A method and system for calibrating the charge state and relative spatial distribution of trapped ions

Abstract

The present invention discloses a method and system for calibrating the charge state and relative spatial distribution of trapped ions, establishes a kinetic quantization model for the synergistic effect of the HCIs-SCIs hybrid ion system, and based on this model, determines the logarithmic dependence relationship between the relative spatial distribution of HCIs-SCIs and the charge state of HCIs, and verifies that this relationship is not affected by factors such as the ion trap potential field and the mass number of highly ionized ions. Furthermore, a charge state-ion relative spacing scale for trapping the HCIs-SCIs hybrid ion system is established, and a scheme for realizing real-time and non-destructive precise inversion of the relative position and charge state of HCIs is given, which has universality for the efficient regulation of HCIs ions in the ion trap.

Description

Technical Field

[0001] The present invention belongs to the technical field of calibration of trapped ion systems, and particularly relates to a method and a system for calibrating the charge state and relative spatial distribution of trapped ions. Background Art

[0002] Based on the trapping, cooling, and fine control of quantum states of single charge states (SCIs), the research and application accuracy of precision measurement physics have been greatly improved. At present, the frequency uncertainty of cold SCIs optical clocks has reached 10 -19 magnitude, which is the preferred high-end time and frequency reference for future timekeeping, time dissemination, time utilization, and metrology industries. Currently, the influence of physical interactions on the electron binding energy or transition frequency has gradually become a key factor restricting the further improvement of the performance of SCIs optical clocks. While further finely controlling the internal state, motion, and environmental field of the SCIs system, preparing a new physical system with a smaller frequency shift effect has become an important solution for developing atomic clocks with higher precision.

[0003] HCIs developed by increasing the ionization charge number can significantly increase the binding energy of valence electrons and enhance the interaction strength between the electron wave function and the nucleus, becoming a new physical system with very prominent characteristics and advantages. The linewidth of the weakly forbidden transition spectral lines of HCIs is extremely narrow, and the influence of the external environmental field micro-perturbation effect is much lower than that of the similar transition spectral lines of SCIs. Its frequency uncertainty is expected to reach 10 -19 -10 -20 magnitude, having the potential advantage of developing into a higher-precision atomic frequency standard. As an extremely relativistic system, HCIs have extremely significant QED effects. Based on the fine control of a series of narrow linewidth transitions of ions with different charge states, it is possible to precisely measure whether the fine structure constant α changes with time at the level of 10 -20 / year, calibrate the change of the electron-proton mass ratio, accurately test the QED theory in the non-perturbation region, study the weak interaction process between electrons and nuclei, develop the relativistic atomic structure theory, test the standard physical model, and explore new physical effects beyond the Standard Model (SM).

[0004] Due to the significant differences in the charge properties, energy level structures, and electron interactions between HCIs and SCIs, it is difficult for existing atomic structure theories to accurately analyze the complex electron distribution structure of HCIs, and the theory for precisely describing the transition spectral lines of HCIs is still incomplete. For a long time, the theoretical calculation accuracy of HCIs has been much lower than that of single-charged atomic (molecular) ion systems. At the same time, the experimental methods for generating, trapping, cooling, and quantum state control of HCIs are much more complex than those of SCIs. Experimentally, precise control of external states cannot be achieved as in single-charged atomic (molecular) ions, and the amount and accuracy of the spectral data obtained are also far less than the latter. Currently, HCIs are mainly generated based on electron beam ion traps (EBITs), high-energy lasers, accelerators, etc. Their initial temperatures are generally as high as megakelvins (MK). After evaporative cooling, the temperature of HCI is still as high as 0.2 MK. The corresponding Doppler broadening and frequency shift effects result in the measurement accuracy of forbidden transitions being lower than that of current optical clocks by 12 orders of magnitude, severely restricting the spectral measurement accuracy and application efficiency of HCIs ions.

