by its high complexity.

[0005] The technical solution for achieving the above purpose is as follows:

[0006] The present invention provides a narrow-linewidth non-Hermitian sensing system based on anti-PT symmetry, comprising:

[0007] A resonator circuit formed by connecting a resistor, an inductor and a capacitor;

[0008] A voltage source connected to the resistor and inductor in the resonator circuit, the voltage source being in parallel with the capacitor;

[0009] An adjustment source in parallel with the capacitor in the resonator circuit, the adjustment source being provided at the other ends of the resistor and the inductor;

[0010] Wherein, the non-Hermitian sensing system has anti-PT symmetry, and the dynamic regulation of the anti-PT symmetry can be achieved by adjusting the generalized coupling coefficient of the non-Hermitian sensing system.

[0011] A further improvement of the present invention based on the anti-PT symmetric narrow linewidth non-Hermitian sensing system is that the adjustment source exerts an independent control force f on the generalized coordinate q of the non-Hermitian sensing system ctrl , where the generalized coordinate q evolves dynamically as: In the formula, M e is the effective mass;

[0012] The control force f ctrl has the following linear relationship with the generalized coupling coefficient k:

[0013] f ctrl = 2kq.

[0014] A further improvement of the present invention based on the anti-PT symmetric narrow linewidth non-Hermitian sensing system is that when adjusting the generalized coupling coefficient, the generalized coupling coefficient is in the range greater than 0 and less than γ, where γ is the intrinsic loss of the system.

[0015] A further improvement of the present invention based on the anti-PT symmetric narrow linewidth non-Hermitian sensing system is that the adjustment source is a current source, and the generalized coupling coefficient is controlled by adjusting the amplitude and phase of the current source, thereby changing the anti-PT symmetry.

[0016] A further improvement of the present invention based on the anti-PT symmetric narrow linewidth non-Hermitian sensing system is that the expression of the current source in the steady-state response is:

[0017]

[0018] Wherein, n = 2ω(γ - k), φ = Arg(m + in), k is the generalized coupling coefficient, c is the capacitance in the circuit, U m is the amplitude of the input voltage, ω is the frequency of the current source, ω 0 is the natural frequency of the system, t is the time variable, φ is the phase angle, m, n are system parameters, γ is the intrinsic loss of the system, and i is the imaginary unit;

[0019] Control and adjust the generalized coupling coefficient according to the expression of the current source in the steady-state response.

[0020] A further improvement of the non-Hermitian sensing system based on anti-PT symmetry with narrow linewidth in the present invention lies in that the relationship between the bandwidth of the non-Hermitian sensing system and the generalized coupling coefficient is approximately:

[0021] BW≈2(γ - k),

[0022] where BW is the bandwidth of the non-Hermitian sensing system, k is the generalized coupling coefficient, and γ is the intrinsic loss of the system.

[0023] Effective control of the bandwidth can be achieved by adjusting the generalized coupling coefficient.

[0024] A further improvement of the non-Hermitian sensing system based on anti-PT symmetry with narrow linewidth in the present invention lies in that the relationship between the sensitivity of the non-Hermitian sensing system and the generalized coupling coefficient is:

[0025]

[0026] where S p is the sensitivity of the non-Hermitian sensing system, is the derivative of the generalized coupling coefficient k, is the derivative of the instantaneous dissipation power P γ .

[0027] The present invention also provides an application of the non-Hermitian sensing system based on anti-PT symmetry with narrow linewidth in the fields of quantum sensing, quantum information processing, and high-precision detection and measurement.

[0028] The beneficial effects of the non-Hermitian sensing system based on anti-PT symmetry with narrow linewidth and its application in the present invention are:

[0029] The present invention first applies the anti-PT symmetry theory to a single-resonator sensing system, thereby dynamically regulating the loss and coupling between resonant modes and achieving a significant improvement in system performance.

[0030] The novel non-Hermitian sensing system based on anti-PT symmetry in the present invention can achieve more efficient and robust detection in the weak coupling region.

[0031] The present invention flexibly regulates the sensing mode by using a simple two-channel excitation mechanism, taking into account the requirements of compact design and high sensitivity.

[0032] The design proposed in the present invention has good scalability and can be further applied to more complex resonant systems and high-order topological sensor designs. Description of the Drawings

[0033] Figure 1This is the simulation circuit diagram of the narrow-linewidth non-Hermitian sensing system based on anti-PT symmetry of the present invention.

