Method for rapidly calculating quantum noise in microcavity soliton optical frequency comb

Abstract

The invention relates to the technical field of quantum noise measurement, in particular to a method for quickly calculating quantum noise in a microcavity soliton optical frequency comb. The method comprises the following steps: establishing a dynamic stability analysis model of solitons in a microcavity system, and solving a steady-state solution; identifying stability characteristics of the steady-state soliton solution in the disturbance space based on the solved steady-state solution; constructing a noise physical model of solitons in the micro-cavity system, wherein the noise physical model is used for evaluating the noise performance of a single soliton micro-comb; calculating the power spectrum density based on the solved steady-state solution and the noise performance of the single soliton micro comb; and solving the noise of the quantum in the soliton optical frequency comb in the microcavity system. According to the method, modeling is carried out on a timing jitter mechanism caused by quantum noise, and a time domain nonlinear coupling system is mapped to a modal feature space. The solution carried out in the feature domain not only improves the calculation precision, but also enhances the numerical stability and rapid convergence capability of the algorithm.

Description

Technical Field

[0001] The present invention relates to the technical field of quantum noise measurement, and in particular to a method for rapidly calculating quantum noise in a microcavity soliton optical frequency comb. Background Art

[0002] Microcavity-based soliton micro-optical frequency combs, due to their high coherence, wide spectral coverage, and on-chip integration capabilities, have recently demonstrated transformative potential in cutting-edge fields such as precision metrology, broadband spectroscopy, high-speed optical communications, and quantum information processing. However, the stability and coherence of soliton micro-combs are susceptible to interference from a variety of intrinsic and extrinsic noise sources, including thermal refraction noise, technical noise in the pump source, and quantum noise arising from quantum fluctuations. Quantum noise, as a fundamental physical limit, cannot be completely suppressed through engineering, inevitably introducing phase perturbations, amplitude fluctuations, and soliton timing jitter. These quantum fluctuations fundamentally affect the coherence, phase stability, and frequency uncertainty of the frequency comb lines, becoming a key bottleneck restricting the performance of high-precision applications. Accurately assessing the frequency drift and jitter induced by quantum noise is particularly crucial in systems such as ultrastable microwave photon sources and atomic optical clocks.

[0003] In microcavity systems, especially those with strong nonlinearities and high-Q cavities such as soliton micro-optical frequency combs, noise analysis is key to understanding their coherence, stability, and spectral purity. Traditionally, modeling quantum noise in microcavities has relied primarily on two classical approaches: the Monte Carlo method and the linearized perturbation method.

[0004] The core idea of ​​the first approach, the Monte Carlo method, is to introduce random source terms into the Lugiato-Lefever equation (LLE) or its extended form to simulate random perturbations such as vacuum fluctuations or technological noise. By statistically averaging the evolution trajectories under hundreds to thousands of independent noise realizations, key metrics such as power spectral density, phase noise spectrum, and jitter variance can be calculated. Although this method is physically intuitive and widely applicable, it suffers from significant computational efficiency bottlenecks. Because each simulation corresponds to only a single noise realization, analytical expressions of statistical quantities cannot be directly obtained, requiring numerous independent integrations to be performed repeatedly. Each integration involves high-resolution time-domain calculations, placing extremely high demands on the time step and nonlinear convergence, resulting in extremely high overall computational overhead. Furthermore, memory usage increases rapidly with simulation dimension, placing significant pressure on data storage, severely limiting its practicality for multi-parameter sweeps, large-scale system analysis, and real-time modeling.

[0005] Another method, the linearized perturbation method, is based on the steady-state solution of the soliton system, and regards the noise as a small perturbation around the steady state, and establishes a set of perturbation equations for the system under linear approximation. This method can directly obtain the impact of noise on different modes by constructing and solving the Jacobian matrix or noise response function of the system, and effectively predict the frequency response and stability characteristics of the system to quantum fluctuations. Its advantages are high computational efficiency and good numerical stability, and it is suitable for small perturbation and linear response analysis. However, this method essentially ignores the deep coupling between nonlinearity and noise, so when dealing with large perturbations near the soliton solution, multi-soliton interference, or situations dominated by non-Gaussian noise, the model accuracy and applicability are limited.

