Alternating magnetic field measurement method based on diamond nv color center phase-locked detection
By using the diamond NV color center phase-locked detection method, alternating magnetic field signals are measured through a continuous adiabatic evolution process. This solves the problems of spectral leakage and low-frequency limitation in existing technologies, and enables accurate measurement of high-frequency magnetic fields and improves noise immunity.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- TAIYUAN UNIVERSITY OF TECHNOLOGY
- Filing Date
- 2026-03-24
- Publication Date
- 2026-07-24
AI Technical Summary
Existing alternating magnetic field measurement methods based on spin echo sequences and dynamic decoupling sequences are suitable for low-frequency bands, but suffer from spectral leakage, which limits the measurement frequency range and noise filtering capability.
A phase-locked detection method based on diamond NV color centers is adopted to measure the in-phase and quadrature components of alternating magnetic field signals through a continuous adiabatic evolution process. A signal modulation function in the form of a trigonometric function is used to avoid spectral leakage and achieve high-frequency magnetic field measurement.
It enables the measurement of higher frequency magnetic fields, improves measurement sensitivity and noise immunity, simplifies data processing, and enhances frequency selectivity.
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Figure CN121933994B_ABST
Abstract
Description
Technical Field
[0001] This invention provides a method for measuring alternating magnetic fields based on diamond NV color center phase-locked detection, belonging to the field of alternating magnetic field measurement technology. Background Technology
[0002] A diamond NV center is a point defect in a diamond crystal. Under certain conditions, its electron spin can be considered as a qubit (with two states, 0 and 1). The quantum state of the NV center's electron spin can be controlled by applying microwave pulses. Under the influence of an external magnetic field, the energy difference between the 0 and 1 states changes. This change in energy difference affects the dynamical phase accumulated during the evolution of the diamond NV center's electron spin quantum state. Therefore, by detecting the dynamical phase accumulated during the evolution of the diamond NV center's electron spin quantum state, the magnetic field strength can be measured. The measurement system used is as follows: Figure 1 As shown.
[0003] Currently, alternating magnetic fields are mainly detected based on spin echo sequences and dynamic decoupling sequences. Specifically, magnetic signal intensity information is obtained by measuring the dynamic phase accumulated by the spin quantum state of the diamond NV center electrons under the action of an alternating magnetic signal. Since the dynamic phase accumulated by the spin quantum state of the diamond NV center electrons under the action of an alternating magnetic field that changes periodically with time cancels each other out within one cycle, it is necessary to apply spin echoes or dynamic decoupling pulses to periodically flip the spin quantum state of the NV center electrons in order to ensure that the dynamic phase is continuously accumulated during the measurement process.
[0004] Current alternating magnetic field detection methods based on spin echo sequences and dynamical decoupling sequences obtain magnetic signal intensity information by measuring the dynamical phase accumulated by the electron spin quantum states in NV center (NV color center) under the influence of an alternating magnetic signal. Therefore, the frequency of the applied pulse must match the frequency of the alternating magnetic field to be measured. However, realizing a microwave π pulse in an NV color center system requires tens of nanoseconds, limiting the spin echo and dynamical decoupling-based alternating magnetic field measurement method to measuring alternating magnetic fields in the 1kHz-10MHz frequency band. Figure 2 As shown, if the microwave pulse in part (a) is too wide (requiring a long implementation time), the signal modulation function y(t) corresponding to the dynamic decoupling sequence in part (b) cannot be considered an ideal square wave, thus affecting the detection results of the alternating signal s(t) in part (c) and the magnetic signal (modulated signal) in part (d). Therefore, the current alternating magnetic field detection method based on spin echo sequences and dynamic decoupling sequences is only suitable for situations where the period of the signal to be measured is much larger than the time required to realize the microwave π pulse.
