Physical model parallel computing method for Rydberg atomic electric field intensity measurement system

Abstract

The invention discloses a physical model parallel computing method of a Rydberg atomic electric field intensity measurement system, belongs to the technical field of quantum measurement, and solves the problem of how to improve the computing efficiency of solving the physical model of the Rydberg atomic electric field intensity measurement system. According to the method, a physical model of the Rydberg atomic electric field intensity measurement system is established by using a Bloch equation; diagonalizing the time discrete matrix, and calculating a physical model of the Rydberg atomic electric field intensity measurement system by using a parallel algorithm; frequency sweeping is carried out on the probe light, a relational expression between the splitting size measured by the transmission spectrum and the RH frequency is established, the splitting size measured by the transmission spectrum is corrected, and the intensity of the electric field to be measured is obtained by combining an analysis and calculation formula of the transmission spectrum; according to the method, on the premise of solving the physical quantity evolution process in the Bloch equation, the calculation efficiency is improved, the physical time concept can be embodied, the convergence is higher, and one-time solving can be carried out.

Description

Technical Field

[0001] The invention belongs to the technical field of quantum measurement and relates to a parallel calculation method for a physical model of a Rydberg atom electric field strength measurement system. Background Art

[0002] Since the famous British physicist Maxwell established the electromagnetic theory in the 19th century, the study of microwave measurement has become an important topic. With the advancement of science and technology, the research on microwave measurement technology plays a very important role in modern basic science and key projects. Common devices based on traditional microwave measurement methods include thermocouples, electro-optical crystals, and metal dipole antennas, but the above devices have many shortcomings in microwave measurement. For example, the traceability chain is relatively complex, making it difficult to achieve absolute measurement; the disturbance to the measured field is large, and the measurement uncertainty is high; the geometric size is relatively large, and high resolution is difficult to achieve; the sensor bandwidth is limited, and broadband detection cannot be achieved, etc.

[0003] With the exploration of quantum science in modern times, measurement methods based on quantum effects have played an important role in the field of high-precision measurement. The advantages of measurement methods based on quantum effects over traditional measurement technologies are:

[0004] Higher sensitivity. Quantum precision measurement can detect very small changes in physical quantities. This is due to the special properties of quantum states, such as quantum superposition and quantum entanglement, which make quantum systems more sensitive to external disturbances. For example, quantum interferometers can measure displacements at the wavelength level, which is usually beyond the reach of traditional instruments.

[0005] Utilize quantum entanglement. Quantum entanglement is a unique quantum phenomenon where two or more particles can be in a state of mutual dependence. In measurements, utilizing entangled states can significantly improve the accuracy of measurements. For example, by measuring with entangled particles, the uncertainty in the measurement process can be reduced, achieving results beyond the classical limit.

[0006] Strong noise resistance. Quantum measurement technology usually has stronger noise resistance. In traditional measurements, noise often affects the accuracy of measurement results. Quantum measurement can selectively enhance signals and suppress noise through methods such as quantum interference, especially in quantum sensors, which can show high sensitivity.

[0007] Multi-dimensional measurement. Quantum measurement can obtain information on multiple physical quantities at the same time. For example, by measuring multiple quantum states, it is possible to simultaneously measure data on multiple dimensions, such as microwave field intensity, phase, and polarization direction, in one experiment.

[0008] Overcoming classical limits. Classical measurement techniques are limited by a variety of physical mechanisms (such as photon statistical noise, etc.). Quantum measurement techniques using density matrices and qubits can overcome these limits and achieve so-called "ultra-precision measurements."

[0009] At present, many measurement systems based on quantum effects have been produced, such as atomic clocks, Rydberg atoms and NV color centers. Among the many quantum measurement systems, the Rydberg atom system is considered to be the best physical platform for realizing the coupling between optical devices and light.

[0010] Compared with ordinary neutral atoms, atoms in the Rydberg state exhibit many good properties. First, the orbital radius of Rydberg atoms is large and has a long lifetime, so the quantum system composed of Rydberg atoms has a long coherence time. Second, Rydberg atoms have a large polarizability and are very sensitive to external fields, and their states can be easily controlled by external fields. Third, the energy level intervals of Rydberg atoms are small, and their transition frequencies can cover the frequency band of microwave signals. Based on the above excellent properties of Rydberg atoms, lasers can be used to control Rydberg atoms to achieve electric field detection and microwave signal reception.