[0006] Therefore, traditional methods have their own limitations when modeling quantum noise in microcavity solitons. While linear perturbation methods are highly efficient in small perturbation analysis, they struggle to capture the true response of the system under strong nonlinear coupling or non-steady-state evolution. Monte Carlo methods, while capable of simulating global dynamic processes, rely on the averaging of a large number of random samples, resulting in extremely low computational efficiency and high resource consumption, making it difficult to support engineering requirements for large-scale parameter sweeps or real-time analysis. Faced with the rapid expansion of microcavity soliton optical frequency comb applications in precision measurement and quantum information, a new computational framework with high efficiency and scalability is urgently needed to overcome existing modeling bottlenecks and enable rapid, accurate prediction and visual analysis of complex quantum noise behavior. Summary of the Invention

[0007] The present invention addresses the problems presented in the prior art by proposing a method for rapidly calculating quantum noise in microcavity soliton optical frequency combs. This method overcomes the bottlenecks faced by traditional Monte Carlo algorithms in simulating quantum noise in microcavity soliton optical combs, such as low computational efficiency, high memory and storage resource usage, and difficult debugging. The present invention achieves efficient and accurate modeling of quantum noise in soliton microcavities. This method linearizes the system's nonlinear time-domain evolution equation near its steady-state solution and further projects it into the eigenmode eigenspace for solution. Specifically, the linear portion is first subjected to modal decomposition. By solving the eigenmodes of this portion, the entire system is transformed into several independent modal equations, significantly reducing the system dimensionality and coupling complexity. Simultaneously, quantum noise is modeled as an equivalent perturbation source driving these modes, and its response in the eigenspace can be rapidly obtained using semi-analytical methods. Furthermore, the power spectral density of soliton timing jitter, frequency noise, and phase noise can be directly constructed without relying on extensive random simulations. By directly leveraging the statistical properties of parameters, this method significantly improves computational speed while maintaining accuracy and significantly reduces memory and storage requirements. Compared to traditional methods, this technique can improve computational efficiency by approximately a thousand times and adapt to the noise analysis needs of large-scale and complex systems, thereby achieving efficient and scalable noise assessment.

[0008] A first aspect of the present invention provides a method for rapidly calculating quantum noise in a microcavity soliton optical frequency comb, comprising the following specific steps:

[0009] Establish a dynamic stability analysis model for solitons in a microcavity system and obtain the steady-state solution; based on the obtained steady-state solution, identify the stability characteristics of the steady-state soliton solution in the perturbation space;

[0010] Construct a physical model of soliton noise in a microcavity system to evaluate the noise performance of a single soliton microcomb;

[0011] The power spectral density is calculated based on the obtained steady-state solution and the noise performance of a single soliton micro-comb; the quantum noise in the soliton optical frequency comb in the microcavity system is solved.

[0012] Furthermore, in the established dynamic stability analysis model, the evolutionary dynamics is mapped from the time domain to the eigenvalue domain, and the eigendecomposition of the system modal structure is performed.

[0013] Furthermore, for the Lugiato-Lefever equation that describes the evolution of the light field in the microcavity, the linear part is modally decomposed, and by solving the eigenmodes of this part, the entire system is converted into several independent modal equations.

[0014] Furthermore, the steps of eigendecomposition of the system modal structure include:

[0015] Solve the Jacobian matrix eigenvalues ​​and eigenvectors of the linear part of the LLE equation;

[0016] Project the system disturbance components into the eigenvector space and transform them into independent modal equations;

[0017] A fast-converging iterative algorithm is used to solve the steady-state solution offset under quantum perturbations.

[0018] Furthermore, in the noise physics model, quantum noise is modeled as an equivalent disturbance source driving the mode, and the noise response is solved by a semi-analytical method.

[0019] Furthermore, the noise sensitivity response in the noise physical model establishes a statistical mapping relationship between the noise source and the timing jitter through equivalent transformation.

[0020] Furthermore, the transfer matrix is ​​constructed using the response function of the steady-state solution to perturbations in the noise physics model.

[0021] A second aspect of the present invention provides a system for rapidly calculating quantum noise in a microcavity soliton optical frequency comb, which uses the above-mentioned method to solve the noise, including:

[0022] Linear stability analysis module, used to analyze the stability of solitons in microcavity systems and obtain steady-state solutions;

[0023] Noise physics model building module for evaluating the noise performance of single soliton microcombs;

[0024] The power spectral density calculation module is used to construct a transfer matrix based on the steady-state solution and the noise performance of the soliton microcomb. By statistically analyzing the characteristic structure of the transfer function, an equivalent noise power spectral density model is constructed to calculate the final noise.

[0025] A third aspect of the present invention provides a computer program product comprising executable instructions, which, when executed by a processor, implement the steps of the above-mentioned method for rapidly calculating quantum noise in a microcavity soliton optical frequency comb.

[0026] A fourth aspect of the present invention provides a computer device comprising a memory and a processor, wherein the memory stores a computer program, and wherein the processor implements the steps of the above-mentioned method for rapidly calculating quantum noise in a microcavity soliton optical frequency comb when executing the computer program.