[0034] Figure 2 In the present invention, two external sources F dirve and F ctrl are used to drive the resonator to establish an anti-PT symmetric non-Hermitian physical model.

[0035] Figure 3 In the present invention, the real and imaginary parts of the normalized characteristic frequency of the narrow-linewidth non-Hermitian sensing system based on anti-PT symmetry are shown as the evolution of a function of k / ω 0

[0036] Figure 4 In the present invention, the magnified imaginary part of the narrow-linewidth non-Hermitian sensing system based on anti-PT symmetry near the resonance frequency ω 0 is shown.

[0037] Figure 5 In the present invention, the phase diagram and the divergent transient amplitude of the resonator of the narrow-linewidth non-Hermitian sensing system based on anti-PT symmetry when k = 1.2γ are shown.

[0038] Figure 6 In the present invention, the steady-state oscillations in the phase space of the narrow-linewidth non-Hermitian sensing system based on anti-PT symmetry when k = 0, 0.6γ, and 0.8γ are shown.

[0039] Figure 7 In an embodiment of the present invention, the amplitude and phase changes of the current source of the normalized frequency ω / ω 0 of the narrow-linewidth non-Hermitian sensing system based on anti-PT symmetry when k = 0.8γ are shown.

[0040] Figure 8 In an embodiment of the present invention, the dissipated power as a function of the normalized generalized coupling coefficient k / γ and the frequency ω / ω 0 of the narrow-linewidth non-Hermitian sensing system based on anti-PT symmetry is shown.

[0041] Figure 9 In an embodiment of the present invention, when ω = ω r , the relationship between the normalized linewidth BW / (2γ) and the relative sensitivity S P / S P0 and the generalized coupling coefficient is shown.

[0042] Figures 10 to 13 In an embodiment of the present invention, the experimental results of anti-PT symmetry-induced linewidth narrowing and high-sensitivity sensing of the narrow-linewidth non-Hermitian sensing system based on anti-PT symmetry are shown. Detailed implementation manners

[0043] ​The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0044] Referring to Figure 1 , the present invention provides a narrow linewidth non-Hermitian sensing system based on anti-PT symmetry and its application. By introducing a dual-channel excitation mechanism, a driving source (implemented by a voltage source) is applied to one channel, and the other channel (i.e., the adjustment source) dynamically regulates the anti-PT symmetry by adjusting the generalized coupling coefficient. The non-Hermitian sensing system of the present invention has the advantages of simple design and excellent detection performance, and is particularly suitable for applications that require a compact system design without affecting high sensitivity. By solving the problems of insufficient sensitivity and robustness of traditional singular point sensing systems, it provides a new solution for quantum sensing, quantum information processing, and other high-sensitivity application fields (such as high-precision detection and measurement in optics, acoustics, and electromagnetics, etc.), and provides a new principle support for the development of the next generation of sensing technologies. The narrow linewidth non-Hermitian sensing system based on anti-PT symmetry and its application of the present invention will be described below in conjunction with the accompanying drawings.

[0045] Referring to Figure 1 , it shows the simulation circuit diagram of the narrow linewidth non-Hermitian sensing system based on anti-PT symmetry of the present invention. The narrow linewidth non-Hermitian sensing system based on anti-PT symmetry of the present invention will be described below in conjunction with Figure 1 .

[0046] As Figure 1 shown, the narrow linewidth non-Hermitian sensing system based on anti-PT symmetry of the present invention includes a resonator circuit, a voltage source U drive and an adjustment source I ctrl . The resonator includes a resistor R, an inductor L, and a capacitor C. The resistor R and the inductor L are connected in parallel, and the capacitor C is connected to one end of the resistor R and the inductor L; the voltage source U drive is connected to the resistor R and the inductor L in the resonator circuit. The voltage source U drive is connected to the other end of the resistor R and the inductor L. The voltage source U drive is connected in parallel with the capacitor C; the adjustment source I ctrl is connected in parallel with the capacitor C in the resonator circuit. The adjustment source I ctrl is provided at one end of the resistor R and the inductor L away from the voltage source U driv . The adjustment source I ctrl and the voltage source U drive are provided at both ends of the resistor R and the inductor L. Among them, the non-Hermitian sensing system exhibits anti-PT symmetry, and the dynamic regulation of the anti-PT symmetry can be achieved by adjusting the generalized coupling coefficient of the non-Hermitian sensing system.

