Method for fast calculation of quantum noise in microcavity soliton optical frequency comb

Abstract

The present application relates to the technical field of quantum noise measurement, in particular to a method for quickly calculating quantum noise in microcavity soliton optical frequency comb. It comprises establishing a dynamic stability analysis model of soliton in microcavity system and solving the steady-state solution; identifying the stability characteristics of the steady-state soliton solution in the perturbation space based on the solved steady-state solution; constructing a noise physical model of soliton in the microcavity system for evaluating the noise performance of a single soliton microcomb; calculating the power spectral density based on the solved steady-state solution and the noise performance of a single soliton microcomb; and solving the quantum noise in the soliton optical frequency comb in the microcavity system. The present application models the timing jitter mechanism caused by quantum noise, and maps the time-domain nonlinear coupling system to the modal characteristic space. The solution in the characteristic domain not only improves the calculation accuracy, but also enhances the numerical stability and fast convergence ability of the algorithm.

Description

Technical Field

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

[0002] Microcavity-based soliton micro-optical frequency combs have shown transformative potential in cutting-edge fields such as precision metrology, broadband spectroscopy, high-speed optical communication, and quantum information processing in recent years due to their high coherence, wide spectral coverage, and on-chip integration capabilities. However, the stability and coherence of soliton microcombs are susceptible to interference from various intrinsic and external noise sources, including thermal refraction noise, pump source technical noise, and quantum noise originating from quantum fluctuations. Among these, quantum noise, as a fundamental physical limit, cannot be completely suppressed by engineering means and inevitably introduces phase perturbations, amplitude fluctuations, and soliton timing jitter. These quantum fluctuations fundamentally affect the coherence, phase stability, and frequency uncertainty of the frequency comb line, becoming a key bottleneck restricting the performance of high-precision applications. Especially in systems such as ultrastable microwave photon sources and atomic optical clocks, accurately assessing the frequency drift and jitter caused by quantum noise is crucial.

[0003] In microcavity systems, especially strongly nonlinear and high-Q cavity systems such as soliton micro-optical frequency combs, noise analysis is crucial for understanding their coherence, stability, and spectral purity. Traditional research on quantum noise in microcavities primarily relies on two classical methods: the Monte Carlo method and the linearization perturbation method.

[0004] The first method, the Monte Carlo method, introduces a random source term into the Lugiato-Lefever equation (LLE) or its extended form to simulate random perturbations such as vacuum fluctuations or technical noise. By statistically averaging the evolution trajectories under hundreds to thousands of independent noise realizations, key indicators 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. Since each simulation corresponds to only one noise realization, it is impossible to directly obtain analytical expressions of the statistics, requiring repeated independent integrations. Each integration involves high-resolution time-domain calculations, which place extremely high demands on time step size and nonlinear convergence, resulting in extremely high overall computational overhead. Furthermore, memory usage increases rapidly with the simulation dimension, leading to significant data storage pressure and severely limiting its practicality in multi-parameter scanning, large-scale system analysis, and real-time modeling.

[0005] Another approach, the linearized perturbation method, is based on the steady-state solution of the system's solitons. It treats noise as a small perturbation around the steady state and establishes a set of perturbation equations for the system under a linear approximation. This method directly obtains the influence of noise on different modes by constructing and solving the system's Jacobian matrix or noise response function, effectively predicting the system's frequency response and stability characteristics to quantum fluctuations. Its advantages lie in high computational efficiency, good numerical stability, and applicability to small perturbations and linear response analysis. However, this method inherently ignores the deep coupling between nonlinearity and noise, thus limiting the model's accuracy and applicability when dealing with large perturbations near the soliton solution, multi-soliton interference, or cases dominated by non-Gaussian noise.