[0027] Compared with the prior art, the present invention has the following beneficial technical effects:

[0028] 1. This patent achieves the eigendecomposition of the system's modal structure by mapping the evolutionary dynamics of the microcavity soliton system from the time domain to the eigenvalue domain. Specifically, for the Lugiato-Lefever equation that describes the evolution of the light field in the microcavity, its linear part is first modally decomposed, that is, by solving the eigenmodes of this part, the entire system is converted into several independent modal equations. On this basis, an iterative solution algorithm with fast convergence characteristics is designed to obtain the steady-state solution and its offset characteristics of the system under quantum perturbations, thereby significantly reducing the required time step and the total number of iterations without sacrificing calculation accuracy, effectively improving the overall solution efficiency.

[0029] 2. A method is proposed to convert the quantum noise effects in the soliton evolution process into equivalent statistical characteristics, thereby efficiently solving the power spectral density of key physical quantities. Traditional methods usually require direct simulation of multiple evolutionary trajectories of the system under quantum fluctuations, and extract the frequency drift distribution or phase shift curve through statistical analysis. The method of this patent no longer relies on a large number of repeated simulations, but is based on the system's sensitivity response to initial small perturbations, and establishes a statistical mapping relationship between the noise source and timing jitter through equivalent transformation. Specifically, this method constructs a transfer matrix based on the response function of the steady-state solution to random perturbations, and constructs an equivalent noise power spectral density model by statistically analyzing the characteristic structure of the transfer function. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 is a flow chart of a calculation method in an embodiment of the present invention;

[0031] Figure 2 Spectrum diagram and time domain waveform diagram of the soliton frequency comb in an embodiment of the present invention;

[0032] Figure 3 is the eigenvalue spectrum of the LLE steady-state solution in an embodiment of the present invention;

[0033] Figure 4 This is a comparison chart of the kinetic method and the Monte Carlo method in the embodiment of the present invention. DETAILED DESCRIPTION

[0034] Example 1

[0035] like Figure 1 As shown, the present invention proposes a method for rapidly calculating quantum noise in a microcavity soliton optical frequency comb, comprising the following specific steps:

[0036] Establish a dynamic stability analysis model for solitons in a microcavity system and obtain the steady-state solution; based on the obtained steady-state solution, identify the stability characteristics of the steady-state soliton solution in the perturbation space;

[0037] Construct a physical model of soliton noise in a microcavity system to evaluate the noise performance of a single soliton microcomb;

[0038] The power spectral density is calculated based on the obtained steady-state solution and the noise performance of a single soliton micro-comb; the quantum noise in the soliton optical frequency comb in the microcavity system is solved.

[0039] In this embodiment, the solution of the present invention is described in detail using the following specific cases:

[0040] Linear stability analysis is a classic and widely used theoretical tool in nonlinear systems, used to determine the response behavior of a system near a specific steady-state solution. When a system has a steady-state solution, we are usually concerned with whether the steady-state solution remains stable after a small perturbation, or whether it will evolve to a new state or even undergo unstable evolution. In optical microcavity systems, microcavity soliton optical frequency combs can be described by the nonlinear Schrödinger equation for damping, driving, and detuning. This equation was originally used to describe spatial self-organization phenomena, whose formation depends on the dual balance between nonlinearity and dispersion, as well as gain and loss.

[0041] In a microresonator, the Kerr nonlinear effect creates nonlinear coupling between different modes, while dispersion affects the propagation characteristics of light. The balance between gain and loss ensures the stable existence of solitons. Through four-wave mixing (FWM), optical sidebands are generated in the microresonator and undergo a self-organization process, ultimately forming soliton pulse trains. This process can be precisely described using LLE.

[0042]

[0043] Among them, t R is the round trip time of the cavity, A(T,τ s ) is the complex amplitude field in the cavity, T is the slow time, τ s For fast time, α i is the loss coefficient in the cavity, θ is the coupling loss coefficient, δ0 is the detuning between the laser and the cavity resonance frequency, L is the cavity length, β2 is the group velocity dispersion, γ is the nonlinear coefficient, and u in is the complex amplitude of the input laser.