[0047] In a specific embodiment of the present invention, the adjustment source applies an independent control force f ctrl to the generalized coordinate q of the non-Hermitian sensing system, where the generalized coordinate q evolves dynamically as: Wherein, M e is the effective mass;

[0048] The control force f ctrl has the following linear relationship with the generalized coupling coefficient k:

[0049] f ctrl = 2kq.

[0050] In a specific embodiment of the present invention, when adjusting the generalized coupling coefficient, the generalized coupling coefficient is within the range greater than 0 and less than γ, where γ is the intrinsic loss of the system. When 0 < k < γ, the system operates stably in the anti-PT symmetric phase without generating additional losses.

[0051] In a specific embodiment of the present invention, the adjustment source is a current source, and the generalized coupling coefficient is controlled by adjusting the amplitude and phase of the current source, thereby changing the anti-PT symmetry.

[0052] Furthermore, for any given generalized coupling coefficient k, when q = 1, according to f ctrl = 2k, the expression of the current source in the steady-state response is:

[0053]

[0054] Wherein, n = 2ω(γ - k), φ = Arg(m + in), k is the generalized coupling coefficient, c is the capacitance in the circuit, U m is the amplitude of the input voltage, ω is the frequency of the current source, ω 0 is the natural frequency of the system, t is the time variable, φ is the phase angle, m, n are system parameters, γ is the intrinsic loss of the system, and i is the imaginary unit;

[0055] The generalized coupling coefficient is controlled according to the expression of the current source in the steady-state response. Specifically, the generalized coupling coefficient k can be controlled by adjusting the amplitude and phase of the current source, thereby changing the anti-PT symmetry.

[0056] In a specific embodiment of the present invention, the relationship between the bandwidth of the non-Hermitian sensing system and the generalized coupling coefficient is approximately:

[0057] BW ≈ 2(γ - k),

[0058] Wherein, BW is the bandwidth of the non-Hermitian sensing system, k is the generalized coupling coefficient, and γ is the intrinsic loss of the system,

[0059] The effective control of the bandwidth can be achieved by adjusting the generalized coupling coefficient.

[0060] In a specific embodiment of the present invention, the relationship between the sensitivity of the non-Hermitian sensing system and the generalized coupling coefficient is:

[0061]

[0062] In the formula, S p is the sensitivity of the non-Hermitian sensing system, is the derivative of the generalized coupling coefficient k, is the derivative of the instantaneous dissipation power P γ .

[0063] The present invention also provides an application of the anti-PT symmetric narrow linewidth non-Hermitian sensing system in the fields of quantum sensing, quantum information processing, and high-precision detection and measurement. The high-precision detection and measurement fields include high-precision detection and measurement fields such as optics, acoustics, and electromagnetics.

[0064] The principle of the anti-PT symmetric narrow linewidth non-Hermitian sensing system of the present invention will be described below.

[0065] For a general linear resonator system, its dynamic equation can be expressed in terms of the generalized coordinates q and momentum p:

[0066]

[0067] In Equation 1, M e is the effective mass, K e is the effective elastic constant, Γ is the system loss, and f drive is the system driving force. The energy of this system can be expressed as To reveal the hidden anti-PT symmetry of the system, the system dynamic equation is rewritten using the normal mode equation, and its generalized coordinates and momentum can be expressed as where E = |a| 2 , and a is the amplitude.

[0068] As Figure 2 shown, an anti-PT symmetric non-Hermitian physical model is established by driving the resonator through two external sources F dirve and F ctrl . According to Equation 1, the system can be expressed in the normal mode equation as where the state vector is ψ = (a, a * ) T , and at the same time i is the imaginary unit. The Hamiltonian of the system can then be written as:

[0069]

[0070] In Equation 2, γ is the system eigen-loss, ω 0is the resonance frequency of the system. In the normal mode equation, the single - cavity system naturally exhibits anti - PT symmetry:

[0071] PTH(PT) -1 =-H Equation 3.