[0005] Furthermore, current magnetic field measurement methods based on spin echo sequences and dynamic decoupling sequences suffer from severe spectral leakage. This leakage arises because the modulation function generated by pulse control is in the form of a bipolar square wave, such as... Figure 3 As shown, the spectrum of this type of modulation function contains both fundamental and odd harmonic components. This means that when measuring alternating magnetic fields using spin echo sequences and dynamically decoupled sequences, the measurement results depend not only on the amplitude of the measured signal at the fundamental frequency but also on noise at the odd harmonic frequencies. Therefore, the spectral leakage problem caused by pulse driving limits the noise filtering capability of the measurement scheme. Summary of the Invention
[0006] To address the technical problems existing in the background art, the present invention provides a method for measuring alternating magnetic fields based on diamond NV color center phase-locked detection, comprising the following measurement steps:
[0007] Step 1: Use diamond NV color centers as detectors to extract target signals from ambient noise;
[0008] Step 2: Perform phase-locked detection on the extracted target signal based on diamond NV color centers;
[0009] Step 3: Measure the in-phase component I of the target signal through two consecutive adiabatic evolution processes. sig ;
[0010] Step 4: Measure the orthogonal component Q of the target signal through two consecutive adiabatic evolution processes. sig ;
[0011] Step 5: Based on the in-phase component I obtained from the measured target signal sig and orthogonal components Q sig The amplitude S0 and initial phase φ of the target signal are calculated.
[0012] The specific method for step one is as follows:
[0013] The expression for a target signal with frequency ω is defined as S(t) = S0cos(ωt + φ), where the measured parameter S0 is the amplitude of the target signal and the measured parameter φ is the initial phase of the target signal.
[0014] The target signal is defined as being submerged in noise N(t), and the expression for the actual signal detected by the detector is M(t) = N(t) + S(t);
[0015] Define the in-phase component I from the actual signal M(t). sig and orthogonal components Q sig The expressions are as follows:
[0016] ;
[0017] Where T is the measurement time.
[0018] The specific method for step two is as follows:
[0019] Define an NV color center in diamond, and select the electron spin ground state of the NV color center. state and The state as a quantum probe and state;
[0020] Under the combined influence of a microwave control field and an external magnetic field, the Hamiltonian of the quantum probe after the rotating wave approximation is:
[0021] ;
[0022] Where, σ x σ y σ z For standard Pauli operators, control Hamiltonian This indicates that a rabbi's frequency is The detuning amount is Phase is The control field;
[0023] Signal Hamiltonian This represents the coupling between the quantum probe and the actual signal M(t) containing noise;
[0024] By controlling the Hamiltonian The driven adiabatic evolution process enables quantum phase-locked detection, including:
[0025] Define the control Hamiltonian The instantaneous eigenstates have the following forms:
[0026] ;
[0027] Where θ(t) is the mixing angle, satisfying , ;
[0028] and The corresponding eigenenergys are respectively and ;
[0029] The initial state is the eigenstate. The system evolves along this eigenstate, and the quantum state changes over time according to the following rules:
[0030] ;
[0031] In the formula, the effective vector potential that generates the geometric phase is... The eigenstate is always equal to zero. Only dynamic phases accumulate during the evolution process. ; t represents time, and t0 represents the moment when the evolution begins;
[0032] In the time-varying basis vectors Within the defined rotational frame, the system's time evolution operator For the unit operator, the expression is:
[0033] ;
[0034] In naked basis vectors The expression for the system's time evolution operator, i.e., the formula for calculating the scene transformation, is as follows:
[0035] ;
[0036] in, for Hermitian conjugate operators; unitary operators describing picture transformations The expression is:
[0037] ;
[0038] Due to the signal Hamiltonian H sig The existence of (t) is given by time-varying basis vectors. In the defined rotational framework, the system's time evolution operator is no longer the unit operator, and its form becomes:
[0039] ;
[0040] Among them, H rot (t', t0) is the Hamiltonian in the rotating frame, expressed as:
[0041] ;
[0042] Quantum signal modulation and filtering are achieved by subjecting the quantum probe to two consecutive adiabatic evolution processes. The first adiabatic process occurs in the time interval [0, ... Within this time interval, the second adiabatic process occurs. Within [T], satisfy =T / 2.
[0043] The specific method for step three is as follows:
[0044] In the first adiabatic process, the Rabi frequency and detuning of the microwave control field are set as follows:
[0045] ;
[0046] ;
[0047] Where A is the maximum value of the Rabi frequency of the microwave control field;
[0048] In this case, the mixing angle θ(t) = ωt;
[0049] Using a first-order Magnus expansion, The approximate evolution operator in the time-rotation framework is represented as:
[0050] ;
[0051] Based on the picture transformation calculation formula and the approximate evolution operator expression in the rotating frame, the first adiabatic process in the bare state basis vector is obtained. The evolution operator is expressed as:
[0052] ;
[0053] in ;
[0054] In the second adiabatic evolution process, the Rabi frequency and detuning of the microwave control field are set as follows:
[0055] ;
[0056] ;
[0057] In this case, the mixed angle ;
[0058] Depend on The evolution process to T is represented by the following evolution operator:
[0059] ;
[0060] The second adiabatic process occurs in the bare state basis vectors The expression for the evolution operator is:
[0061] ;
[0062] in, ;
[0063] Therefore, in naked basis vectors The following expression describes the evolution operator for the two consecutive adiabatic evolution processes described above:
[0064] ;
[0065] in ;
[0066] This indicates that if the quantum probe is initialized to a superposition state... + ) / After undergoing the two consecutive adiabatic evolution processes described above, the superposition state will obtain The relative phase will Dividing by the evolution time T yields the in-phase component I. sig .
