A method for magnetic detection or temperature measurement of NV color centers based on zero-field splitting coefficient

Abstract

The present invention belongs to the field of quantum precision sensing technology, and specifically relates to a method for NV color center magnetic detection or temperature measurement based on the zero-field splitting coefficient. The present invention infers the imaginary magnetic field vector based on the structural characteristics of the diamond tetrahedron lattice, and calculates the zero-field splitting coefficient by the amplitude of the vector. The frequency offset introduced by the transverse magnetic field is fully considered, and the accuracy is improved on the basis of the above steps. Compared with the existing method, the calculated zero-field splitting coefficient is more accurate, and an error analysis method is provided. The above method can achieve more accurate D value to measure the magnetic field or temperature.

Description

Technical Field

[0001] The present invention belongs to the field of quantum precision sensing technology, and specifically relates to a method for NV color center magnetic detection or temperature measurement based on the zero-field splitting coefficient. Background Art

[0002] The nitrogen-vacancy color center in diamond consists of a nitrogen atom that replaces a carbon atom and a nearby vacancy. This structure absorbs an electron from the surrounding and forms a negatively charged NV. - structure, equivalent to a spin-1 electron, due to its 0 Color centers are more sensitive to magnetic fields and can be used in magnetic detection. In magnetic detection applications, negative NV is abbreviated as NV. NV has a triplet ground state, m s = ±1 and m s = 0, due to the dipole-dipole interaction between electrons, m s = ±1 and m s =0 state degenerates. This phenomenon is not caused by the Zeeman splitting caused by the magnetic field. Therefore, it is distinguished as the zero-field splitting coefficient, abbreviated as ZFS, and represented by D in the Hamiltonian, D≈2.87GHz.

[0003] The NV color center structure has a symmetry axis, which is most sensitive to the parallel component of the magnetic field along the symmetry axis. To a certain extent, the two transition processes of the ground state spin-1 electron The transition frequency (f ± =D±γ e B) The difference Δf=f + -f - It is proportional to the size of the magnetic field projection, that is, the parallel component of the magnetic field contributes to the differential mode component of the transition frequency. However, the perpendicular component of the magnetic field relative to the symmetry axis still contributes to the transition frequency f ± Contributes to the transition frequency f ± Although it has little effect on the magnetic field projection result calculated by the difference Δf to a certain extent, it has a great influence on the magnetic field modulus calculation formula and the polar angle calculation formula obtained by Hamiltonian analysis, because the common mode component caused by the transverse magnetic field will interfere with the measurement of the zero-field splitting coefficient.

[0004] On the other hand, existing research has found that the zero-field splitting coefficient is temperature-dependent, dD / dT≈-74kHz / K. Based on this property, NV color centers can also be used in the field of temperature sensors. ± The common mode component, f ± =D+(dD / dT)*T±γ eB. In the NV color center magnetic detection method based on optical detection magnetic resonance, the necessary microwave antenna will heat the diamond sample, causing the ambient temperature to constantly change. This causes D to shift from its initial value of 2.87 GHz in the absence of a magnetic field. Magnetic fields of different directions and amplitudes introduce different transverse magnetic fields, further shifting the transition frequency and making the measurement of D even more difficult.

[0005] The existing zero-field splitting coefficient measurement method focuses more on dD / dT and does not require a high accuracy value of D. The usual method is to measure the fluorescence spectrum of the NV color center to the microwave frequency of the frequency sweep under the geomagnetic field by the optical detection magnetic resonance method, and obtain the fitted transition frequency f by fitting the spectrum. ± A simple way to calculate the zero-field splitting coefficient is to take the average of the two transition frequencies, D fit =(f + +f - ) / 2, D can also be fitted by analytical Hamiltonian fit In this method, on the one hand, because the exact value of the zero-field splitting coefficient is not considered, the transition frequency offset caused by the initial temperature and the geomagnetic field is ignored. On the other hand, even if this method no longer uses the geomagnetic field and instead applies a strong magnetic field to improve the fitting accuracy of the transition frequency, the vertical component of the vector magnetic field on the NV color center in various directions will cause different degrees of common-mode shift, increasing the difficulty of fitting and even giving multiple results. Therefore, this method cannot give an accurate value for the zero-field splitting coefficient, and the error introduced in the vector magnetic field detection is too large to be tolerated.

[0006] Another method utilizes the temperature-dependent Debye-Waller coefficient (DWF), obtained by measuring high-resolution spectra at the NV color center zero-phonon line. The temperature obtained by this method can be used to calculate the accurate value of the zero-field splitting coefficient using the calibrated dD / dT method described above. However, on the one hand, the measurement mechanism of this method is not compatible with magnetic detection, and the two cannot usually be performed simultaneously. On the other hand, this method requires fitting the zero-phonon line. The fitting function consists of two Lorentzian line shapes and a linear function. Setting the fitting parameters of multiple functions can cause DWF instability and is relatively time-consuming.