[0072] To further adjust the anti - PT symmetry of the system, a new control channel is introduced, and an independent control force f is applied to the generalized coordinate q ctrl , as Figure 2 shown, the dynamic evolution of q is: When the control force f ctrl is linearly related to q with f ctrl = 2kq, where k is the generalized coupling coefficient, the dynamic equation can be simplified to: The Hamiltonian of the system becomes:

[0073]

[0074] where γ e = γ - k and κ = γ + k, γ e is the effective loss coefficient, κ is the coupling strength. In this case, both the incoherent factor (diagonal term) and the coherent factor (off - diagonal term) of the Hamiltonian operator are affected by the generalized coupling coefficient k, and the characteristic frequencies of the system correspond to Figure 3 and Figure 4 respectively show the evolution of the imaginary and real parts of the characteristic frequencies in the broken - symmetry phase (k < - ω 0 - γ or k > ω 0 - γ) and the anti - PT - symmetric phase (- ω 0 - γ < k < ω 0 - γ). In particular, when k > γ, as shown on the left side of Figure 5 , when k = 1.2γ, the gain of the system is greater than the loss. The unstable phase diagram corresponds to the system gain exceeding the loss, resulting in the divergence of the phase space and the exponential growth of the oscillation amplitude, as shown on the right side of Figure 5 . On the other hand, when k < 0, k acts as a loss, increasing the total dissipation and broadening the linewidth. Therefore, to make the system operate stably in the anti - PT - symmetric phase without additional losses, the generalized coupling coefficient k must be in the range of 0 < k < γ, as shown in the magnified inserted part of Figure 4 . As k increases, the ellipse begins to expand, indicating a significant increase in the system energy, which is beneficial for the detection of weak signals, as shown in Figure 6 . Figure 3 and Figure 4 show the anti - PT - symmetric (anti - PT - symmetry - broken) phases in blue and orange respectively, where γ = ω 0 / 13.5.

[0075] Then consider the change in the dissipated power. The transient dissipated power of the system is the derivative of the energy:

[0076]

[0077] In Equation 5 and P ctrl = k(a + a * ) 2 respectively represent the transient power provided by the driving force and the control force to the system, and P γ = -γ(a - a * ) 2 is the instantaneous dissipated power. For a general resonator system, in the region near the resonance frequency, it exhibits an obvious narrow linewidth and field localization response, and the loss is usually very small, meeting the detection conditions, that is, ω ≈ ω 0 and γ << ω 0 . In this case, the average value of the dissipated power can be approximated as:

[0078]

[0079] The peak position can be approximated as As the coupling factor k increases, the peak frequency gradually decreases. At the peak position ω p , the system sensitivity S p is defined as: And the bandwidth can be approximated as BW ≈ 2(γ - k). It can be seen that effective control of the bandwidth can be achieved by adjusting the generalized coupling coefficient k.

[0080] Next, the performance of the non-Hermitian sensing system with narrow linewidth based on anti-PT symmetry of the present invention is verified through experiments.

[0081] Based on the RLC resonator circuit, construct an anti-PT symmetric system driven by a dual source, as Figure 1 shown, the driving source is the voltage source U drive = U m sin(ωt), and the adjustment source is the current source I ctrl connected in parallel with the capacitor. The circuit corresponding expressions of each parameter in the dynamic equation are shown in Table 1, where R is the resistance, L is the inductance, C is the capacitance, I L is the inductor current, and U C is the capacitor voltage.

[0082] Table 1 Related expressions of each parameter in the dynamic equation in the circuit

[0083]

[0084] For any given generalized coupling coefficient k, according to f ctrl= 2k (where q = 1), and the current source expression during steady-state response is: where n = 2ω(γ - k), φ = Arg(m + in). Therefore, the generalized coupling coefficient k can be controlled by adjusting the amplitude and phase of the current source, thereby changing the anti-PT symmetry.

[0085] Here, the circuit parameters are set as U m = 0.5 V, R = 14.55 Ω, L = 65.96 μH, C = 6.86 bnF. Figure 7 Shows the relationship between the amplitude (blue line) and phase (red dashed line) of the current source and the normalized frequency when k = 0.8γ. In Figure 8 , when k = 0, the peak dissipation power is 8.6 mW, and the corresponding bandwidth is 2 times, as shown in the three-dimensional surface plot and the peak normalized projection plane in Figure 8 . As the generalized coupling coefficient k increases, the bandwidth linearly narrows, as shown by the green solid line in the figure. At the same time, the peak dissipation power and the relative sensitivity S p / S p0 (where S p0 is the sensitivity when k = 0) both increase significantly, as shown by the red dashed line in Figure 9 . When k increases to 0.8γ, the peak dissipation power increases to 218 mW, an increase of 24.4 times, the relative sensitivity increases by 125 times, and the bandwidth decreases to 0.4γ, as shown by the blue solid line in Figure 9 , a decrease of 80%.