[0011] The core of solving the Rydberg atomic physics model is to solve the Bloch equation. There are many solving methods in the prior art, such as direct solution, iterative solution (Runge-Kutta) and direct solution of wave function. These methods have their own characteristics. For example, direct solution is faster, but it cannot simulate the evolution process of physical quantities and can only calculate steady states; direct solution of wave functions is more complicated and difficult to analyze complex problems; commonly used iterative solution can better reflect the quantum state change process, but due to its weak convergence and long calculation time, the solution efficiency is low when considering the Doppler effect and multi-level coupling. Summary of the invention

[0012] The technical solution of the present invention is used to solve the problem of how to improve the calculation efficiency of solving the physical model of the Rydberg atom electric field strength measurement system.

[0013] A parallel calculation method for the physical model of the Rydberg atom electric field strength measurement system.

[0014] The present invention solves the above technical problems through the following technical solutions:

[0015] The present invention provides a parallel calculation method for a physical model of a Rydberg atom electric field strength measurement system, comprising the following steps:

[0016] Step 1, determine the atom type, energy level structure, frequency and Rabi frequency of the laser and the electric field to be measured, size of the alkali atom gas chamber, and atomic density used in the Rydberg atomic electric field strength measurement system, and use the Bloch equation to establish a physical model of the Rydberg atomic electric field strength measurement system;

[0017] Step 2, diagonalizing the time discrete matrix, and using a parallel algorithm to calculate the physical model of the Rydberg atomic electric field strength measurement system;

[0018] Step 3: Sweep the detection light to establish a relationship between the splitting size measured by the transmission spectrum and the Rabi frequency, correct the splitting size measured by the transmission spectrum, and then obtain the electric field strength to be measured by combining the analysis and calculation formula of the transmission spectrum.

[0019] Furthermore, the method for establishing the physical model of the Rydberg atomic electric field strength measurement system using the Bloch equation described in step 1 is specifically as follows:

[0020] The analysis and calculation of the transmission spectrum is as follows:

[0021]

[0022] Among them, E MW is the electric field strength, μ MW is the transition dipole moment, is Planck's constant, Ω MW is the Rabbi frequency;

[0023] By calculating the medium responsivity, the imaginary part of the relative dielectric constant of the alkali atom gas chamber medium is calculated, and then the Rabi frequency is obtained. The calculation formula is as follows:

[0024]

[0025] ε r =1+χ (4)

[0026] Among them, χ is the medium responsivity, ε0 ​​is the vacuum dielectric constant, and ε r is the relative dielectric constant of the medium, I is the transmitted light intensity, I0 is the incident light intensity, L is the length of the alkali atom gas cell, λ p To detect the wavelength of light, Im[] is the operation of taking the imaginary part;

[0027] The polarizability P is related to the transition of the outermost electrons of the atom. The calculation formula of the polarizability is as follows:

[0028]

[0029] Where N is the number of atoms, which is determined by the atomic density and volume in the alkali atom gas chamber; w 21 is the frequency of electron transition caused by the detection light; ρ 21 is the atomic transition probability, which is an element of the density matrix in the Bloch equation; μ 21 To detect the dipole moment of electrons that transition between two energy levels caused by light;

[0030] The expression of the Bloch equation for a four-level system is as follows:

[0031]

[0032] Among them, ρ is the density matrix, The elements on the main diagonal of the density matrix represent the probability of an electron being at one of the four energy levels, and the elements on the off-diagonal represent the probability of an electron transition between two energy levels. i is an imaginary unit. is the reduced Planck constant, [] is the commutative operator, H is the Hamiltonian, Ω p ,Ω c ,Ω f are the Rabi frequencies of the probe light, coupled light and the electric field to be measured; Δ p , Δ c , Δ f are the detuning of the detection light, coupled light and measured electric field relative to the energy level transition frequency, L(ρ) is the decoherence term, Γ i (i=1,2,3,4) is the atomic decay rate, γ ij (i,j=1,2,3,4)=(Γ i +Γ j ) / 2,ρ ij (i,j=1,2,3,4) are the elements in the density matrix.