[0006] Therefore, traditional methods have limitations in modeling quantum noise in microcavity solitons. While linear perturbation methods are efficient in small perturbation analysis, they struggle to capture the true response of the system under strong nonlinear coupling or unsteady evolution. Monte Carlo methods, although capable of simulating global dynamic processes, rely on averaging large numbers of random samples, resulting in extremely low computational efficiency and high resource consumption, making them unsuitable for large-scale parameter scanning or real-time analysis. Given the rapid expansion of microcavity soliton optical frequency comb applications in precision measurement and quantum information, there is an urgent need for a novel computational framework that maintains physical accuracy while possessing high efficiency and scalability. This framework should overcome existing modeling bottlenecks and enable rapid, accurate prediction and visualization analysis of complex quantum noise behavior. Summary of the Invention

[0007] The purpose of this invention is to address the problems existing in the background technology by proposing a method for rapidly calculating quantum noise in microcavity soliton optical frequency combs, overcoming a series of bottlenecks faced by traditional Monte Carlo algorithms in simulating quantum noise in microcavity soliton optical combs, such as low computational efficiency, large memory and storage resource consumption, and difficult debugging. This invention achieves efficient and accurate modeling of quantum noise in soliton microcavities. The method linearizes the nonlinear time-domain evolution equations of the system near the steady-state solution and further projects them onto the eigenmode feature space for solution. Specifically, the linear part is first modally decomposed; that is, by solving the eigenmodes of this part, the entire system is transformed into several independent modal equations, significantly reducing the system dimensionality and coupling complexity. Simultaneously, quantum noise is modeled as the equivalent perturbation source driving these modes, and its response in the feature space can be quickly obtained through semi-analytical methods. Furthermore, the power spectral density of soliton timing jitter, frequency noise, and phase noise can be directly constructed without relying on a large number of stochastic simulations. This method, by directly utilizing the statistical properties of parameters, significantly improves computational speed while maintaining computational accuracy, and substantially reduces memory and storage requirements. Compared to traditional methods, this technique can improve computational efficiency by approximately one thousand times and adapt to the noise analysis needs of large-scale, complex systems, thereby achieving efficient and scalable noise assessment.

[0008] The first aspect of this invention provides a method for rapidly calculating quantum noise in a microcavity soliton optical frequency comb, comprising the following specific steps: A dynamic stability analysis model of solitons in a microcavity system is established, and the steady-state solution is obtained. Based on the obtained steady-state solution, the stability characteristics of the steady-state soliton solution in the perturbation space are identified. A noise physics model of solitons in a microcavity system was constructed to evaluate the noise performance of a single soliton microcomb. Power spectral density is calculated based on the obtained steady-state solution and the noise performance of a single soliton microcomb; the noise of quanta in the soliton optical frequency comb in the microcavity system is solved.

[0009] Furthermore, in the established dynamic stability analysis model, the evolutionary dynamics are mapped from the time domain to the eigenvalue domain to perform eigenvalue decomposition of the system's modal structure.

[0010] Furthermore, for the Lugiato-Lefever equation describing the evolution of the optical field in the microcavity, the linear part is decomposed into modes. By solving the characteristic modes of this part, the entire system is transformed into several independent mode equations.

[0011] Furthermore, the steps for intrinsic decomposition of the system's modal structure include: Find the eigenvalues ​​and eigenvectors of the Jacobian matrix for the linear part of the LLE equation; The system disturbance components are projected onto the eigenvector space and transformed into independent modal equations; The offset of the steady-state solution under quantum perturbation is solved using a fast convergent iterative algorithm.

[0012] Furthermore, in the noise physics model, quantum noise is modeled as an equivalent perturbation source of the driving mode, and the noise response is solved by a semi-analytical method.

[0013] Furthermore, in the noise physical model, the noise sensitivity response is established through equivalent transformation to establish a statistical mapping relationship between the noise source and timing jitter.

[0014] Furthermore, the transition matrix is ​​constructed in the noise physical model using the response function of the steady-state solution to the perturbation.