[0086] Figure 7 The blue solid line in shows the amplitude change, and the red dashed line shows the phase change. Figure 8 The green line in the upper projection plane in shows the half-height position of the dissipation power, and the white dashed line shows the peak of the dissipation power.

[0087] To verify the effectiveness of the anti-PT symmetry-induced linewidth narrowing, the predicted behavior of the RLC series resonant circuit was demonstrated experimentally. The experimental system was driven by a signal generator (Aglient 33600A) to generate the required U drive and I ctrl signals. These signals were amplified using a power amplifier (Buff634) and input into the resonant circuit to precisely control the generalized coupling coefficient k. A direct current (DC) power supply (DH1766-2) was used to provide the necessary DC voltage for the power amplifier. The inductor was provided by a high-permeability Mn-Zn ferrite core (PC95PQ50 / 50Z-12), the capacitor was provided by a thin-film capacitor, and the resistor was provided by a precision non-inductive resistor. In addition, AC analysis was performed using LTSpice simulation software, where an ideal voltage-controlled current source (I ctrl)Automatically provide the generalized coupling coefficient k. The input voltage U of the controlled current source c and the output current I crtl The relationship between them is given by I ctrl = 2kCU c .

[0088] In Figure 10 , the dissipated power at different values of k / γ = 0, 0.3, 0.6, and 0.8 was first observed. Both the experimental (points) and theoretical (solid lines) results show excellent agreement. As k increases, the resonance linewidth decreases significantly, and the peak power increases significantly. Next, the variation of the dissipated power with different resistances was studied. As Figure 11 shown, when the resistance decreases from R 0 = 28.4 Ω (blue line) to R 0 = 14.6 Ω (red line), the linewidth of the system without dual-channel control (k = 0) decreases from 3.9γ to 2γ. However, when the generalized coupling coefficient k increases to 0.8γ, the linewidth decreases sharply from 2.3γ to 0.4γ, a reduction of 82.6%, as Figure 12 shown.

[0089] Figures 10 to 13 Shows the experimental results of anti-PT-symmetry-induced linewidth narrowing and high-sensitivity sensing. Figure 10 Is the variation of the dissipated power calculated (solid lines) and measured (points) at k / γ = 0 (blue), 0.3 (indigo), 0.6 (orange), and 0.8 (red), respectively. Figure 11 And Figure 12 Are the comparisons of the dissipated power of theory (solid lines), simulation (dashed lines), and experiment (points) when k / γ = 0 and k / γ = 0.8, and the resistance decreases from 28.4 Ω (blue) to 14.6 Ω (red). Figure 13 Is the variation of the dissipated power at the resonance frequency ω 0 for different k / γ: 0 (blue), 0.6 (orange), 0.8 (red).

[0090] In addition, the variation of the dissipated power when the resistance decreases from 28.4 Ω to 14.6 Ω at a fixed frequency ω 0 was also measured, as shown in 13. For the case of R 0 = 28.4 Ω, the dissipated power for all values of k is still very low (below 15 mW), showing minimal variation. However, as the resistance R 0 decreases, the increase in the dissipated power is more significant, and the generalized coupling coefficient k is also higher. When R 0 = 14.6 Ω, the dissipated power at k = 0 is 8.5 mW, but when k = 0.6γ and k = 0.8γ, the dissipated power increases to 51.4 mW and 160 mW, respectively, an increase of 6 times and 18.6 times.