[0033] Furthermore, the method of performing diagonal processing on the time discrete matrix in step 2 and using a parallel algorithm to calculate the physical model of the Rydberg atomic electric field strength measurement system is specifically as follows:

[0034] First, establish the following differential equation:

[0035]

[0036] Among them, M and K are the coefficient matrices in the differential equation, is the differential of the quantity to be solved with respect to time, U(t) is the quantity to be solved, f(t) is an arbitrary time-dependent function, U(0) is the value of the quantity to be solved at time zero, and U0 is the given initial condition;

[0037] The derivative of the quantity to be solved U with respect to time is transformed into an algebraic form, and the quantity to be solved U at each moment is integrated in the form of a matrix, so that the differential equation of formula (7) becomes the following form:

[0038]

[0039] Among them, B1 and B2 are of order N t The Toeplitz matrix, N t is the number of time steps, A is the coefficient matrix, u is the quantity to be solved, and b is a constant;

[0040] The Bloch equation can be transformed into the following formula:

[0041]

[0042] in, It is a 16×1 column vector expanded row by row by ρ. The expression of [G] is as follows:

[0043]

[0044] Among them, I is the fourth-order identity matrix, D is obtained by the decoherence term, and the expression of D is as follows:

[0045]

[0046] The initial conditions for the Bloch equation are:

[0047]

[0048] Move all the terms of the Bloch equation deformation formula (9) to the left and compare them with formula (7) to obtain the following mapping relationship:

[0049]

[0050] Among them, I x The order is N x The identity matrix of order, N x Represents the number of elements in the density matrix;

[0051] Then the equation (8) is transformed into:

[0052]

[0053] Where b = (b1 T ,0,...,0) T , ρ(0) is the initial condition of the density matrix, Δt1 is the first time step;

[0054] Multiply both sides of formula (13) by get:

[0055]

[0056] Let B2 in formula (14) -1 B1 is the matrix B, and the matrix B is diagonalized; first, the matrix B is diagonalizable, which requires that the time step is non-uniform, that is:

[0057] Δt n =Δt1τ n-1 , n≥1 (15)

[0058] Among them, Δt n is the non-uniform time step, τ is the non-uniform step factor;

[0059] Matrix B1 is used to describe the time difference process, and matrix B2 is used to describe the variable approximation process. The difference approximation expression of the equation of formula (9) is as follows:

[0060]

[0061] The corresponding matrices B1 and B2 are in the following form:

[0062]

[0063] B=B2 -1 B1 (18)

[0064] Among them, the value of θ is 0.5 or 1;

[0065] The matrix B can be diagonalized as follows:

[0066]

[0067] in,

[0068]

[0069] According to the operation rules of direct product, the result of diagonalizing matrix B is brought back to formula (13) to obtain:

[0070]

[0071] Finally we get:

[0072]

[0073] Since the matrix B is diagonalized, are all triangular matrices, Can perform block inversion;

[0074] Final solution The specific calculation is divided into the following three steps:

[0075] Step (a):

[0076]

[0077] Step (b):

[0078]

[0079] Step (c):

[0080]

[0081] At this point, the value of the density matrix at each time point is calculated at one time.

[0082] Furthermore, the relationship between the splitting size and the Rabi frequency measured by the transmission spectrum described in step 3 is as follows:

[0083]

[0084] Where Δf is the splitting size measured by transmission spectrum, λ c , p are the wavelengths of the coupled light and the probe light, respectively.

[0085] Furthermore, the formula for correcting the splitting size measured by the transmission spectrum in step 3 is as follows:

[0086]

[0087] Where Δf s is the splitting size measured by the corrected transmission spectrum, and Δ is the detuning amount between the frequency of the electric field to be measured and the transition frequency between the two energy levels coupled by the electric field to be measured.

[0088] The present invention also provides an electronic device, comprising a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the above-mentioned parallel calculation method of the physical model of the Rydberg atomic electric field strength measurement system, and the processor is configured to execute the program stored in the memory.

[0089] The present invention also provides a storage medium on which a computer program is stored. When the computer program is run by a processor, the steps of the parallel calculation method for the physical model of the Rydberg atomic electric field strength measurement system are executed.

[0090] The advantages of the present invention are:

[0091] The present invention establishes a physical model of a Rydberg atomic electric field strength measurement system by using the Bloch equation; performs diagonalization processing on a time discrete matrix and uses a parallel algorithm to calculate the physical model of the Rydberg atomic electric field strength measurement system; performs frequency sweeping on a detection light to establish a relationship between the splitting size measured by a transmission spectrum and a Rabi frequency, corrects the splitting size measured by the transmission spectrum, and then obtains the size of the electric field strength to be measured by combining the analytical calculation formula of the transmission spectrum; the method of the present invention can improve the calculation efficiency on the premise of solving the evolution process of physical quantities in the Bloch equation; compared with direct solution, the method of the present invention can reflect the concept of physical time; compared with iterative solution (Runge-Kutta), the method of the present invention has stronger convergence, can perform one-time solution, has higher calculation efficiency, and is helpful for studying transient and complex calculation problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 It is a flow chart of the parallel calculation method of the physical model of the Rydberg atom electric field strength measurement system of the present invention;