[0005] Currently, based on EBITs, the generation of most charge states of HCIs can be achieved. By decelerating and guiding them into a radiofrequency ion trap, the motional effects can be greatly suppressed through the cooperative cooling effect of laser-cooled SCIs, which is one of the effective methods for carrying out high-resolution spectral measurements of HCIs. The quantum state control method for this HCIs-SCIs dual-ion system integrates the respective advantages of the two types of ions, enabling HCIs ions to indirectly achieve high-resolution spectral measurements. Currently, the quantum logic spectroscopy measurement method for the dual-ion system is further expanding towards more complex multi-ion optical clock systems. In summary, by combining the generation of HCIs based on EBITs with technologies such as radiofrequency ion trap trapping, cooperative cooling, quantum logic operations, and ultra-narrow linewidth laser spectroscopy detection, precise manipulation and measurement of the quantum states of HCIs can be achieved, and it is very likely to improve the existing measurement accuracy of HCIs by nearly ten orders of magnitude.

[0006] The kinetic coupling characteristics between the HCIs-SCIs mixed ion systems are closely related to the ionization charge number of HCIs and the relative spatial distribution of HCIs-SCIs. The accurate detection and control of the ionization charge number in HCIs are the basis and key to achieving high-precision spectroscopic measurements. Currently, in EBIT, methods such as Wien filter and transfer beamline are mainly used to monitor the charge state of HCIs. Since the evolution path of ions has a certain adaptation range to environmental potential fields such as external magnetic fields and radio frequency stable constraint parameters, there are certain limitations in directly using them for high-purity separation, guiding, and trapping of specific charge states of HCIs. In addition, even if high-purity preparation of HCIs ions with a specific ionization charge number is achieved, the collision charge transfer effect will shorten the trapping lifetime of HCIs ions and lead to the occurrence of composite charge HCIs, thereby reducing the signal-to-noise ratio of HCIs spectroscopic measurements and even causing measurement failure. Therefore, developing a real-time, non-destructive, and high-precision monitoring and evaluation method for the ionization charge number of HCIs is of great significance for the precise manipulation of HCIs in a linear radiofrequency ion trap. The fluorescence collection efficiency of the co-cooled HCIs system is extremely low, and it usually appears as dark ions. Accurately predicting its relative spatial distribution is the key to quantum operations such as efficient optical exploration of the quantum states of dark ions. Currently, the optical quantum operations of dark ions are mainly limited to the axial direction of chain-like ion systems, and it is difficult to achieve precise matching between the laser beam waist and dark ions. Therefore, developing a real-time, high-precision position calibration method applicable to HCIs is of great significance for the three-dimensional (3D) quantum state control of HCIs.

[0007] The public literature has not covered the quantitative methods for charge state evaluation and spatial distribution calibration of HCIs ions in a linear trap. Currently, PTB mainly uses the method of charge state screening before entering the trap; the position calibration of HCIs ions mainly relies on experimental experience and the method of blind axial optical pumping, and a precise quantitative calibration method has not been formed. The current experiments have the following problems:

[0008] (1) HCIs ions have high outer state energies, and the charge state purity and accuracy of the screening before entering the trap are low. After entering the trap, charge recombination and charge transfer effects lead to continuous evolution of the charge state, and it is impossible to objectively and quantitatively evaluate the charge state in real time in the ion trap. The reliability and precision of the experiment are extremely poor, and the effective utilization efficiency of HCIs is low.

[0009] (2) The method for determining the spatial distribution of HCIs ions mainly relies on blind axial scanning of the spectroscopic exploration laser, with poor accuracy and great blindness, and it is difficult to quantitatively control the coupling between the electromagnetic field and the ions. The current method is still unable to carry out radial Doppler-free measurements, which limits the efficient control of ions.

[0010] (3) Regarding the co-control of the HCIs-SCIs mixed ion system, it is mainly based on experimental experience. The research on the kinetic quantitative model is still blank. Summary of the Invention

[0011] Technical problem solved by the present invention: Overcoming the deficiencies of the prior art, providing a method and system for calibrating the charge state and relative spatial distribution of trapped ions, filling the gap in the calculation model of the interaction between the charge state and the radiofrequency trapped ion ensemble, and providing strong support for the quantitative evaluation and regulation of the charge state additional effect.