[0067] The specific method for step four is as follows:
[0068] In the first adiabatic evolution process, the Rabi frequency and detuning of the microwave control field are set as follows:
[0069] ;
[0070] ;
[0071] In this case, the mixed angle ;
[0072] Using a first-order Magnus expansion, The approximate evolution operator in the time-rotation framework is represented as:
[0073] ;
[0074] Based on the picture transformation calculation formula and the approximate evolution operator expression in the rotating frame, the first adiabatic process in the bare state basis vector is obtained. The evolution operator is expressed as:
[0075] ;
[0076] in ;
[0077] In the second adiabatic evolution process, the Rabi frequency and detuning of the microwave control field are set as follows:
[0078] ;
[0079] ;
[0080] In this case, the mixed angle ;
[0081] Depend on The evolution process to T is represented by the following evolution operator within the rotation framework:
[0082] ;
[0083] The second adiabatic process occurs in the bare state basis vectors The expression for the evolution operator is:
[0084] ;
[0085] in ;
[0086] Therefore, in naked basis vectors The following expression describes the evolution operator for the two consecutive adiabatic evolution processes described above:
[0087] ;
[0088] in ;
[0089] This indicates that if the initial state of the quantum probe is After undergoing the two consecutive adiabatic evolution processes described above, the final state is: After detecting two consecutive adiabatic evolutions The population of the state is used to measure the orthogonal component Q. sig .
[0090] The specific method for step five is as follows:
[0091] Calculate the amplitude S0 and initial phase φ of the target signal, respectively, where:
[0092] The formula for calculating amplitude S0 is:
[0093] ;
[0094] The formula for calculating the initial phase φ is:
[0095] .
[0096] The advantages of this invention compared to existing technologies are as follows: This invention provides an alternating magnetic field measurement method based on diamond NV center phase-locked detection. It primarily achieves signal modulation by continuously controlling the adiabatic evolution of the electron spin quantum state of the diamond NV center. Due to the use of pulse-free continuous control, this invention can realize a signal modulation function in the form of a trigonometric function. Compared to the bipolar square wave modulation function generated by pulse control in traditional measurement schemes, the trigonometric function modulation function fundamentally solves the spectral leakage problem. The measurement result depends only on the amplitude and phase of the measured signal at a frequency equal to the modulation frequency, and is largely unaffected by other frequency components in the background noise. Simultaneously, the trigonometric function modulation function facilitates the extraction of amplitude and phase information of the target signal from the measurement result, avoiding complex data post-processing. Furthermore, compared to pulse control, continuous control can achieve higher modulation frequencies under the same control field strength, thus enabling the measurement of higher frequency magnetic fields. Moreover, quantum adiabatic evolution has strong robustness to experimental errors such as timing errors and control field strength errors, which helps to extend the coherence time of the diamond NV center electron spin quantum state, thereby improving measurement sensitivity. Attached Figure Description
[0097] The present invention will be further described below with reference to the accompanying drawings:
[0098] Figure 1 This is a schematic diagram of the current diamond NV color center magnetic field measurement system;
[0099] Figure 2 This is a schematic diagram of the current principle of alternating magnetic signal measurement based on dynamic decoupling pulses;
[0100] Figure 3 The spectrum diagram of the current bipolar square wave modulation function;
[0101] Figure 4 This is a schematic diagram of the magnetic signal phase-locked detection method based on diamond NV color centers according to the present invention. Detailed Implementation
[0102] like Figure 4 As shown, this invention proposes an alternating magnetic field measurement method based on diamond NV color center phase-locked detection to solve the problems of pulse manipulation speed limiting the frequency range of measurable magnetic fields and spectral leakage. This method can extract the amplitude and phase information of the alternating signal under test submerged in background noise with high precision and has good frequency selectivity and noise immunity.