[0007] It can be seen that at room temperature, the zero-field splitting coefficient D is 2.87 GHz, but under the influence of magnetic field and temperature, the actual value of D will be offset. The current method cannot accurately obtain the actual value of D after the offset, which affects the accuracy of NV color center magnetic detection or temperature measurement. Summary of the Invention

[0008] In order to solve the above technical problems, the present invention provides a method for NV color center magnetic detection or temperature measurement based on the zero-field splitting coefficient. During the magnetic detection or temperature measurement process, the D value can be calculated accurately in real time, and more reliable results can be given in the calculation of the magnetic field modulus and direction, which helps to improve the accuracy of magnetic detection or temperature measurement. The method of the present invention can be used for magnetic detection and temperature measurement at the same time, and has good compatibility.

[0009] The present invention is specifically achieved through the following technical solutions.

[0010] The present invention provides a method for magnetic detection or temperature measurement of NV color centers based on the zero-field splitting coefficient. When the NV color center is used for magnetic detection, the zero-field splitting coefficient measurement method includes the following steps:

[0011] S1. Place the diamond in the magnetic field to be measured to obtain the diamond ODMR spectrum (optical detection magnetic resonance spectrum). Read the first transition frequency and the second transition frequency on the ODMR spectrum, which are the microwave frequencies corresponding to the peak positions in the ODMR spectrum, respectively f and f. +,i and f -,i , where f +,i and f -,i is a pair of transition frequencies, i = 1, 2, 3, 4, i is the type of NV color centers with four orientations existing in the diamond sample.

[0012] S2. The value of the room temperature zero-field splitting coefficient, 2.87 GHz, is used as the initial value of the zero-field splitting coefficient D. ini , through D ini and the transition frequency f read out by S1 +,i and f -,i Get the initial calculated angle θ ini,i , 4 initial calculated angles θ ini,i Composed of 1×4 angle vectors [θ ini ]; It should be noted that [θ ini ]All are acute angles, not the true angles between the magnetic field and the NV axis (the angle between vectors may be acute or obtuse), and do not include the positive or negative sign of the projection of the magnetic field on the NV axis.

[0013] θ ini,i Specifically obtained through the following formula:

[0014]

[0015] D in the above formula ini is 2.87 GHz, and E is the off-diagonal electric field / stress splitting energy.

[0016] S3, obtained from S2 [θ ini ], and obtain the minimum value Δ θ.min , using Δθ.min Verify the readout f +,i and f -,i Is it correct?

[0017] Specifically through the minimum value formula: [Δ θ,min j Δ ]=min(|[cosθ ini ][p Δ ]|), get the minimum value Δ θ.min ; Among them, [Δ θ，min j Δ ] represents the angle discriminant that satisfies the lattice structure constraint, j Δ Indicates the minimum value Δ θ.min The number of columns, When the minimum value Δ θ.min When it deviates from 0, it means f +,i and f -,i The reading is wrong. This is a problem with the experiment. Reread f +,i and f -,i ; until Δ θ.min =0, get the correct f +,i and f -,i .

[0018] In addition, according to the minimum value formula, the minimum value Δ can also be calculated. θ.min [p Δ ]'s jth Δ Column [p], this column represents the positive and negative signs of the magnetic field projection on the NV axis. After obtaining [p], we can calculate the positive and negative signs according to p. i The sign of θ is modified by mi,i , get the direction polar angle θ B,i , θ B,i is the true angle between the magnetic field vector and the NV axis vector.

[0019] S4, the symbol vector [p] obtained using S3, and the verified f +,i And the verified f -,i Obtain magnetic field projection [B p ], using the NV color center ensemble model to reconstruct the vector direction of the magnetic field in the relative coordinate system with a selected axis orientation as the reference, based on the magnetic field projection [B p ] and the relative coordinate system, construct the initial vector of the magnetic field

[0020] The specific formula is:

[0021]

[0022] Among them, the symbol vector [p] takes [p Δ ]'s jthΔ Column; θ NV =109.47°.

[0023] S5, after S3 verification, f +,i And the verified f -,i and S4 obtained Substitute the following formula to obtain the reference value D of the zero-field splitting coefficient ref :

[0024]

[0025] S6, D ref Substitute the following formula to obtain the angle reference value θ ref , and obtain the angle reference value vector [θ ref ]:

[0026]

[0027] E is the off-diagonal electric field / stress splitting energy.

[0028] [θ ref ] is substituted into the following formula to obtain the error δD between the reference value of the zero-field splitting coefficient and the true value of the zero-field splitting coefficient:

[0029] Correcting D by δD ref , and obtain a result D close to the true value of the zero-field splitting coefficient D res .