[0044] In the ideal case without interference, the steady-state solution of the system can be obtained through linear stability analysis. The specific solution is:

[0045]

[0046] in,

[0047] In order to study the stability of the system, a small perturbation A = A0 + Δu is introduced. Due to the existence of complex conjugate properties, the system is further divided into two parts. Let Δv and Δw represent the perturbation components of the real and imaginary parts of the steady-state solution, respectively. Then Δu can be expressed as

[0048]

[0049] Substituting these expressions into equation (1), we obtain the perturbed first-order partial differential equation:

[0050]

[0051] Where Δu=f(Δu,Δu * ,A0,A * 0,α i ,θ,δ0,γ). Then the Jacobian matrix J can be given by the following formula:

[0052]

[0053] In equation (4), since the system variables contain complex components, the continuous time variable t is discretized into N points, thereby converting the original N-dimensional variable into a 2N-dimensional variable. The relevant eigenvalue equation is given by , and its corresponding characteristic equation can be expressed as:

[0054] JΦ j =λ j Φ j (6)

[0055] Among them, {λ j} is the eigenvalue, {Φj} is the right eigenvector corresponding to the eigenvalue. Therefore, the Jacobian matrix can be calculated from the steady-state solution, which can then be used to further analyze the stability of the system's soliton states. Specifically, the characteristic spectral structure of this Jacobian matrix can effectively identify the stability characteristics of the steady-state soliton solution in perturbation space. If the real parts of all eigenvalues ​​are negative, the corresponding system is linearly stable; otherwise, unstable modes exist.

[0056] The dynamics approach is also applicable to noisy LLEs, allowing the noise performance of single soliton microcombs to be evaluated. However, calculating the noise performance only makes sense when starting from a stable soliton solution, that is, after a stability analysis. The quantum noise of the soliton microcomb, i.e., the phase jitter noise, is an additive noise that can be directly added to the equation. Based on the steady-state solution A0 obtained above, in order to consider more complex processes, the single-photon noise S(t,T) is introduced into equation (4), resulting in the perturbation dynamics equation:

[0057]

[0058] The statistical characteristics of single-photon noise S(t,T) satisfy:

[0059] <S(t,T)S * (t,T)>=Dδ(t-t')δ(T-T') (8)

[0060] where δ(·) is the Dirac function, which characterizes the spatiotemporal irrelevance of the noise, and D is defined as the noise intensity coefficient.

[0061]

[0062] Where h is Planck's constant and υ0 is the center frequency of the light field.

[0063] Assume that given an independent eigenvector ε k , Δu can be expressed as

[0064]

[0065] where c k is ε k The complex coefficients of . Function and inner product theorem, we can get Used to relate the steady-state solution to the power spectral density. Project the system perturbation into any physical direction to extract the relevant physical quantities, where h x Transfer the statistical properties of the noise to the perturbation,

[0066]

[0067] Given a physical quantity Δx(T), according to formulas (10) and (11), we can get the vector h x The inner product of and perturbation Δu is:

[0068]

[0069] Since the physical quantity Δx(T) is expressed as a linear superposition of perturbation modes, the power spectral density of quantum noise can be expressed as a linear combination of perturbation terms. The power spectral density of the noise is calculated as:

[0070]

[0071] Among them D jk It can be expressed as Φ j and ε k The inner product of D jk =<Φ j ,ε k >.

[0072] The timing jitter caused by single-photon noise can be expressed as Δψ = 2πΔt c / T R , which corresponds to the jitter observed at the RF after the optical signal is detected by the photodetector. In most experimental studies, this constant is called timing jitter. Considering the Fourier transform property dΔx / dT = δx(T), the differentiation in the time domain corresponds to multiplication by iω in the frequency domain, and the power spectral density of the timing jitter can be obtained:

[0073] S δx (f) = (2πf) 2 S x (f) (14)

[0074] The above method was experimentally verified, and the results are as follows:

[0075] Figure 2 The spectral characteristics of the soliton state in the microcavity and the analytical results of the Newton solution are demonstrated. Figure 2 (a) Shows the instantaneous spectrum of a single pulse microcomb calculated using the Newton-Raphson method. Figure 2 (b) shows the corresponding instantaneous time domain image. The blue curve represents the analytical initial guess, and the red curve represents the calculated single pulse solution. The two are approximately consistent, verifying the accuracy of the calculation model.

[0076] Figure 3 is the eigenvalue spectrum calculated using the obtained single-pulse solution. Figure 3 (a) shows the distribution of eigenvalues ​​on the complex plane. In order to more accurately analyze the distribution of eigenvalues ​​in the key area, Figure 3 (b) and Figure 3 (c) shows the magnified images of different areas. Figure 3 It can be seen that all eigenvalues ​​are strictly distributed in the left half plane of the complex plane (Re(λ)<0), which verifies that the single-pulse solution is a stable equilibrium state and can be used for subsequent calculations.