[0103] This invention aims to extract target signals from extreme environmental noise. First, the target signal with a known frequency ω is defined as S(t) = S0cos(ωt + φ), where the amplitude S0 and the initial phase φ are the parameters to be measured. The target signal is submerged in noise N(t), so the signal actually detected by the detector is M(t) = N(t) + S(t).
[0104] Define the in-phase component I from the actual signal M(t). sig and orthogonal components Q sig for:
[0105] (1);
[0106] Where T is the measurement time.
[0107] By measuring the in-phase component I sig and orthogonal components Q sig The amplitude and initial phase information of the target signal can then be obtained, where:
[0108] The formula for calculating amplitude is:
[0109] ;
[0110] The formula for calculating the initial phase is:
[0111] .
[0112] Consider an NV color center in diamond, and select the electron spin ground state of the NV color center. state and The state as a quantum probe and The quantum probe is a two-level quantum system. This invention measures the alternating magnetic field by measuring the phase generated by the two-level system during its controlled evolution.
[0113] Under the combined influence of a microwave control field and an external magnetic field, the Hamiltonian of the quantum probe after the rotating wave approximation is:
[0114] (2);
[0115] Where, σ x σ y σ z For standard Pauli operators, control Hamiltonian This indicates that a rabbi's frequency is The detuning amount is Phase is The control field;
[0116] Signal Hamiltonian This represents the coupling between the quantum probe and the actual signal M(t) containing noise;
[0117] Assuming the actual signal M(t) is much weaker than the control field, in this case... It can be considered as a perturbation term; the objective of this invention is to control the Hamiltonian. Driven adiabatic evolution to achieve quantum phase-locked detection, the process includes:
[0118] Controlling Hamiltonian The instantaneous eigenstates have the following forms:
[0119] (3);
[0120] Where θ(t) is the mixing angle, satisfying , ;
[0121] and The corresponding eigenenergys are respectively and ;
[0122] According to the quantum adiabatic theorem, if the Hamiltonian is controlled... If the change is slow enough, then the initial state is an eigenstate. The system will evolve along this eigenstate, and the quantum state changes over time according to the following rules:
[0123] (4);
[0124] In the above equation, the effective vector potential that generates the geometric phase is... The eigenstate is always equal to zero; therefore, the eigenstate is... Only dynamic phases accumulate during the evolution process. ; t represents time, and t0 represents the moment when the evolution begins;
[0125] Therefore, in the time-varying basis vectors Within the defined rotational frame, the system's time evolution operator For the unit operator, the expression is:
[0126] (5);
[0127] In naked basis vectors The expression for the system's time evolution operator, i.e., the formula for calculating the scene transformation, is as follows:
[0128] (6);
[0129] in, for Hermitian conjugate operators; unitary operators describing picture transformations The expression is:
[0130] (7).
[0131] Due to the signal Hamiltonian H sig The existence of (t) is given by time-varying basis vectors. In the defined rotational framework, the system's time evolution operator is no longer the unit operator, and its form becomes:
[0132] (8);
[0133] Among them, H rot (t', t0) is the Hamiltonian in the rotating frame, expressed as:
[0134] (9);
[0135] Quantum signal modulation and filtering can be achieved by subjecting the quantum probe to two consecutive adiabatic evolution processes; the first adiabatic process occurs in the time interval [0, ... Within this time interval, the second adiabatic process occurs. Within [T], where =T / 2.
[0136] In formula (1) I sig Measurements are taken through two consecutive adiabatic evolution processes, specifically including:
[0137] In the first adiabatic process, the Rabi frequency and detuning of the microwave control field are set as follows:
[0138] ;
[0139] ;
[0140] In this case, the mixing angle θ(t) = ωt; the value of parameter A is much greater than the highest frequency ω present in the noise N(t). max .
[0141] Using a first-order Magnus expansion, The approximate evolution operator in the time-rotation framework is represented as:
[0142] (10);
[0143] It is worth noting that the off-diagonal terms in equation (9) do not contribute to the evolution operator in equation (10), because when At that time, these terms oscillate rapidly, and their effects are averaged out over the course of evolution.
[0144] Based on the scene transformation calculation formula (6) and the approximate evolution operator expression (10) in the rotating frame, the first adiabatic process in the bare state basis vector is obtained. The evolution operator is expressed as:
[0145] (11);
[0146] in .