[0012] To solve the above technical problems, the present invention discloses a method for calibrating the charge state and relative spatial distribution of trapped ions, including:

[0013] Establishing a quantitative kinetic model of the synergistic effect of the HCIs-SCIs hybrid ion system;

[0014] Determining the logarithmic dependence relationship between the relative spatial distribution of HCIs-SCIs and the charge state of HCIs according to the quantitative kinetic model of the synergistic effect of the HCIs-SCIs hybrid ion system;

[0015] Establishing a charge state-ion relative spacing scale for the trapped HCIs-SCIs hybrid ion system according to the logarithmic dependence relationship between the relative spatial distribution of HCIs-SCIs and the charge state of HCIs;

[0016] Calibrating the charge state and relative spatial distribution of trapped ions according to the charge state-ion relative spacing scale of the trapped HCIs-SCIs hybrid ion system, and giving a scheme for realizing real-time and non-destructive precise inversion of the relative position and charge state of HCIs.

[0017] In the above method for calibrating the charge state and relative spatial distribution of trapped ions, establishing a quantitative kinetic model of the synergistic effect of the HCIs-SCIs hybrid ion system includes:

[0018] Establishing a model of the trapped SCIs ion ensemble;

[0019] Establishing a steady-state resonant trapping system for the HCIs-SCIs hybrid ion system.

[0020] In the above method for calibrating the charge state and relative spatial distribution of trapped ions, establishing a model of the trapped SCIs ion ensemble includes:

[0021] An electromagnetic field confinement test device for an ion ensemble is established. Taking the original parameters of the SCIs ion ensemble and the electromagnetic field parameters as the initial value conditions, according to the Mathieu dynamics equation of the ion ensemble, a radio frequency dynamic confinement model for confining the SCIs ion ensemble is constructed, the motion spectrum of the SCIs ion system is extracted, and the precise matching with the secular motion excitation spectrum is achieved by improving the accuracy of the geometric factor; among them, the original parameters of the SCIs ion ensemble include: the mass M of the ion, the charge Q of the ion, and the number N of ions in the ion ensemble; the electromagnetic field parameters of the SCIs ion ensemble include: the frequency Ω of the radio frequency potential, the amplitude U of the radio frequency potential rf , the static DC bias voltage U applied to the radio frequency field dc , the radial geometric factor parameter κ of the ion trap r , the axial geometric factor parameter κ of the ion trap z , the minimum radial distance r from the geometric center of the ion trap to the surface of the ion trap 0 , the equivalent capacitance value C of the ion trap under resonance matching, and the potential well depth D

[0022] In the above method for calibrating the charge state and relative spatial distribution of trapped ions, a steady-state resonance confinement system for the HCIs-SCIs hybrid ion system is established, including:

[0023] Optimizing and modifying the electromagnetic field confining the SCIs ion ensemble to make it further compatible and match the stable confinement conditions of HCIs, injecting HCIs into the SCIs ion ensemble, evaluating the influence of HCIs on the dynamic characteristics of SCIs, realizing the steady-state confinement with a low heating rate of the HCIs-SCIs hybrid ion ensemble, and establishing a steady-state dynamic resonance confinement model for the HCIs-SCIs hybrid ion system

[0024] In the above method for calibrating the charge state and relative spatial distribution of trapped ions, according to the cooperative dynamics quantization model of the HCIs-SCIs hybrid ion system, the logarithmic dependence relationship between the relative spatial distribution of HCIs-SCIs and the charge state of HCIs is determined, including:

[0025] Based on the fast FFT method, the motion spectrum of the HCIs-SCIs hybrid ion ensemble is extracted to verify whether the motion spectrum of the HCIs-SCIs hybrid ion ensemble is consistent with the resonant frequency points of the low-order mode coupling theory; if not, increase the order of the high-order anharmonic potential of the HCIs-SCIs hybrid ion ensemble until precise matching; if matching, further extract the characteristic temperature of the HCIs-SCIs hybrid ion ensemble under different charge states, obtain the influence of the charge state on the dynamic coupling relationship of HCIs-SCIs, and determine the logarithmic dependence relationship between the relative spatial distribution of HCIs-SCIs and the charge state of HCIs

[0026] In the above method for calibrating the charge state and relative spatial distribution of trapped ions, according to the logarithmic dependence relationship between the relative spatial distribution of HCIs-SCIs and the charge state of HCIs, a charge state-ion relative spacing scale for the trapped HCIs-SCIs mixed ion system is established, including:

[0027] Taking the actual trapping potential and the parameters of the HCIs-SCIs mixed ion ensemble as the initial values, the three-dimensional time-dependent position vectors of the entire dynamic steady-state process of the mixed ion ensemble are obtained by using the ion dynamics trajectory tracking method. By inverting the time-dependent position vectors, the equilibrium state spatial distribution diagrams of the HCIs-SCIs mixed ion ensemble with different charge states are determined. The relative positions of SCIs and HCIs in the equilibrium state spatial distribution of the HCIs-SCIs mixed ion ensemble under each charge state are statistically calibrated, and the logarithmic dependence relationship between the relative spatial distribution of the chain-like HCIs-SCIs ion ensemble and the charge state of HCIs is fitted. Experimentally, through a high magnification imaging system, the fluorescence of SCIs ions is collected and imaged at the single photon level in a specific dimension; then, the fitting resolution of the mixed ion ensemble in the same dimension is adjusted to precisely match the imaging resolution of the trapped ion experimental detection system, and further, a charge state-ion relative spacing scale for the trapped HCIs-SCIs mixed ion system corrected by the imaging resolution of the trapped ion experimental detection system is established.

[0028] In the above method for calibrating the charge state and relative spatial distribution of trapped ions, according to the charge state-ion relative spacing scale of the trapped HCIs-SCIs mixed ion system, the charge state and relative spatial distribution of trapped ions are calibrated, including:

[0029] The relative spatial distribution of the HCIs-SCIs ion composition chain-like ion system is not affected by the trapping potential field and the ion mass number, and is only related to the ionization charge number of HCIs ions; the dHCIs-SCIs / dSCIs-SCIs of the chain-like mixed ion system satisfies a logarithmic transformation function relationship with the ionization charge number of HCIs ions; based on the charge state-ion relative spacing scale of the trapped HCIs-SCIs mixed ion system, a visual precision inversion scale diagram of the HCIs charge state and spatial distribution for precise comparison by the experimental system is reconstructed in sequence; in the reconstructed visual precision inversion scale diagram of the HCIs charge state and spatial distribution, by accurately identifying the maximum probability position distribution and fluorescence broadening of SCIs, the relative position and precise charge state characteristics of HCIs can be accurately inverted, and the charge state and relative spatial distribution of trapped ions can be calibrated.

[0030] Correspondingly, the present invention also discloses a system for calibrating the charge state and relative spatial distribution of trapped ions, including:

[0031] A model construction module for establishing a cooperative action dynamics quantization model of the HCIs-SCIs mixed ion system;

[0032] A relationship determination module, configured to determine the logarithmic dependence relationship between the relative spatial distribution of HCIs-SCIs and the charge state of HCIs according to the cooperative action kinetic quantization model of the HCIs-SCIs mixed ion system;

[0033] A scale establishment module, configured to establish a charge state-ion relative spacing scale for confining the HCIs-SCIs mixed ion system according to the logarithmic dependence relationship between the relative spatial distribution of HCIs-SCIs and the charge state of HCIs;

[0034] A calibration module, configured to calibrate the charge state and relative spatial distribution of the trapped ions according to the charge state-ion relative spacing scale of the trapped HCIs-SCIs mixed ion system, and gives a scheme for realizing real-time and non-destructive precise inversion of the relative position and charge state of HCIs.