[0077] Figure 4 A comparison chart of the dynamic method and the Monte Carlo method. Figure 4 The figure shows a comparison of phase noise power spectral density curves calculated using the dynamic method and the Monte Carlo method. As shown in the figure, the red curve represents the calculation result of the dynamic method, and the blue curve corresponds to the simulation result of the Monte Carlo method. The curves obtained by the two methods are highly consistent, demonstrating the good accuracy and reliability of the dynamic method in phase noise analysis. This result effectively verifies the feasibility and precision of the dynamic method compared to the Monte Carlo method.

[0078] The method proposed in this embodiment is based on the system dynamics model. It directly simulates the influence of quantum noise on soliton evolution through evolution equations, avoiding a large number of random sampling processes and fundamentally improving computational efficiency. Compared with the traditional Monte Carlo method, this dynamic method improves computational efficiency by about a thousand times while maintaining accuracy. At the same time, it significantly reduces dependence on computing resources, reduces memory usage and data storage. In addition, this method has higher repeatability and traceability, which is conducive to error detection, location and correction, greatly improving the controllability and stability of simulation work, and providing new ideas and technical means for the efficient study of quantum noise in microcavity soliton optical combs.

[0079] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited thereto. Various changes can be made within the scope of knowledge possessed by those skilled in the art without departing from the spirit of the present invention.

Claims

1. A method for rapidly calculating quantum noise in a microcavity soliton optical frequency comb, characterized in that: The specific steps include: A dynamic model describing the evolution of solitons in a microcavity system is established and a steady-state solution is obtained. Based on the obtained steady-state solution, the stability characteristics of the soliton steady state in the perturbation space are identified through linear stability analysis. Construct a physical model of a microcavity soliton system taking into account quantum noise sources to characterize the noise response characteristics of the soliton microcomb; Based on the steady-state solution and noise model, the power spectral density of the target physical quantity is calculated; the quantum noise of the soliton optical frequency comb in the microcavity system is solved.

2. The method for rapidly calculating quantum noise in a microcavity soliton optical frequency comb according to claim 1, characterized in that: The dynamic stability analysis model realizes the eigendecomposition of the system modal structure by mapping the soliton evolution process from the time domain to the eigenvalue domain.

3. The method for rapidly calculating quantum noise in a microcavity soliton optical frequency comb according to claim 2, characterized in that: The linear part of the Lugiato-Lefever equation describing the evolution of the light field in the microcavity is modally decomposed and its characteristic modes are solved. Convert the system into a set of independent modal response equations.

4. The method for rapidly calculating quantum noise in a microcavity soliton optical frequency comb according to claim 3, characterized in that: The steps for eigendecomposition of the system modal structure include: Construct and solve the Jacobian matrix corresponding to the linear part of the Lugiato-Lefever equation to obtain its eigenvalues ​​and eigenvectors; Project the system disturbance components into the eigenvector space and transform them into a set of independent modal equations; An efficient iterative algorithm is used to solve the linear response characteristics of each mode driven by quantum perturbations.

5. The method for rapidly calculating quantum noise in a microcavity soliton optical frequency comb according to claim 1, characterized in that: The noise physics model equivalently models quantum noise as an external disturbance source that drives modal evolution, and uses a semi-analytical method to solve the noise response of each mode under this disturbance.

6. The method for rapidly calculating quantum noise in a microcavity soliton optical frequency comb according to claim 5, characterized in that: In the noise physical model, the noise sensitivity response is equivalently established by establishing a statistical mapping relationship between the noise source and the timing jitter.

7. The method for rapidly calculating quantum noise in a microcavity soliton optical frequency comb according to claim 5, characterized in that: The transfer matrix of the system is constructed by the linear response function based on the steady-state solution to describe the transmission relationship between quantum noise perturbation and output response.

8. A system for rapidly calculating quantum noise in a microcavity soliton optical frequency comb, using the method according to any one of claims 1 to 7 to solve the noise, characterized in that: include: Linear stability analysis module, used to analyze the stability of solitons in microcavity systems and obtain steady-state solutions; Noise physics model building module, used to build quantum noise perturbation models based on steady-state solutions; The power spectral density calculation module is used to construct the system's transfer function, perform statistical analysis on the perturbation response of quantum noise based on this function, and obtain the equivalent quantum noise power spectral density of the soliton optical frequency comb.

9. A computer program product comprising executable instructions, characterized in that: When the instructions are executed by a processor, the steps of the method for rapidly calculating quantum noise in a microcavity soliton optical frequency comb as claimed in any one of claims 1 to 7 are implemented.

10. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method for rapidly calculating quantum noise in a microcavity soliton optical frequency comb according to any one of claims 1 to 7 are implemented.

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