[0030] S7, use S6 to get D res Conduct NV color center magnetic detection or temperature measurement.

[0031] Preferably, the ODMR spectrum is obtained using the following system:

[0032] The system includes a diamond NV color center sample, an optical path system, a microwave generating device, a magnetic field generating device and a digital control system.

[0033] The optical path system includes a laser generator, which is used to emit laser light. An acousto-optic modulator and a beam splitter are sequentially arranged along the laser emission direction. After passing through the acousto-optic modulator and the beam splitter, the laser light is split into laser light in a first direction and laser light in a second direction. A low-pass dichroic mirror and a first lens are sequentially arranged along the first direction, and the first lens is arranged close to the diamond NV color center sample. A third lens and a second photodetector are sequentially arranged along the second direction. The laser light in the first direction passes through the low-pass dichroic mirror and is focused on the diamond NV color center sample by the first lens. The photoluminescence of the diamond NV color center sample is collected by the first lens and reflected by the low-pass dichroic mirror. A high-pass filter, a second lens and a first photodetector are sequentially arranged along the reflection direction. The reflected light is filtered and split by the high-pass filter and finally focused on the first photodetector by the second lens. The laser light in the second direction is focused on the second photodetector through the third lens.

[0034] The microwave generating device includes a microwave generator and a microwave antenna. The microwave antenna is placed close to the diamond NV color center sample. The microwave generator is used to output microwaves, and the microwave antenna is used to transmit microwaves to the diamond NV color center sample.

[0035] The magnetic field generating device includes a set of Helmholtz coils or an electromagnet and a matching current source, and the diamond NV color center sample is placed in the uniform field area in the center of the coil or electromagnet.

[0036] The digital control system consists of a voltage acquisition system, a PID controller, a signal generator, and a host computer. The voltage acquisition system is used to collect output signals from a first photodetector and the signal generator. The PID controller is used to negatively feedback control the acousto-optic modulator to stabilize the light intensity based on the laser light intensity measured by the second photodetector. The signal generator is used to provide a reference signal for the frequency scanning of the microwave generator. The reference signal and the photoelectric signal of the first photodetector are sent to the host computer for processing, and the ODMR spectrum line is finally obtained.

[0037] Preferably, the mode of the microwave generator is set to a frequency sweep function, with 2870 MHz as the center frequency and a sweep depth of 200 MHz.

[0038] Preferably, the reference value of the zero field splitting coefficient is corrected with an error until ∑cos2θ ref When +4 / 3=0, the zero-field splitting coefficient D close to the true value is obtained. res ,θ ref is the angle reference value.

[0039] Preferably, when the NV center is used as a temperature sensor, the magnetic field to be measured in S1 is replaced by a calibrated standard magnetic field applied to the NV center sample by a magnetic field generating device. The magnetic field in the NV center sensing area is uniform. In this case, the calculation formula is as follows: Where B is the standard magnetic field modulus.

[0040] Preferably, when the NV color center is used as a temperature sensor, the f read in S3 is verified +,i and f -,i Is the correct step to change to: Using the minimum formula [Δ θ,min j Δ ]=min(|[cosθ ini ][p Δ ]|), get the minimum value Δ θ.min ; Among them, [Δ θ，min j Δ ] represents the angle discriminant that satisfies the lattice structure constraint, j Δ Indicates the minimum value Δ θ.min The number of columns, When the minimum value Δ θ.min If it deviates from 0, it means that the first transition frequency and the second transition frequency are not read correctly. Return to S1 to read the first transition frequency and the second transition frequency until Δ θ.min = 0, obtaining the correct first and second transition frequencies. When the NV color center is used as a temperature sensor for temperature measurement, the zero-field splitting coefficient is measured at different temperatures using a standard temperature source to obtain the dD / dT relationship. The zero-field splitting coefficient close to the true value is substituted into this relationship to obtain the temperature value.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] The present invention proposes a method for magnetic detection or temperature measurement of NV color centers based on the zero-field splitting coefficient. The method first uses the diamond lattice structure to limit the measurement of the zero-field splitting coefficient, and then uses the zero-field splitting coefficient to perform magnetic detection or temperature measurement. The present invention can accurately calculate the D value in real time during the magnetic detection or temperature measurement process, providing more reliable results in the calculation of the magnetic field modulus and direction, and helping to improve the accuracy of magnetic detection or temperature measurement. Specifically:

[0043] The present invention first obtains the diamond ODMR spectrum line and reads the transition frequency f on the ODMR spectrum line. +,i and f -,i, taking the value of the room temperature zero-field splitting coefficient of 2.87GHz as the initial value (imaginary value) of the zero-field splitting coefficient, the initial vector of the magnetic field is obtained by calculation. The key of the present invention is to infer the imaginary magnetic field vector based on the structural characteristics of the diamond tetrahedron lattice, and realize the measurement of the zero-field splitting coefficient by the modulus value of the vector. The effect is that the created imaginary magnetic field vector is only affected by the readout error of the first transition frequency and the second transition frequency, and the influencing factors come from the system error. The calculated zero-field splitting coefficient is more reliable, has a unique solution, and the unique solution has high stability. Compared with the first method in the background technology, that is, the resonance frequency averaging method, the problem of multiple solutions of the non-unique resonance frequency average value under strong magnetic field is solved.

[0044] The key to this invention lies in comprehensively analyzing and quantifying the impact of the error between the reference and true zero-field splitting coefficients on the angle reference value calculated from the readout frequency. This effectively accounts for the frequency offset introduced by the transverse magnetic field, further improving accuracy. Compared to existing methods, the measured zero-field splitting coefficients are more accurate and provide a method for error analysis.

[0045] Through the above content of the present invention, the zero-field splitting coefficient can be used more accurately to measure the magnetic field or temperature. In the zero-field splitting coefficient measurement method applied to magnetic detection, the measured magnetic field provides a magnetic field environment, but the zero-field splitting coefficient value is required to measure the measured magnetic field. Therefore, the zero-field splitting coefficient value is calculated by reading the ODMR spectrum line and transition frequency under the measured magnetic field, and a more accurate magnetic field amplitude and magnetic field angle are obtained. In the zero-field splitting coefficient value measurement method applied to temperature measurement, since there is no measured magnetic field, it is necessary to manually apply a magnetic field, so the amplitude of this magnetic field is known. The more accurately the zero-field splitting coefficient value is measured through the dD / dT value, the more accurately the temperature is measured. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 Schematic diagram of the system structure used in the present invention to obtain diamond ODMR spectrum lines.

[0047] Figure 2 In the figure, (a) is the NV color center axis orientation model, and (b) is the schematic diagram of the ODMR spectrum line.

[0048] Figure 3 In the figure, (a) is the error function judgment standard, and (b) is the flow chart diagram. DETAILED DESCRIPTION

[0049] In order to enable those skilled in the art to better understand and implement the technical solution of the present invention, the present invention is further described below with reference to specific embodiments and drawings, but the embodiments are not intended to limit the present invention.

[0050] Explanation of symbols:

[0051] D: Zero-field splitting coefficient.

[0052] D ref : Reference value of zero-field splitting coefficient.

[0053] D res : Zero-field splitting coefficient close to the true value.

[0054] i: orientation of NV color center in diamond sample, i = 1, 2, 3, 4.

[0055] f +,i and f -,i : The first transition frequency and the second transition frequency.

[0056] [f ± ]:A 2×4 matrix consisting of 4 pairs of f_+,i and f_-,i.

[0057] |B i |: Magnetic field modulus, used to calculate D value.

[0058] θ B : The angle between the magnetic field vector and the NV axis vector.

[0059] [θ B ]: A 1×4 angle vector consisting of the angles between the magnetic field vector and the NV axis vectors of the four orientations.

[0060] θ B,i : Direction polar angle, the angle between the magnetic field vector and each NV axis vector.

[0061] θ ini,i : Initial calculation angle.

[0062] [θ ini ]: A 1×4 angle vector consisting of the four initial calculated angles.

[0063] [p]: Sign vector, a 4×1 column vector consisting of the positive and negative signs of the projection of the magnetic field vector on the NV axis vector in the four orientations. It reflects whether the angle between the magnetic field vector and the NV axis is acute or obtuse.

[0064] [p Δ ]:Calculation symbol matrix used for testing, no special meaning, symbol vector is one of the columns.

[0065] θ ref : Angle reference value.

[0066] [θ ref ]: Angle reference value vector.

[0067] The zero-field splitting coefficient (ZFS), often abbreviated as D in the Hamiltonian, arises from the dipole-dipole interaction within the diamond lattice of nitrogen-vacancy (NV) centers. It degenerates the ground-state spin state of the NV center and is treated as a constant in most studies. However, recent studies on the temperature dependence of NV centers and vector magnetic detection have revealed that the ZFS is a temperature-dependent quantity and is involved in the calculation of the magnetic field magnitude and direction in magnetic field detection. Therefore, measuring or precalculating the ZFS is crucial for vector and scalar magnetic detection based on NV centers. Existing research has largely focused on calibrating the sensitivity of the ZFS to temperature, T, i.e., dD / dT, while paying less attention to the precise value of ZFS. The D value measured using existing methods often results in significant errors in the calculation of magnetic field magnitude and angle. The present invention proposes a method for measuring zero-field splitting energy limited by the diamond lattice structure. This method can accurately calculate the D value in real time during magnetic detection or temperature measurement, providing more reliable results in calculating the magnetic field modulus and direction, thereby helping to improve the accuracy of magnetic detection or temperature measurement. Furthermore, the method can be used for both magnetic detection and temperature measurement, with good compatibility. The method provided by the present invention comprises the following steps:

[0068] S1. Place the diamond in a magnetic field and obtain the diamond ODMR spectrum line, and read the first transition frequency f on the ODMR spectrum line. +,i and the second transition frequency f -,i , where f +,i and f -,i is a pair of transition frequencies, i = 1, 2, 3, 4, and i is the orientation of the NV color center in the diamond sample.

[0069] S2, take 2.87GHz as the initial value of zero-field splitting coefficient D ini , through D ini and f read from S1 +,i and f -,i Get the initial calculated angle θ ini,i , 4 initial calculated angles θ ini,i Composed of 1×4 angle vectors [θ ini ].

[0070] S3, obtained from S2 [θ ini ], and obtain the minimum value Δ by the minimum value calculation formula θ.min and the minimum value Δ θ.min The corresponding symbol vector [p], using Δ θ.min Verify the f read by S1 +,i and f -,i Is it correct?

[0071] S4, the symbol vector [p] obtained using S3, and f after verification by S3+,i And after verification f -,i Obtain magnetic field projection [B p ], using the NV color center ensemble model to reconstruct the vector direction of the magnetic field in the relative coordinate system with a selected axis orientation as the reference, based on the magnetic field projection [B p ] and the relative coordinate system, construct the initial vector of the magnetic field And obtain the initial vector of the magnetic field The modulus value of .

[0072] S5, using the modulus of the initial vector of the magnetic field, f after verification in S3 +,i And after verification f -,i Obtain the reference value D of the zero-field splitting coefficient ref .

[0073] S6. Use D ref 、After verification +,i And after verification f -,i Get the angle reference value [θ ref ], using [θ ref ]Get D ref The error δD between the true value of the zero-field splitting coefficient D is used to correct D ref , obtain the zero-field splitting coefficient D close to the true value res .

[0074] S7, use S6 to get D res Conduct NV color center magnetic detection or temperature measurement.

[0075] The present invention will be described in detail below.

[0076] like Figure 1As shown, the experimental system of the present invention consists of a diamond NV color center sample 13, an optical system, a microwave generator, a magnetic field generator, and a digital control system. The optical system includes a 532nm laser generator 1. The laser passes through an acousto-optic modulator 2 and a beam splitter 3, and is focused by a first lens 14 onto the diamond NV color center sample 13. The photoluminescence of the diamond NV color center sample 13 is collected by the first lens 14, filtered and split by a low-pass dichroic mirror 4 and a high-pass filter 6, and finally focused by a second lens 7 onto a first photodetector 16. Another portion of the laser light passes through a third lens 5 and is focused onto a second photodetector 17. The microwave generator includes a microwave generator 11 with a microwave frequency range of 2 GHz to 4 GHz and a microwave antenna 12. Microwave antenna 12 is placed near the diamond NV color center sample 13. The microwave generator 11 is set to a frequency sweep function, with a center frequency of 2870 MHz and a sweep depth of approximately 200 MHz. The magnetic field generating device includes a set of Helmholtz coils 15 or an electromagnet, and a matching current source 10, wherein the diamond NV color center sample 13 should be placed in the uniform field area at the center of the Helmholtz coil 15 or the electromagnet. The digital control system consists of a voltage acquisition system, a PID controller, a signal generator 9 and a host computer 8. The voltage acquisition system is used to collect the output signals of the first photodetector 16 and the signal generator 9. The PID controller is used to negatively feedback control the acousto-optic modulator 2 to stabilize the light intensity based on the laser light intensity measured by the second photodetector 17. The signal generator 9 is used to provide a reference signal for the frequency scanning of the microwave generator 11. The reference signal and the photoelectric signal of the first photodetector 16 are sent to the host computer 8 for processing, and the final result is as follows: Figure 2 The ODMR spectrum is shown in the figure below. Due to the constraints of the diamond tetrahedral lattice structure, there are four types of NV color centers in the diamond sample, with the angle between their symmetry axes being 109.47°. When the vector magnetic field interacts with the four types of NV color centers in a certain direction, its magnetic field projection on the four symmetry axes will produce four pairs of transition frequencies f ±,i (i.e. f +,i and f -,i ), i=1,2,3,4, corresponding to Figure 2 The microwave frequencies corresponding to the four pairs of peaks in the ODMR spectrum shown in the middle and lower figures. The magnetic field modulus |B can be obtained by analyzing the ground state energy level Hamiltonian of the NV color center. i |、Angle θ between the magnetic field vector and the NV axis vector B With each pair of transition frequencies f ±,i The relationship between them is:

[0077]

[0078] Where E is the off-diagonal electric field / stress splitting energy, which is a known constant in the present invention and is usually much smaller than D, γ e =28GHz / T is the NV color center gyromagnetic ratio. As can be seen from Equations (1) and (2), D directly affects the magnetic field calculation results in both scalar and vector magnetic sensing, and its weight is even more significant when calculating the magnetic field angle. Therefore, when using NV color centers for magnetic detection, the D value is required to measure the measured magnetic field.