[0035] The present invention has the following advantages:

[0036] (1) The method of the present invention constructs a mechanical model library of trapped ions based on the time-dependent finite element method, and on this basis, establishes a sub-nanosecond resonant dynamics model of the HCIs-SCIs mixed ion ensemble with the molecular dynamics trajectory tracking method as the core. Based on this model and combined with experimental mechanical parameters, the quantitative resonant and cooling dynamics coupling relationship of the HCIs-SCIs mixed ions is obtained, and then the efficiency boundary of the charge state on the cooperative action of the mixed ions is quantitatively calibrated. This method fills the blank of the calculation model of the interaction between the charge state and the radiofrequency trapped ion ensemble, and provides strong support for the quantitative evaluation and regulation of the charge state additional effect.

[0037] (2) Based on the sub-nanosecond resonant dynamics model of the HCIs-SCIs mixed ion ensemble, the present invention integrates the kinematic time-delay exposure method to realize sub-micron resolution imaging of the HCIs-SCIs mixed ion ensemble, and performs co-resolution matching with the experimental detection system, and then obtains the charge-dependent spatial distribution map of the HCIs-SCIs mixed ion ensemble. The logarithmic dependence relationship between the relative spatial distribution of HCIs-SCIs and the charge state of HCIs is established for the first time. Based on this relationship, a charge state-ion relative spacing scale for confining the mixed ion ensemble is established, and real-time non-destructive precise inversion of the relative position and charge state of HCIs is realized. This method is a real-time non-destructive quantitative evaluation method, and has extremely accurate predictability for the dynamic characteristics of the HCIs-SCIs mixed ion ensemble.

[0038] (3) This invention focuses on the research of a cooperative regulation kinetic quantization model for HCIs-SCIs hybrid ion ensembles. It is not restricted by ion types or experimental objective conditions, has stronger universality and higher analysis accuracy, fills the modeling gap of HCIs, and can guide the matching of HCIs-SCIs ion ensembles and the optimization of radio frequency trapping parameters in applications, supporting the efficient regulation of HCIs. This method provides a quantization basis for regulating the external state coupling strength, achieving efficient cooperative cooling, and high-fidelity logical measurement, and has important guiding significance for promoting the engineering application process of high-performance ion clocks. Brief Description of the Drawings

[0039] Figure 1 It is a flowchart of the steps of a method for calibrating the charge state and relative spatial distribution of trapped ions in an embodiment of the present invention;

[0040] Figure 2 is a single 9 Be + Schematic diagram of the axial (a) and radial (b) resonant motion spectra when a single ion is trapped alone;

[0041] Figure 3 is for cooperative cooling of 1 9 Be + -1 58 Ni 12+ Ion pair and schematic diagram of the axial (a) and radial (b) resonant motion spectra when the two ions are trapped alone;

[0042] Figure 4 is 1 9 Be + Ion cooperative cooling of different charge states of 1 58 Ni Q+ (Q HCI = +1 to 28e) to the equilibrium state, schematic diagram of the three-dimensional energy distribution characteristics of the two ions;

[0043] Figure 5 is 2 9 Be + Cooperatively cooling a single different charge state of 58 Ni Q+ To the steady state, schematic diagram of the corresponding relationship between the axial relative distribution of the ion system and the ion charge state;

[0044] Figure 6 is a schematic diagram of the precise inversion scale of the HCIs charge state and spatial distribution. Detailed Embodiments

[0045] To make the objectives, technical solutions, and advantages of the present invention clearer, the following will further describe in detail the disclosed embodiments of the present invention in conjunction with the accompanying drawings.