[0015] A second aspect of the present invention provides a system for rapidly calculating quantum noise in a microcavity soliton optical frequency comb, wherein the noise is solved using the method described above, including: The linear stability analysis module is used to analyze the stability of solitons in a microcavity system and obtain the steady-state solution. A noise physics model building module is used to evaluate the noise performance of a single soliton microcomb; 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.

[0016] A third aspect of the present invention provides a computer program product comprising executable instructions that, when executed by a processor, implement the steps of the above-described method for rapidly calculating quantum noise in a microcavity soliton optical frequency comb.

[0017] A fourth aspect of the present invention provides a computer device including a memory and a processor, the memory storing a computer program, characterized in that the processor executes the computer program to implement the steps of the above-described method for rapidly calculating quantum noise in a microcavity soliton optical frequency comb.

[0018] Compared with the prior art, the present invention has the following beneficial technical effects: 1. This invention achieves eigenvalue decomposition of the modal structure of a microcavity soliton system by mapping the evolution dynamics of the system from the time domain to the eigenvalue domain. Specifically, for the Lugiato-Lefever equation describing the evolution of the optical field in the microcavity, its linear part is first modally decomposed, that is, by solving the eigenmodes of this part, the entire system is transformed into several independent modal equations. Based on this, an iterative solution algorithm with fast convergence characteristics is designed to obtain the steady-state solution and its offset characteristics under quantum perturbation, thereby significantly reducing the required time step and the total number of iterations without sacrificing computational accuracy, effectively improving the overall solution efficiency.

[0019] 2. This paper proposes a method to transform the influence of quantum noise in the soliton evolution process into equivalent statistical properties, thereby efficiently solving the power spectral density of key physical quantities. Traditional methods typically require direct simulation of the system's evolution trajectory under quantum fluctuations multiple times, extracting frequency drift distributions or phase shift curves through statistical analysis. The method of this invention no longer relies on a large number of repetitive simulations, but instead establishes a statistical mapping relationship between the noise source and timing jitter based on the system's sensitivity response to initial small perturbations through equivalent transformation. Specifically, this method constructs a transfer matrix based on the steady-state solution's response function to random perturbations, and constructs an equivalent noise power spectral density model by statistically analyzing the characteristic structure of this transfer function. Attached Figure Description

[0020] Figure 1 This is a flowchart of the calculation method in an embodiment of the present invention; Figure 2 The image shows the spectrum and time-domain waveform of the soliton frequency comb in this embodiment of the invention. Figure 3 This is the eigenvalue spectrum of the LLE steady-state solution in this embodiment of the invention; Figure 4 This is a comparison diagram of the dynamic method and the Monte Carlo method in the embodiments of the present invention. Detailed Implementation

[0021] Example 1 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: A dynamic stability analysis model of solitons in a microcavity system is established, and the steady-state solution is obtained. Based on the obtained steady-state solution, the stability characteristics of the steady-state soliton solution in the perturbation space are identified. A noise physics model of solitons in a microcavity system was constructed to evaluate the noise performance of a single soliton microcomb. Power spectral density is calculated based on the obtained steady-state solution and the noise performance of a single soliton microcomb; the noise of quanta in the soliton optical frequency comb in the microcavity system is solved.

[0022] In this embodiment, the following specific examples are used to describe the solution of the present invention in detail: Linear stability analysis is a classic and widely used theoretical tool in nonlinear systems to determine the system's response behavior near a specific steady-state solution. When a system has a steady-state solution, we are usually concerned with whether the steady state can remain stable after being subjected to small perturbations, or whether it will evolve to a new state or even undergo unstable evolution. In optical microcavity systems, microcavity soliton frequency combs can be described by the nonlinear Schrödinger equation of damping, driving, and detuning. This equation was originally used to describe spatial self-organization phenomena, the formation of which depends on a dual balance between nonlinearity and dispersion, as well as gain and loss.

[0023] In microresonators, the Kerr nonlinearity causes 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 a four-wave mixing process, optical sidebands in the microresonator are generated and undergo a self-organization process, ultimately forming a soliton pulse sequence. This process can be accurately described using LLE (Light Lesion Emission).