[0093] Figure 2 This is the experimental principle diagram of the Rydberg atomic electric field strength measurement system;

[0094] Figure 3 It is a comparison chart of three methods of solving the steady state of the Bloch equation: direct solution, iterative solution and parallel calculation method;

[0095] Figure 4 It is a comparison chart of the two methods of solving the transient state of the Bloch equation: iterative solution and parallel calculation method;

[0096] Figure 5 This is a comparison chart between the simulation results using parallel computing methods and the experimental results in existing literature. DETAILED DESCRIPTION

[0097] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in combination with the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0098] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and specific embodiments:

[0099] Embodiment 1

[0100] like Figure 1 As shown, a parallel calculation method for a physical model of a Rydberg atom electric field strength measurement system according to an embodiment of the present invention comprises the following steps:

[0101] 1. Establish the physical model of the Rydberg atomic electric field strength measurement system

[0102] According to the experimental conditions, the parameters are calculated and set to physically model the Rydberg atomic electric field strength measurement system. For the experimental device, the atomic type, energy level structure, frequency and Rabi frequency of the laser and the field to be measured, size of the alkali atom gas chamber, and atomic density used in the measurement system are determined, and the Bloch equation is used to establish the physical model of the measurement system.

[0103] like Figure 2The Rydberg atom electric field strength measurement system shown in the figure usually uses two laser beams (probe light and coupling light) to transmit in reverse through the alkali atom gas chamber to excite the atoms to the Rydberg state, and then couple with the electric field to be measured, and use a photodetector to receive the transmitted light of the probe light. By analyzing and calculating the transmission spectrum, the traceable measurement of the electric field strength is achieved.

[0104] The analysis and calculation formula for the transmission spectrum is as follows:

[0105]

[0106] Among them, E MW is the electric field strength, μ MW is the transition dipole moment, is Planck's constant, Ω MW is the Rabi frequency.

[0107] From formula (1), it can be obtained that when the transition coupling energy level caused by the electromagnetic field to be measured is determined, the electric field strength is linearly related to the Rabi frequency, and the Rabi frequency can be directly obtained from the laser transmission spectrum.

[0108] When physically modeling the Rydberg atomic electric field strength measurement system, the alkali atom gas chamber is regarded as a uniform medium. By calculating the medium responsivity, the imaginary part of the medium relative dielectric constant can be calculated, and then the Rabi frequency can be obtained. The calculation formula is as follows:

[0109]

[0110] ε r =1+χ (4)

[0111] Among them, χ is the medium responsivity, ε0 ​​is the vacuum dielectric constant, and ε r is the relative dielectric constant of the medium, I is the transmitted light intensity, I0 is the incident light intensity, L is the length of the alkali metal atom gas cell, λ p To detect the wavelength of light, IM[] is the imaginary part operation.

[0112] The polarizability P is related to the transition of the outermost electrons of the atom. The calculation formula of the polarizability is as follows:

[0113]

[0114] Where N is the number of atoms, which is determined by the atomic density and volume in the alkali atom gas chamber; w 21 is the frequency of electron transition caused by the detection light; ρ 21 is the atomic transition probability, which is an element of the density matrix in the Bloch equation; μ 21 To detect the dipole moment of an electron that transitions between two energy levels caused by light.

[0115] The Bloch equation is often used to solve the problem of interaction between light and the object under study. The Bloch equation is also used to describe the interaction between Rydberg atoms and external fields. Taking the four-level system as an example, its expression is as follows:

[0116]

[0117] Among them, ρ is the density matrix, The elements on the main diagonal of the density matrix represent the probability of an electron being at one of the four energy levels, and the elements on the off-diagonal represent the probability of an electron transition between two energy levels. i is an imaginary unit. is the reduced Planck constant, [] is the commutative operator, H is the Hamiltonian,

[0118] Ω p ,Ω c ,Ω f are the Rabi frequencies of the probe light, coupled light and the electric field to be measured; Δ p , Δ c , Δ f are the detuning of the detection light, coupled light and measured electric field relative to the energy level transition frequency, L(ρ) is the decoherence term,

[0119] Γ i (i=1,2,3,4) is the atomic decay rate, γ ij (i,j=1,2,3,4)=(Γ i +Γ j ) / 2,ρ ij (i,j=1,2,3,4) are the elements in the density matrix.