[0046] One of the core ideas of the present invention is to overcome the deficiencies of the prior art in being unable to quantitatively evaluate the charge state of trapped ions and the relative spatial position of dark ions in real time and non-destructively, and to provide an accurate evaluation and calibration method for the charge state and relative spatial position of trapped ions that can be used in fields such as ion clocks, precision test metrology, quantum computing, and mass spectrometry. Based on the fine inversion of the dynamic correlation coupling characteristics between SCIs and HCIs from the dynamic information of the trapped ion ensemble, the charge state and relative spatial distribution characteristics of HCIs are decoupled to serve the precise control of HCIs. On the one hand, it solves the problems that the charge state is uncontrollable and cannot be accurately evaluated in real time and non-destructively during the ionization and stable trapping processes of ions in the previous linear radiofrequency trap. On the other hand, it solves the problem that the spatial position and dynamic behavior of ions with different charge states as dark ions without radiative fluorescence cannot be accurately sensed and calibrated. Based on the present invention, the accurate evaluation and calibration of the charge state and relative spatial distribution of trapped ions can provide a quantitative basis for the precise quantum state control of HCIs and the development of HCI atomic clocks.

[0047] Such as Figure 1 , in this embodiment, the method for calibrating the charge state and relative spatial distribution of trapped ions includes:

[0048] Step 101, establish a kinetic quantization model for the synergistic effect of the HCIs-SCIs hybrid ion system.

[0049] In this embodiment, the kinetic quantization model for the synergistic effect of the HCIs-SCIs hybrid ion system may specifically include: a trapped SCIs ion ensemble model and a steady-state resonant trapping system for the HCIs-SCIs hybrid ion system.

[0050] Preferably, the establishment process of the trapped SCIs ion ensemble model is as follows: establish an electromagnetic field trapping test device for the ion ensemble, take the original parameters of the SCIs ion ensemble and the electromagnetic field parameters as the initial value conditions, construct a radiofrequency dynamic binding model for the trapped SCIs ion ensemble according to the Mathieu kinetic equation of the ion ensemble, extract the motion spectrum of the SCIs ion system, and achieve an accurate match with the secular motion excitation spectrum by improving the accuracy of the geometric factor; among them, the original parameters of the SCIs ion ensemble include: the mass M of the ion, the charge Q of the ion, and the number N of ions in the ion ensemble; the electromagnetic field parameters of the SCIs ion ensemble include: the frequency Ω of the radiofrequency potential, the amplitude U of the radiofrequency potential rf , the static DC bias voltage U applied to the radiofrequency field dc , the radial geometric factor parameter κ of the ion trap r , the axial geometric factor parameter κ of the ion trap z , the minimum radial distance r from the geometric center of the ion trap to the surface of the ion trap 0 , the equivalent capacitance value C of the ion trap under resonance matching, and the potential well depth D.

[0051] The radio-frequency dynamic confinement model for trapping SCI ions ensemble characterizes the equivalent secular motion, micromotion and equivalent resonant potential of the ions ensemble, and the specific expressions are as follows:

[0052]

[0053] Where r is the coordinate vector of the ions ensemble in the radial central plane, r = (x, y), and x and y are the coordinates of the ions ensemble in the x-direction and y-direction in the rectangular coordinate system of the radial central plane, respectively. t is time, a is the absolute value of the stable confinement parameter of the ions in the x-direction of the axial plane, and q is the absolute value of the stable confinement parameter of the ions in the x-direction of the radial plane.

[0054]

[0055]

[0056] The kinetic model of trapped ions and its characteristic parameters are mainly determined by the characteristics of the electromagnetic field for trapping ions. Therefore, in order to achieve stable trapping of the ion system, it is necessary to optimize and match the trapping electromagnetic field so that the radio-frequency modulation kinetic effect of the ions is greatly suppressed.

[0057] The specific steps for optimizing the electromagnetic field in the stable region of trapped ions are as follows:

[0058] a. Measure the equivalent capacitance value C of the ion trap under resonant matching based on the LC resonance equivalent capacitance method. According to the equivalent capacitance value C, calculate the frequency Ω range in the equivalent pseudopotential model of the electromagnetic field for trapping ions in combination with the principle of capacitive reactance matching circuit.