[0024] (1) in, The round-trip time of the cavity. The complex amplitude field within the cavity, For slow time, To save time, The loss coefficient within the cavity, This is the coupling loss coefficient. This represents the detuning between the laser frequency and the cavity resonant frequency. For cavity length, For group velocity dispersion, These are nonlinear coefficients. The complex amplitude of the input laser.

[0025] In the ideal case without disturbance terms, the steady-state solution of the system can be obtained through linear stability analysis, specifically as follows: (2) in, .

[0026] To study the stability of the system, a small perturbation is introduced. Due to the existence of complex conjugation properties, the system is further divided into two parts, let and Let represent the perturbation components of the real and imaginary parts of the steady-state solution, respectively. It can be represented as (3) Substituting these representations into equation (1), we obtain the first-order partial differential equation of the perturbation as follows: (4) in, Then the Jacobian matrix J can be given by the following formula: (5)

[0027] In equation (4), since the system variable contains complex components, the continuous-time variable t is discretized into N points, thus transforming the original N-dimensional variable into a 2N-dimensional variable. The relevant eigenvalue equation is given, and its corresponding characteristic equation can be expressed as: (6) in,{ } represents the eigenvalues, { Let} be the right eigenvector corresponding to the eigenvalues. Therefore, the Jacobian matrix can be obtained from the steady-state solution, and then the stability of the soliton states of the system can be further analyzed. Specifically, the eigenspectral structure of this Jacobian matrix can be used to effectively identify the stability characteristics of the steady-state soliton solutions in the perturbation space. If all eigenvalues ​​have negative real parts, the corresponding system has linear stability; otherwise, there are unstable modes.

[0028] The kinetic method is also applicable to noisy LLEs, thus allowing for the evaluation of the noise performance of a single soliton microcomb. However, calculating the noise performance is only meaningful when starting from a stable soliton solution, i.e., after stability analysis. The quantum noise of the soliton microcomb, i.e., phase jitter noise, is an additive noise that can be directly added to the equation. Based on the steady-state solution A0 obtained above, single-photon noise is introduced into equation (4) to consider a more complex process. The perturbation dynamics equations can be obtained as follows: (7) Single-photon noise The statistical properties satisfy: (8) in Let be the Dirac function, characterizing the spatiotemporal uncorrelation of noise. D Defined as the noise intensity coefficient.

[0029] (9) in It is Planck's constant. It is the center frequency of the light field.

[0030] Suppose we have an independent eigenvector. It can Represented as (10) in for The complex coefficients. Using the Krönecker function and the inner product theorem, we can obtain... This is used to relate the steady-state solution to the power spectral density. The system perturbation is projected onto arbitrary physical directions to extract relevant physical quantities, where... The statistical characteristics of the noise are transferred to the disturbance. (11) Given a physical quantity According to formulas (10) and (11), the vector can be obtained. and perturbation The inner product is: (12) because Physical quantities are represented as a linear superposition of perturbation modes. The power spectral density of quantum noise can be represented as a linear combination of perturbation terms. Therefore, the power spectral density of the noise is calculated as follows: (13) in It can be represented as and The inner product, i.e. .

[0031] Timing jitter caused by single-photon noise can be expressed as This corresponds to the jitter observed at the radio frequency after the optical signal is detected by the photodetector. In most experimental studies, this constant is called timing jitter. Considering the properties of the Fourier transform... The time domain derivative corresponds to multiplying by iω in the frequency domain, which yields the power spectral density of the timing jitter: (14) The above method was experimentally verified, and the results are as follows: Figure 2 The spectral characteristics of soliton states in a microcavity and the analytical results of finding Newton's solution are presented. 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 in close agreement, which verifies the accuracy of the calculation model.