[0120] 2. Use parallel algorithms to calculate the physical model of the Rydberg atomic electric field strength measurement system

[0121] The idea of ​​the parallel algorithm is to transform the problem of solving time-related differential equations into the problem of solving algebraic matrix equations, and then simplify the solution by using the matrix characteristics; when using the parallel algorithm to calculate the physical model of the Rydberg atomic electric field strength measurement system, the time discrete matrix B is diagonalized to achieve the purpose of fast solution.

[0122] First, establish the following differential equation:

[0123]

[0124] Among them, M and K are the coefficient matrices in the differential equation, is the differential of the quantity to be solved with respect to time, U(t) is the quantity to be solved, f(t) is an arbitrary time-dependent function, U(0) is the value of the quantity to be solved at time zero, and U0 is the given initial condition;

[0125] The derivative of the quantity to be solved U with respect to time is converted into an algebraic form, and the quantity to be solved U at each moment (same as U(t) above) is integrated in the form of a matrix, so that the differential equation of formula (7) becomes the following form:

[0126]

[0127] Among them, B1 and B2 are of order N t The Toeplitz matrix, N t is the number of time steps, A is the coefficient matrix, u is the quantity to be solved, and b is a constant.

[0128] Compared with the differential equation form of formula (7), formula (8) is simpler and can be solved at one time.

[0129] The Bloch equation can be transformed into the following formula:

[0130]

[0131] in, It is a 16×1 column vector expanded row by row by ρ. The expression of [G] is as follows:

[0132]

[0133] Among them, I is the fourth-order unit matrix, D is obtained by the attenuation term, and the expression of D is as follows:

[0134]

[0135] The initial conditions for the Bloch equation are:

[0136]

[0137] The physical meaning of formula (11) is that the electron is in the ground state at time zero.

[0138] Move all the terms of the Bloch equation deformation formula (9) to the left and compare them with formula (7) to obtain the following mapping relationship:

[0139]

[0140] Among them, I x The order is N x The identity matrix of order, N x Represents the number of elements in the density matrix.

[0141] Then the equation (8) is transformed into:

[0142]

[0143] Where b = (b1T ,0,...,0) T , The values ​​and meanings of θ are shown in Table 1 below, ρ(0) is the initial condition of the density matrix, and Δt1 is the first time step.

[0144] Multiply both sides of formula (13) by get:

[0145]

[0146] From formula (14), we can see The first term is the expansion of the time discrete form in the density matrix, and the second term is the expansion of the mutual constraint relationship of the elements in the density matrix at different time points. This combination allows the equation to be restored to the original system of equations after expansion according to the matrix multiplication rule. This is also the basic principle of the method of the present invention that can be split into matrix form. Let B2 in the above formula -1 B1 is the B matrix, which is a time-discrete matrix. In order to make this one-time solution faster, the B matrix is ​​diagonalized. First, it is necessary to ensure that the matrix B is diagonalizable, which requires that the time step is non-uniform, that is:

[0147] Δt n =Δt1τ n-1 , n≥1 (15)

[0148] Among them, Δt n is the non-uniform time step, and τ is the non-uniform step factor.

[0149] In the previous description, only the equation change process is explained, and the specific forms of B1 and B2 are not described. In fact, matrix B1 is used to describe the time difference process, and matrix B2 is used to describe the variable approximation process. The difference approximation expression of the equation of formula (9) is as follows:

[0150]

[0151] The corresponding matrices B1 and B2 are in the following form:

[0152]

[0153] B=B2 -1 B1 (18)

[0154] Different θ represent different approximation methods, as shown in Table 1 below. Among the approximation methods, the forward Euler method is an explicit method with a limited stable region and low calculation accuracy; the backward Euler method is an implicit method with stability for any time step, suitable for solving rigid and oscillating problems, and it also has a numerical damping effect, which can ensure that the numerical solution is smoother and more stable, which is reflected in the subsequent comparison with the Runge Kutta method; the trapezoidal approximation has similar properties to the second-order Runge Kutta method to a certain extent, so the results obtained are relatively close. In the method of the present invention, only the θ value is taken as 0.5 or 1 for approximation.

[0155] Table 1. θ values ​​and approximation methods

[0156] θ Approximate method 0 Forward Euler method 0.5 Equivalent to the trapezoidal approximation 1 Backward Euler method

[0157] The matrix B can be diagonalized as follows:

[0158]

[0159] in,

[0160]

[0161] According to the operation rules of direct product, the result of diagonalizing matrix B is brought back to formula (13) to obtain:

[0162]

[0163] Finally we get:

[0164]

[0165] Since the matrix B is diagonalized, are all triangular matrices, The inversion can be performed in blocks.