[0079] Although we do not know the absolute directions of the four orientations of the NV color center axis in the laboratory frame, due to the symmetry of the crystal, we can use the following NV color center ensemble model to reconstruct the vector direction of the magnetic field in the relative coordinate system based on a selected axis orientation, as follows: Figure 2 shown.

[0080]

[0081] The row vector is represented as a unit vector of four axis orientations. For the convenience of calculation, the reference vector Parallel to the z-axis.

[0082] Since the magnetic field modulus is unknown during the magnetic detection process, formula (1) is not suitable for giving the exact value of D. At the same time, the preset zero-field splitting coefficient initial value D is substituted into formula (2): ini (2.87GHz) often gives unstable angle calculation results, which are not of reference value. Therefore, other methods are needed to mathematically express the constraints on the D value. ± The calculated magnetic field projection can give the modulus of the magnetic field without the participation of D, which can be used to give the reference value of the iterative algorithm of D. ± What is actually calculated is the absolute value of the magnetic field projection, that is, the response of the NV color center to a pair of oppositely directed magnetic field vectors is consistent, only the transition frequency is exchanged. We first need to solve the problem of how to obtain the sign of the magnetic field projection. This corresponds to how to determine the 1×4 angle vector [θ] composed of the angles between the magnetic field vector and the four oriented NV axis vectors. B ] is an acute angle or an obtuse angle. Due to the characteristics of the double angle, formula (2) can only calculate the initial calculation angle θ of the magnetic field polar angle. ini,i ∈(0,π / 2) acute angle, so in the calculation we have to calculate the polar angle θ for each direction B,i Consider θ ini,i and π-θ ini,i The two results correspond to the positive and negative signs of the projection of the magnetic field on the NV axis.

[0083] The angle between the vector magnetic field and the axis orientation should satisfy the NV color axis angle θ constrained by the diamond tetrahedron lattice structure. NV =109.47°, that is:

[0084]

[0085] According to [θ B ] and [θ ini ], modify formula (4) as the judgment condition of the symbol vector [p],

[0086]

[0087] where p i =1 or -1 represents the positive and negative sign of the magnetic field projection on the NV axis, as well as the direction polar angle θ B,i With the initial calculated angle θ ini,i The relationship between:

[0088]

[0089] When reading out the 4 groups of transition frequencies [f ± ], with the initial value of zero field splitting coefficient D ini Calculate the initial angle matrix [θ ini ], considering the readout error of the transition frequency and the initial value of the zero-field splitting coefficient D ini The error between the true value and the true value, formula (5) can be expanded to

[0090] [Δ θ,min j Δ ]=min([cosθ ini ][p Δ ]) (7)

[0091] in

[0092]

[0093] j Δ Indicates the minimum value Δ θ.min The number of columns, the symbolic vector [p] takes [p Δ ]'s jth Δ Column. Although the calculation of the symbol matrix requires the preset D ini Participate, but the sign vector [p] given by the angle relationship is more stable and has an initial value D for the zero-field splitting coefficient ini The dependence of D is weak, so D is not introduced when calculating the magnetic field modulus. ini error.

[0094] Substitute the symbol vector [p] into the calculated magnetic field projection [B p ]:

[0095]

[0096] The initial vector of the magnetic field can be constructed based on the relative coordinate system defined by formula (3):

[0097]

[0098] Among them [B p The absolute value of the transition frequency [f ± ] is given, θ NV Determined by the diamond lattice structure, only [B p ] and D ini Although the D value changes in a large range will give an unstable [θ B ], but due to the generous judgment conditions in formula (7), [p] can still be kept stable, so For the preset D ini The dependence is weak, which ensures good robustness. Substituting the modulus of the initial magnetic field vector into formula (1) can calculate the iterative D value:

[0099]

[0100] Considering the readout error of the transition frequency, there may be some deviations in the D values ​​calculated for the four pairs of transition frequencies. Therefore, the average of the calculated results is taken as a reference value.