[0091] The non-Hermitian sensing system with narrow linewidth based on anti-PT symmetry of the present invention. First, by introducing a dual-channel excitation mechanism, a driving source is applied to one channel, and the other channel realizes the dynamic regulation of anti-PT symmetry by adjusting the generalized coupling coefficient. Secondly, using this strategy can effectively optimize the loss and coupling between resonant modes, and a single-resonator circuit driven by dual sources is designed for simulation and experimental verification. The experimental and simulation results show that the present invention can significantly improve the system performance, with the linewidth reduced by 80%, the peak signal enhanced by 24.4 times, and the sensitivity increased by 125 times. In addition, the present invention has the characteristics of simple system design and excellent detection performance, and is particularly suitable for applications that require a compact system design without affecting high sensitivity. By solving the problems of insufficient sensitivity and robustness of traditional singular point sensing systems, this system provides a new solution for quantum sensing, quantum information processing, and other high-sensitivity application fields, and provides new theoretical support for the development of the next-generation sensing technology.

[0092] The present invention has been described in detail above in conjunction with the embodiments with reference to the drawings. Those of ordinary skill in the art can make various variations to the present invention according to the above description. Therefore, certain details in the embodiments should not constitute a limitation to the present invention, and the protection scope of the present invention will be defined by the scope of the appended claims.

Claims

1. A narrow linewidth non-Hermitian sensing system based on anti-PT symmetry, characterized in that: include: A resonator circuit formed by connecting a resistor, an inductor and a capacitor; a voltage source connected to the resistor and the inductor in the resonator circuit, the voltage source being connected in parallel with the capacitor; a regulating source connected in parallel with the capacitor in the resonator circuit, the regulating source being arranged at the other end of the resistor and the inductor; The non-Hermitian sensing system exhibits anti-PT symmetry, and dynamic regulation of the anti-PT symmetry can be achieved by adjusting the generalized coupling coefficient of the non-Hermitian sensing system.

2. The narrow linewidth non-Hermitian sensing system based on anti-PT symmetry according to claim 1, characterized in that: The regulating source applies an independent control force f to the generalized coordinate q of the non-Hermitian sensing system ctrl , where the generalized coordinate q dynamically evolves as follows: Where M e is the effective mass; Control force ctrl It has the following linear relationship with the generalized coupling coefficient k: <h2 style=";text-align:left;direction:ltr">f<h2 style=";text-align:left;direction:ltr"> ctrl <h2 style=";text-align:left;direction:ltr"> <2kq.

3. The narrow linewidth non-Hermitian sensing system based on anti-PT symmetry according to claim 1, characterized in that: When adjusting the generalized coupling coefficient, the generalized coupling coefficient is set within a range of greater than 0 and less than γ, wherein γ is the intrinsic loss of the system.

4. The narrow linewidth non-Hermitian sensing system based on anti-PT symmetry according to claim 1, characterized in that: The regulating source is a current source, and the generalized coupling coefficient is controlled and regulated by adjusting the amplitude and phase of the current source, thereby changing the anti-PT symmetry.

5. The narrow linewidth non-Hermitian sensing system based on anti-PT symmetry according to claim 4, characterized in that: The expression of the current source in steady-state response is: in, n=2ω(γ-k), φ=Arg(m+in), k is the generalized coupling coefficient, c is the capacitance in the circuit, U m is the amplitude of the input voltage, ω is the current source frequency, ω0 is the natural frequency of the system, t is the time variable, φ is the phase angle, m and n are system parameters, γ is the intrinsic loss of the system, and i is the imaginary unit; The generalized coupling coefficient is controlled and adjusted according to the expression of the current source in steady-state response.

6. The narrow linewidth non-Hermitian sensing system based on anti-PT symmetry according to claim 1, characterized in that: The relationship between the bandwidth and the generalized coupling coefficient of the non-Hermitian sensing system is approximately: BW≈2(γ-k), Where BW is the bandwidth of the non-Hermitian sensing system, k is the generalized coupling coefficient, γ is the intrinsic loss of the system, The bandwidth can be effectively controlled by adjusting the generalized coupling coefficient.

7. The narrow linewidth non-Hermitian sensing system based on anti-PT symmetry according to claim 1, characterized in that: The relationship between the sensitivity of the non-Hermitian sensing system and the generalized coupling coefficient is: In the formula, S p is the sensitivity of the non-Hermitian sensing system, is the derivative of the generalized coupling coefficient k, is the instantaneous dissipated power P γ The derivative of .

8. An application of the narrow linewidth non-Hermitian sensing system based on anti-PT symmetry as claimed in claim 1 in the fields of quantum sensing, quantum information processing, and high-precision detection and measurement.

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