[0166] Final solution The specific calculation can be divided into the following three steps:

[0167] Step (a):

[0168]

[0169] Step (b):

[0170]

[0171] Step (c):

[0172]

[0173] At this point, the value of the density matrix at each time point can be calculated at one time. The calculation error is positively correlated with the condition number of the eigenvector matrix V of the matrix B. Its fundamental source is the approximate method, the non-uniform step size factor τ and the number of time steps N. t The calculation error of the setting has no effect on the electric field strength calculation (AT splitting size) and will not be discussed here.

[0174] 3. Calculate the strength of the electric field to be measured

[0175] The detection light is swept to establish the relationship between the splitting size measured by the transmission spectrum and the Rabi frequency, and the splitting size measured by the transmission spectrum is corrected. Then, the electric field strength to be measured is obtained by combining the analysis calculation formula of the transmission spectrum (Formula (1) in step 1).

[0176] The relationship between the splitting size and the Rabi frequency measured by the transmission spectrum is as follows:

[0177]

[0178] Where Δf is the splitting size measured by transmission spectrum, λ c , p are the wavelengths of the coupled light and the probe light, respectively.

[0179] The formula for correcting the splitting size measured by the transmission spectrum is as follows:

[0180]

[0181] Where Δf s is the splitting size measured by the corrected transmission spectrum, and Δ is the detuning amount between the frequency of the electric field to be measured and the transition frequency between the two energy levels coupled by the electric field to be measured.

[0182] Test verification

[0183] In order to verify the effectiveness of the method of the present invention, the calculation results of the parallel algorithm are compared with the calculation results of the direct solution method and the iterative method to verify the advantages of the method of the present invention, and combined with the experimental results, the correctness of the method of the present invention is verified.

[0184] Verification 1: Use direct solution method, parallel method and iterative method to calculate 1001 detuned steady-state results respectively, compare the calculation time of parallel algorithm and iterative method, and verify the efficiency of parallel algorithm. In the simulation, the parallel algorithm and iterative method take the result of 10us of physical time as the steady-state result and compare it with the steady-state result obtained by the direct method. The parallel method sets the time step number N tThe step growth factor τ is 18, the step growth factor τ is 1.16, and θ is set to 1. The iterative method uses the second-order Runge-Kutta method, and the number of iterations is set to 4000. The Doppler effect is not considered in the calculations. Other key parameter settings are shown in Table 2. The comparison results are shown in Figure 3 .

[0185] In the simulation, parallel computing takes 1.15 seconds and iterative computing takes 74.6 seconds. The computing speed of the parallel method is about 50 times that of the iterative calculation.

[0186] Table 2 Key parameters of steady-state simulation

[0187] symbol <![CDATA[Ω c ]]> <![CDATA[Ω p ]]> <![CDATA[Ω f ]]> <![CDATA[Δ c Scope]]> <![CDATA[Δ p ]]> <![CDATA[Δ f ]]> Numeric <![CDATA[40×10 6 ]]> <![CDATA[20×10 6 ]]> <![CDATA[40×10 6 ]]> <![CDATA[[-70,70]×10 6 ]]> 0 0

[0188] Verification 2: Compare the transient results calculated by the iterative method and the parallel method.

[0189] In the simulation, a three-level system is used for verification, the simulation physical time is set to 0.8us, and the second-order Runge-Kutta method is used to compare with two different approximation methods in the parallel method. The important setting parameters are shown in Table 3.

[0190] Table 3 Key parameters of transient simulation

[0191] symbol <![CDATA[Ω c ]]> <![CDATA[Ω p ]]> <![CDATA[Δ p ]]> <![CDATA[Δ c ]]> Numeric <![CDATA[2π×10 7 ]]> <![CDATA[2π×1.2×10 6 ]]> 0 0

[0192] from Figure 4 The results show that the calculation results of the parallel algorithm are basically consistent with those of the Runge-Kutta method. The waveform of the parallel algorithm using the trapezoidal approximation method is closer to the calculation results of the second-order Runge-Kutta method in a short time, while the parallel algorithm using the Euler approximation has a numerical damping effect, converges faster, and has a smoother waveform.