[0147] In the second adiabatic evolution process, the Rabi frequency and detuning of the microwave control field are set as follows:
[0148] ;
[0149] ;
[0150] In this case, the mixed angle ;
[0151] Depend on The evolution process to T is represented by the following evolution operator:
[0152] (12);
[0153] The second adiabatic process occurs in the bare state basis vectors The expression for the evolution operator is:
[0154] (13);
[0155] in, .
[0156] Therefore, in naked basis vectors The following expression describes the evolution operator for the two consecutive adiabatic evolution processes described above:
[0157] (14);
[0158] in .
[0159] This indicates that if the quantum probe is initialized to a superposition state... + ) / And after undergoing the above two consecutive adiabatic evolution processes, the superposition state will obtain The relative phase will Dividing by the evolution time T yields the in-phase component I in formula (1). sig .
[0160] The orthogonal component Q in formula (1)sig It is also measured through two consecutive adiabatic evolution processes, specifically including:
[0161] In the first adiabatic evolution process, the Rabi frequency and detuning of the microwave control field are set as follows:
[0162] ;
[0163] ;
[0164] In this case, the mixed angle ;
[0165] Using a first-order Magnus expansion, The approximate evolution operator in the time-rotation framework is represented as:
[0166] (15);
[0167] Based on the scene transformation calculation formula (6) and the approximate evolution operator expression (15) in the rotating frame, the first adiabatic process in the bare state basis vector is obtained. The evolution operator is expressed as:
[0168] (16);
[0169] in .
[0170] In the second adiabatic evolution process, the Rabi frequency and detuning of the microwave control field are set as follows:
[0171] ;
[0172] ;
[0173] In this case, the mixed angle ;
[0174] Depend on The evolution process to T is represented by the following evolution operator within the rotation framework:
[0175] (17);
[0176] The second adiabatic process occurs in the bare state basis vectors The expression for the evolution operator is:
[0177] (18);
[0178] in .
[0179] Therefore, in naked basis vectors The following expression describes the evolution operator for the two consecutive adiabatic evolution processes described above:
[0180] (19);
[0181] in .
[0182] This indicates that if the initial state of the quantum probe is After undergoing the two consecutive adiabatic evolution processes described above, the final state is: After detecting two consecutive adiabatic evolutions The population of the state is used to measure the orthogonal component Q. sig .
[0183] The in-phase component I can be obtained by performing the above measurement process. sig and orthogonal components Q sig This allows us to obtain the amplitude and phase information of the alternating signal under test. In practical operation, two quantum probes can be used to simultaneously measure the in-phase component I. sig and orthogonal components Q sig Alternatively, a quantum probe can be used to probe the in-phase component I. sig The orthogonal component Q is executed after the measurement process ends on an integer number of cycles. sig The measurement process is the same as the result obtained by measuring with two sensors simultaneously. In the above general measurement scheme, only the detection process consisting of two continuous adiabatic evolutions is considered. In practical applications, microwave control pulses can be repeated periodically to accumulate more relative phase, thereby realizing the detection of weak signals.
[0184] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for measuring alternating magnetic fields based on diamond NV color center phase-locked detection, characterized in that: The measurement steps include the following: Step 1: Using diamond NV color centers as detectors to extract target signals from ambient noise. The specific method is as follows: The expression for a target signal with frequency ω is defined as S(t) = S0cos(ωt + φ), where the measured parameter S0 is the amplitude of the target signal and the measured parameter φ is the initial phase of the target signal. The target signal is defined as being submerged in noise N(t), and the expression for the actual signal detected by the detector is M(t) = N(t) + S(t); Define the in-phase component I from the actual signal M(t). sig and orthogonal components Q sig The expressions are as follows: ; Where T is the measurement time; Step 2: Perform phase-locked detection on the extracted target signal based on diamond NV color centers; Step 3: Measure the in-phase component I of the target signal through two consecutive adiabatic evolution processes. sig The specific method is as follows: In the first adiabatic process, the Rabi frequency and detuning of the microwave control field are set as follows: ; ; Where A is the maximum value of the Rabi frequency of the microwave control field; In this case, the mixing angle θ(t) = ωt; Using a first-order Magnus expansion, The approximate evolution operator in the time-rotation framework is represented as: ; Based on the picture transformation calculation formula and the approximate evolution operator expression in the rotating frame, the first adiabatic process in the bare state basis vector is obtained. The evolution operator is expressed as: ; in ; In the second adiabatic evolution process, the Rabi frequency