[0101] So far, we have set the reference value D ref Anchored near the true value of D, but if you want to get the D value more accurately, the calculation accuracy of formula (9) can no longer guarantee the accuracy. The subsequent calculation will be based on the angle [θ ref ]. By reference value D ref Calculated [θ ref ] gives the relative direction of the vector magnetic field in the relative coordinate system defined by formula (5):

[0102]

[0103] in,

[0104]

[0105]

[0106] Determined by the modulus of the created unit vector, [θ ref ]Another condition still needs to be met, namely:

[0107]

[0108] The error in the equation comes from [θ ref ], that is, D substituted into formula (2) ref The error δD between the true value of D and D, considering Dref =D+δD Substituting into formula (2), we obtain formula (15) with error, namely:

[0109]

[0110] Since the reference value D ref It is already near the true value of D, so δD<<D, which can be approximately considered as ∑cos2θ ref ∝δD, and when δD=0, ∑cos2θ ref =-4 / 3, so we can get ref A small change δD is added to the basis to find D. For the convenience of calculation, the error function is set to:

[0111]

[0112] Error function changes with δD Figure 3 , when D is used as the reference quantity, Err(δD=0)=0; when D is used as the reference quantity with error, ref When it is a reference quantity, for example, D ref When δD > D, Err(δD < 0) = 0, and D is corrected by δD. ref To get a result closer to D res .

[0113] When the NV color center is used as a temperature sensor for temperature measurement, since there is no magnetic field to be measured, a magnetic field needs to be artificially applied. Specifically, a calibrated standard magnetic field can be applied to the NV color center through a magnetic field generating device. Since the sensing area of ​​the NV color center is usually in the micron to millimeter size, and the uniform area of ​​the magnetic field generating device such as the coil and magnet is often much larger than this size, it can be considered that the magnetic field in the sensing area of ​​the NV color center is uniform. Therefore, in formula (1), |B i | should be consistent. The D value can be calculated based on the known standard magnetic field modulus:

[0114]

[0115] In addition, the angle calculation formula in formula (2) can be used to verify D ref If the calculated D value does not satisfy formula (5), the transition frequency f ± There is a large error in the reading, or there is a magnetic material in the measurement system that makes the standard magnetic field amplitude inaccurate. This can be verified by the subsequent steps. ref Correctness of the value.

[0116] The D value at different temperatures T is measured according to a standard temperature source to obtain dD / dT. Therefore, the D value calculated according to the method of the present invention can be used to obtain the temperature T value, and the more accurate the D value is, the more accurate the measured T value is.

[0117] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications of the present invention fall within the scope of the claims and their equivalents, such changes and modifications are intended to be included.

Claims

1. A method for magnetic detection or temperature measurement of NV color centers based on the zero-field splitting coefficient, characterized in that: The following steps are involved: Placing the diamond in a magnetic field and obtaining a diamond ODMR spectrum line, and reading a first transition frequency and a second transition frequency on the ODMR spectrum line, wherein the first transition frequency and the second transition frequency form a pair of transition frequencies and are microwave frequencies corresponding to a peak position in the ODMR spectrum line; The value of the zero-field splitting coefficient at room temperature is used as the initial value of the zero-field splitting coefficient, and the initial calculated angle is obtained by the initial value of the zero-field splitting coefficient and the read first transition frequency and second transition frequency, and the initial calculated angle constitutes an angle vector; Obtain a minimum value and a sign vector corresponding to the minimum value from the obtained angle vector using a minimum value calculation formula, and use the minimum value to verify whether the read first transition frequency and second transition frequency are correct; Obtaining a magnetic field projection using the symbol vector, the verified first transition frequency, and the verified second transition frequency, constructing an initial vector of the magnetic field, and obtaining a modulus value of the initial vector of the magnetic field; Obtaining a reference value of a zero-field splitting coefficient using the modulus of the initial vector of the magnetic field, the verified first transition frequency, and the verified second transition frequency; Obtaining an angle reference value using a reference value of the zero-field splitting coefficient, a verified first transition frequency, and a verified second transition frequency, obtaining an error between the reference value of the zero-field splitting coefficient and a true value of the zero-field splitting coefficient using the angle reference value, and correcting the reference value of the zero-field splitting coefficient using the error to obtain a zero-field splitting coefficient close to the true value; The zero-field splitting coefficient close to the true value is used for NV color center magnetic detection or temperature measurement.