[0193] Verification 3: Comparison with experimental results from existing literature

[0194] The paper "Simultaneous use of Cs and Rb Rydberg atoms for dipole moment assessment and RF electric field measurements via electromagnetically induced transmission" uses rubidium 85 atoms to conduct experiments, using 5S 1 / 2 -5P 3 / 2 -61D 5 / 2 -62P 3 / 2The four energy levels are used as the ground state, excited state, first Rydberg state, and second Rydberg state of the measurement system. The wavelength of the detection light is 780.24nm, and the Rabi frequency is 50MHz; the wavelength of the coupling light is 480.04nm, and the Rabi frequency is 50MHz. The power of the signal generator is -11dBm, and the electric field strength can be calculated by the following formula.

[0195]

[0196] Where x is the distance from the signal source to the atomic gas cell, which is set to 31.8 cm. The calculated electric field strength at the gas cell position is 1.29 V / m, 61D 5 / 2 -62P 3 / 2 The transition dipole moment between the two energy levels is 3055.04ea0, where a0 is the Bohr radius.

[0197] The Rabi frequency can be calculated to be 50.40 MHz by formula (1). In the experiment, the probe light is swept, and the transmission spectrum splitting size and the Rabi frequency satisfy formula (27). The splitting size of the transmission spectrum is 31.01 MHz. It is also considered that the detuning between the signal generator and the three- and four-level transition frequency is Δ = (9.222-9.2269) GHz, which will cause the two peaks in the transmission spectrum to be different and will also affect the splitting size. The transmission spectrum splitting size can be corrected using formula (28), and the final calculated result is 31.39 MHz, which is in line with Figure 5 The experimental results in .

[0198] Embodiment 2

[0199] An electronic device includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the parallel calculation method of the physical model of the Rydberg atomic electric field strength measurement system in Example 1, and the processor is configured to execute the program stored in the memory.

[0200] Embodiment 3

[0201] A storage medium stores a computer program, which, when executed by a processor, executes the steps of the parallel calculation method for the physical model of the Rydberg atom electric field strength measurement system in the first embodiment.

[0202] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A parallel calculation method for the physical model of the Rydberg atomic electric field strength measurement system, characterized in that: The following steps are involved: Step 1, determine the atom type, energy level structure, frequency and Rabi frequency of the laser and the electric field to be measured, size of the alkali atom gas chamber, and atomic density used in the Rydberg atomic electric field strength measurement system, and use the Bloch equation to establish a physical model of the Rydberg atomic electric field strength measurement system; Step 2, diagonalizing the time discrete matrix, and using a parallel algorithm to calculate the physical model of the Rydberg atomic electric field strength measurement system; Step 3: Sweep the detection light to establish a relationship between the splitting size measured by the transmission spectrum and the Rabi frequency, correct the splitting size measured by the transmission spectrum, and then obtain the electric field strength to be measured by combining the analysis and calculation formula of the transmission spectrum.

2. The parallel calculation method of the physical model of the Rydberg atomic electric field strength measurement system according to claim 1, characterized in that: The method for establishing the physical model of the Rydberg atomic electric field strength measurement system using the Bloch equation described in step 1 is as follows: The analysis and calculation of the transmission spectrum is as follows: Among them, E MW is the electric field strength, μ MW is the transition dipole moment, is Planck's constant, Ω MW is the Rabbi frequency; By calculating the medium responsivity, the imaginary part of the relative dielectric constant of the alkali atom gas chamber medium is calculated, and then the Rabi frequency is obtained. The calculation formula is as follows: e r =1+x (4) Among them, χ is the medium responsivity, ε0 ​​is the vacuum dielectric constant, ε r is the relative dielectric constant of the medium, I is the transmitted light intensity, I0 is the incident light intensity, L is the length of the alkali atom gas cell, λ p To detect the wavelength of light, IM[] is the operation of taking the imaginary part; The polarizability P is related to the transition of the outermost electrons of the atom. The calculation formula of the polarizability is as follows: Where N is the number of atoms, which is determined by the atomic density and volume in the alkali atom gas chamber; w 21 is the frequency of electron transition caused by the detection light; ρ 21 is the atomic transition probability, which is an element of the density matrix in the Bloch equation; μ 21 To detect the dipole moment of electrons that transition between two energy levels caused by light; The expression of the Bloch equation for a four-level system is as follows: Among them, ρ is the density matrix, The elements on the main diagonal of the density matrix represent the probability of an electron being at one of the four energy levels, and the elements on the off-diagonal represent the probability of an electron transition between two energy levels. i is an imaginary unit. is Planck's constant, [] is the commutative operator, H is the Hamiltonian, Ω p ,Ω c ,Ω f are the Rabi frequencies of the probe light, coupled light and the electric field to be measured; Δ p , Δ c , Δ f are the detuning of the detection light, coupled light and measured electric field relative to the energy level transition frequency, L(ρ) is the decoherence term, Γ i (i=1,2,3,4) is the atomic decay rate, γ ij (i,j=1,2,3,4)=(Γ i +Γ j ) / 2,ρ ij (i,j=1,2,3,4) are the elements in the density matrix.