and detuning of the microwave control field are set as follows: ; ; In this case, the mixed angle ; Depend on The evolution process to T is represented by the following evolution operator: ; The second adiabatic process occurs in the bare state basis vectors The expression for the evolution operator is: ; in, ; Therefore, in naked basis vectors The following expression describes the evolution operator for the two consecutive adiabatic evolution processes described above: ; in ; This indicates that if the quantum probe is initialized to a superposition state... + ) / After undergoing the two consecutive adiabatic evolution processes described above, the superposition state will obtain The relative phase will Dividing by the evolution time T yields the in-phase component I. sig ; Step 4: Measure the orthogonal component Q of the target signal through two consecutive adiabatic evolution processes. sig The specific method is as follows: In the first adiabatic evolution process, the Rabi frequency and detuning of the microwave control field are set as follows: ; ; In this case, the mixed angle ; Using a first-order Magnus expansion, The approximate evolution operator in the time-rotation frame is represented as: ; Based on the picture transformation calculation formula and the approximate evolution operator expression in the rotating frame, the first adiabatic process in the bare state basis vector is obtained. The evolution operator is expressed as: ; in ; In the second adiabatic evolution process, the Rabi frequency and detuning of the microwave control field are set as follows: ; ; In this case, the mixed angle ; Depend on The evolution process to T is represented by the following evolution operator within the rotation framework: ; The second adiabatic process occurs in the bare state basis vectors The expression for the evolution operator is: ; in ; Therefore, in naked basis vectors The following expression describes the evolution operator for the two consecutive adiabatic evolution processes described above: ; in ; This indicates that if the initial state of the quantum probe is After undergoing the two consecutive adiabatic evolution processes described above, the final state is: After detecting two consecutive adiabatic evolutions The population of the state is used to measure the orthogonal component Q. sig ; Step 5: Based on the in-phase component I obtained from the measured target signal sig and orthogonal components Q sig The amplitude S0 and initial phase φ of the target signal are calculated.
2. The alternating magnetic field measurement method based on diamond NV color center phase-locked detection according to claim 1, characterized in that: The specific method for step two is as follows: Define an NV color center in diamond, and select the electron spin ground state of the NV color center. state and The state as a quantum probe and state; Under the combined influence of a microwave control field and an external magnetic field, the Hamiltonian of the quantum probe after the rotating wave approximation is: ; Where, σ x σ y σ z For standard Pauli operators, control Hamiltonian This indicates that a rabbi's frequency is The detuning amount is Phase is The control field; Signal Hamiltonian This represents the coupling between the quantum probe and the actual signal M(t) containing noise; By controlling the Hamiltonian The driven adiabatic evolution process enables quantum phase-locked detection, including: Define the control Hamiltonian The instantaneous eigenstates have the following forms: ; Where θ(t) is the mixing angle, satisfying , ; and The corresponding eigenenergys are respectively and ; The initial state is the eigenstate. The system evolves along this eigenstate, and the quantum state changes over time according to the following rules: ; In the formula, the effective vector potential that generates the geometric phase is... The eigenstate is always equal to zero. Only dynamic phases accumulate during the evolution process. ; t represents time, and t0 represents the moment when the evolution begins; In the time-varying basis vectors Within the defined rotational frame, the system's time evolution operator For the unit operator, the expression is: ; In naked basis vectors The expression for the system's time evolution operator, i.e., the formula for calculating the scene transformation, is as follows: ; in, for Hermitian conjugate operators; unitary operators describing picture transformations The expression is: ; Due to the signal Hamiltonian H sig The existence of (t) is given by time-varying basis vectors. In the defined rotational framework, the system's time evolution operator is no longer the unit operator, and its form becomes: ; Among them, H rot (t', t0) is the Hamiltonian in the rotating frame, expressed as: ; Quantum signal modulation and filtering are achieved by subjecting the quantum probe to two consecutive adiabatic evolution processes. The first adiabatic process occurs in the time interval [0, ... Within this time interval, the second adiabatic process occurs. Within [T], satisfy =T / 2.
3. The alternating magnetic field measurement method based on diamond NV color center phase-locked detection according to claim 2, characterized in that: The specific method for step five is as follows: Calculate the amplitude S0 and initial phase φ of the target signal, respectively, where: The formula for calculating amplitude S0 is: ; The formula for calculating the initial phase φ is: 。