[0032] Figure 3 It is the eigenvalue spectrum calculated using the obtained single-pulse solution. Figure 3 (a) illustrates the distribution of eigenvalues ​​in the complex plane. To more accurately analyze the distribution of eigenvalues ​​in key regions, Figure 3 (b) and Figure 3 (c) provides enlarged views of different regions. From Figure 3 It can be seen that all eigenvalues ​​are strictly distributed in the left half of the complex plane (Re(λ)<0), which verifies that the single-pulse solution is a stable equilibrium state that can be used for subsequent calculations.

[0033] Figure 4 This is a comparison diagram of the dynamic method and the Monte Carlo method. Figure 4 The figure shows a comparison of the phase noise power spectral density curves calculated using the dynamic method and the Monte Carlo method. 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, indicating that the dynamic method has good accuracy and reliability in phase noise analysis. This result effectively verifies the feasibility and accuracy of the dynamic method compared to the Monte Carlo method.

[0034] The method proposed in this embodiment is based on a system dynamics model and directly simulates the impact of quantum noise on soliton evolution through evolutionary 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, and significantly reduces dependence on computing resources, memory usage, and data storage. In addition, this method has higher repeatability and traceability, which is beneficial for error checking, location, and correction, greatly improving the controllability and stability of simulation work, and providing a new approach and technical means for efficiently studying quantum noise in microcavity soliton optical combs.

[0035] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, 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 the following: A dynamic model describing the evolutionary behavior 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. The dynamic stability analysis model achieves eigenvalue decomposition of the system's modal structure by mapping the soliton evolution process from the time domain to the eigendomain. For the Lugiato-Lefever equation describing the evolution of the optical field in the microcavity, its linear part is modally decomposed, and by solving its eigenmodes, the system is transformed into a set of mutually independent modal response equations. A physical model of a microcavity soliton system considering quantum noise sources is constructed to characterize the noise response characteristics of soliton microcombs; 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. The noise physics model treats quantum noise as an external perturbation source driving mode evolution and uses a semi-analytical method to solve the noise response of each mode under the perturbation.

2. The method for rapidly calculating quantum noise in a microcavity soliton optical frequency comb according to claim 1, characterized in that, The steps for intrinsic decomposition of the system's modal structure include: Construct and solve the Jacobian matrix corresponding to the linear part of the Lugiato-Lefever equation, and obtain its eigenvalues ​​and eigenvectors; The system disturbance components are projected onto the eigenvector space and transformed into a set of independent modal equations. The offset of the steady-state solution under quantum perturbation is solved using a fast convergent iterative algorithm.

3. The method for rapidly calculating quantum noise in a microcavity soliton optical frequency comb according to claim 1, characterized in that, In the noise physical model, the noise sensitivity response is established by equivalently establishing a statistical mapping relationship between the noise source and the timing jitter.

4. The method for rapidly calculating quantum noise in a microcavity soliton optical frequency comb according to claim 1, characterized in that, The system's transition matrix is ​​constructed based on the linear response function of the steady-state solution to describe the transmission relationship between quantum noise perturbation and output response.

5. A system for rapidly calculating quantum noise in a microcavity soliton optical frequency comb, wherein the noise is solved using the method described in any one of claims 1-4, characterized in that, include: The linear stability analysis module is used to analyze the stability of solitons in a microcavity system and obtain the steady-state solution. The noise physics model building module is used to construct quantum noise perturbation models based on steady-state solutions; The power spectral density calculation module is used to construct the system's transfer matrix based on the steady-state solution and the noise performance of the soliton microcomb. Based on this function, the perturbation response of quantum noise is statistically analyzed to obtain the equivalent quantum noise power spectral density of the soliton optical frequency comb.

6. A computer program product comprising executable instructions, characterized in that, When the instruction is executed by the processor, it implements the steps of the method for fast computation of quantum noise in microcavity soliton optical frequency comb as described in any one of claims 1-4.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method for rapidly calculating quantum noise in a microcavity soliton optical frequency comb as described in any one of claims 1-4.

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