3. The parallel calculation method of the physical model of the Rydberg atomic electric field strength measurement system according to claim 2, characterized in that: The method described in step 2 for diagonalizing the time discrete matrix and using a parallel algorithm to calculate the physical model of the Rydberg atomic electric field strength measurement system is as follows: First, establish the following differential equation: Among them, M and K are the coefficient matrices in the differential equation, is the differential of the quantity to be solved with respect to time, U(t) is the quantity to be solved, f(t) is an arbitrary time-dependent function, U(0) is the value of the quantity to be solved at time zero, and U0 is the given initial condition; The derivative of the quantity to be solved U with respect to time is converted into an algebraic form, and the quantity to be solved U at each moment is integrated in the form of a matrix, so that the differential equation of formula (7) becomes the following form: Among them, B1 and B2 are of order N t The Toeplitz matrix, N t is the number of time steps, A is the coefficient matrix, u is the quantity to be solved, and b is a constant; The Bloch equation can be transformed into the following formula: in, It is a 16×1 column vector expanded row by row by ρ. The expression of [G] is as follows: Among them, I is the fourth-order identity matrix, D is obtained by the decoherence term, and the expression of D is as follows: The initial conditions for the Bloch equation are: Move all the terms of the Bloch equation deformation formula (9) to the left and compare them with formula (7) to obtain the following mapping relationship: Among them, I x The order is N x The identity matrix of order, N x Represents the number of elements in the density matrix; Then the equation (8) is transformed into: Where b = (b1 T ,0,...,0) T , is the initial condition of the density matrix, Δt1 is the first time step; Multiply both sides of formula (13) by get: Let formula (14) For matrix B, diagonalize matrix B; first, ensure that matrix B is diagonalizable, which requires that the time step is non-uniform, that is: Δt n =Δt1τ n-1 ,n≥1 (15) Among them, Δt n is the non-uniform time step, τ is the non-uniform step factor; Matrix B1 is used to describe the time difference process, and matrix B2 is used to describe the variable approximation process. The difference approximation expression of the equation of formula (9) is as follows: The corresponding matrices B1 and B2 are in the following form: <h2 style=";text-align:left;direction:ltr">B=B2<h2 style=";text-align:left;direction:ltr"> -1 <h2 style=";text-align:left;direction:ltr"> B1 (18) Among them, the value of θ is 0.5 or 1; The matrix B is diagonalized as follows: in, According to the operation rules of direct product, the result of diagonalizing matrix B is brought back to formula (13) to obtain: Finally we get: Since the matrix B is diagonalized, are all triangular matrices, Can perform block inversion; Final solution The specific calculation is divided into the following three steps: Step (a): Step (b): Step (c): At this point, the value of the density matrix at each time point is calculated at one time.

4. The parallel calculation method for the physical model of the Rydberg atomic electric field strength measurement system according to claim 3, characterized in that: The relationship between the cleavage size and the Rabi frequency measured by the transmission spectrum described in step 3 is as follows: Where Δf is the splitting size measured by transmission spectrum, λ c , p are the wavelengths of the coupled light and the probe light, respectively.

5. The parallel calculation method of the physical model of the Rydberg atomic electric field strength measurement system according to claim 4, characterized in that: The formula for correcting the cleavage size in the transmission spectrum measurement described in step 3 is as follows: Where Δf s is the splitting size measured by the corrected transmission spectrum, and Δ is the detuning amount between the frequency of the electric field to be measured and the transition frequency between the two energy levels coupled by the electric field to be measured.

6. An electronic device, comprising a memory and a processor, characterized in that: The memory is used to store a program that supports the processor to execute the parallel calculation method of the physical model of the Rydberg atomic electric field strength measurement system as described in any one of claims 1 to 5, and the processor is configured to execute the program stored in the memory.

7. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the parallel calculation method of the physical model of the Rydberg atom electric field strength measurement system according to any one of claims 1 to 5 are executed.

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