2. The method according to claim 1, characterized in that The ODMR spectrum is obtained using the following system: The system comprises a diamond NV color center sample (13), an optical path system, a microwave generating device, a magnetic field generating device and a digital control system; The optical path system comprises a laser generator (1), which is used to emit laser light. An acousto-optic modulator (2) and a beam splitter (3) are sequentially arranged along the laser emission direction. After the laser light passes through the acousto-optic modulator (2) and the beam splitter (3), it is split into laser light in a first direction and laser light in a second direction. A low-pass dichroic mirror (4) and a first lens (14) are sequentially arranged along the first direction. The first lens (14) is arranged close to a diamond NV color center sample (13). A third lens (5) and a second photodetector (17) are sequentially arranged along the second direction. The laser light in the first direction passes through the acousto-optic modulator (2) and the beam splitter (3). A low-pass dichroic mirror (4) is focused on a diamond NV color center sample (13) by a first lens (14); photoluminescence of the diamond NV color center sample (13) is collected by the first lens (14) and reflected by the low-pass dichroic mirror (4); a high-pass filter (6), a second lens (7) and a first photodetector (16) are sequentially arranged along the reflection direction; the reflected light is filtered and split by the high-pass filter (6) and finally focused on the first photodetector (16) by the second lens (7); laser light in a second direction is focused on the second photodetector (17) by a third lens (5); The microwave generating device comprises a microwave generator (11) and a microwave antenna (12), wherein the microwave antenna (12) is placed close to the diamond NV color center sample (13); the microwave generator (11) is used to output microwaves, and the microwave antenna (12) is used to transmit microwaves to the diamond NV color center sample (13); The magnetic field generating device comprises a set of Helmholtz coils (15) or an electromagnet and a matching current source (10), and the diamond NV color center sample (13) is placed in the uniform field region at the center of the Helmholtz coils (15) or the electromagnet; The digital control system comprises a voltage acquisition system, a PID controller, a signal generator (9) and a host computer (8), wherein the voltage acquisition system is used to acquire output signals of a first photodetector (16) and the signal generator (9), the PID controller is used to negatively feedback control the acousto-optic modulator (2) to stabilize the light intensity according to the laser light intensity measured by a second photodetector (17), and the signal generator (9) is used to provide a reference signal for the frequency scanning of a microwave generator (11), and the reference signal and the photoelectric signal of the first photodetector (16) are sent to the host computer (8) for processing, and finally an ODMR spectrum line is obtained.

3. The method according to claim 2, characterized in that The mode of the microwave generator (11) is set to a frequency sweep function, with 2870 MHz as the center frequency and a sweep depth of 200 MHz.

4. The method according to claim 1, wherein When NV color centers are used for magnetic detection, the magnetic field is the magnetic field to be measured.

5. The method according to claim 4, characterized in that When NV color centers are used for magnetic detection, the steps to verify whether the read first transition frequency and second transition frequency are correct are as follows: using the minimum formula [Δ θ,min j Δ ]=min(|[cosθ ini ][p Δ ]|), to obtain the minimum value; where Δ θ.min Indicates the minimum value, [Δ θ，min j Δ ] represents the angle discriminant that satisfies the lattice structure constraint, j Δ Indicates the number of columns with the minimum value. When the minimum value deviates from 0, it indicates that the first transition frequency and the second transition frequency are read incorrectly. The first transition frequency and the second transition frequency are read again until the minimum value reaches 0, thereby obtaining the correct first transition frequency and the second transition frequency.

6. The method according to claim 2, characterized in that When the NV color center is used as a temperature sensor for temperature measurement, the magnetic field is: a calibrated standard magnetic field is applied to the diamond NV color center sample through the magnetic field generating device, and the magnetic field in the sensing area of ​​the diamond NV color center sample is uniform. At this time, the modulus value of the initial vector of the magnetic field is the modulus value of the standard magnetic field.

7. The method according to claim 6, characterized in that When the NV color center is used as a temperature sensor, the steps to verify whether the read first transition frequency and second transition frequency are correct are: using the minimum formula [Δ θ,min j Δ ]=min(|[cosθ ini ][p Δ ]|), to obtain the minimum value; where Δ θ.min is the minimum value, [Δ θ，min j Δ ] represents the angle discriminant that satisfies the lattice structure constraint, j Δ Indicates the minimum value Δ θ.min The number of columns, When the minimum value deviates from 0, it indicates that the first transition frequency and the second transition frequency are read incorrectly. The first transition frequency and the second transition frequency are read again until the minimum value reaches 0, thereby obtaining the correct first transition frequency and the second transition frequency.

8. The method according to claim 1, characterized in that Use the error correction to correct the reference value of the zero-field splitting coefficient until φcos2θ ref When +4 / 3=0, the zero-field splitting coefficient close to the true value is obtained, θ ref is the angle reference value.

9. The method according to claim 1, characterized in that The NV color center is used as a temperature sensor for temperature measurement. The zero-field splitting coefficient D is measured at different temperatures T according to a standard temperature source to obtain the dD / dT relationship. The zero-field splitting coefficient close to the true value is substituted into the relationship to obtain the temperature value.

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