[0059] b. Evaluate the potential well depth of the ions ensemble under the equivalent pseudopotential model, and inversely determine the theoretical optimal radio-frequency potential parameter interval under the constraint of the frequency Ω range in the equivalent pseudopotential model of the electromagnetic field for trapping ions, so that the radial stable confinement parameter q of the ions within the radio-frequency potential parameter interval is within [0.2, 0.3]; the radio-frequency potential parameters include the frequency Ω of the radio-frequency potential and the amplitude U of the radio-frequency potential rf 。

[0060] c. Substitute the theoretical optimal radio-frequency potential parameter interval determined in step b into the LC resonance test system to optimize the resonance matching of the LC resonance circuit and obtain the optimized radio-frequency potential.

[0061] d. Use physical field modeling software to establish a three-dimensional dynamic potential model of the trapping space of the ion trap under the theoretical optimal radio-frequency potential parameters, and adjust the axial geometric factor of the three-dimensional dynamic potential model to be consistent with the axial direction of the hyperbolic ideal resonant potential model, so as to accurately fit and obtain the axial geometric factor parameter κ of the ion trap z; Adjust the radial geometric factor of the three-dimensional dynamic potential model to be radially consistent with the ideal hyperbolic harmonic potential model, so as to accurately fit and obtain the radial geometric factor parameter κ of the ion trap r 。

[0062] e. Determine the initial energy E of the ion ensemble according to the type of ions to be regulated and the ionization method 0 , and combine the three-dimensional structure of the actual ion trap to set the potential well depth, and the potential well depth satisfies two conditions:

[0063] The first condition is that the potential well depth and the radio frequency potential parameters satisfy the following relationship:

[0064] The second condition is that the potential well depth is 7 to 13 times the initial energy E of the ion ensemble 0 ;

[0065] That is: 7E 0 ≤D≤13E 0 。

[0066] The method for extracting the motion spectrum of the SCIs ion ensemble is as follows:

[0067] The dynamic characteristics of a single SCIs system trapped and cooled by a linear radio frequency trap can be described by the resonant pseudopotential approximation model, and the axial resonant motion characteristics of a single ion are determined by the axial electrostatic potential. After the optimal compensation of the radial additional micromotion of the ions is realized based on the radio frequency photon correlation method, the force characteristics and resonant motion characteristics of the ion system in the radial x and y dimensions tend to be consistent, which are mainly determined by the radio frequency potential and the axial electrostatic potential together. Based on the original parameters of the trapped ion system and the radio frequency dynamic binding model, the Leap Frog kinematic algorithm is used to evaluate the time evolution information of the three-dimensional position vector and velocity vector of all ions during the process of reaching the steady state. Perform Fourier spectrum transformation on this time-dependent kinematic information to obtain the resonant motion spectrum information of the ions

[0068] The method for matching the motion spectrum of a single-component ion system with the excitation frequency points of secular motion is as follows:

[0069] Apply an extremely weak external micro-rotation excitation field to the trapped ion system, scan the excitation field frequency. When the excitation field frequency is close to the resonant secular motion frequency of the ions, the ions will exhibit a resonant enhancement phenomenon. Based on this phenomenon, the secular motion characteristic spectrum of the ions is independently obtained. However, due to the excitation broadening effect, the full width at half maximum of its characteristic spectrum is greater than the result of the Fourier transform spectrum. If the characteristic peak of the Fourier transform spectrum is within the error range of the secular motion excitation spectrum, the rationality of the Fourier transform spectrum can be verified; if the characteristic peak of the Fourier transform spectrum is not within the error range of the secular motion excitation spectrum, it is necessary to further return to the first step to improve the accuracy of the ion trap geometric factor in the original parameters until the characteristic peak of the final Fourier transform spectrum enters the error range of the secular motion excitation spectrum

[0070] As shown in Figure 2 , the three-dimensional harmonic motion spectrum of a single 9 Be + is given. The axial and radial harmonic motion modes are mainly the fundamental modes, and the characteristic peaks of the harmonic motion spectrum are ω Be-z = 238.920 kHz; ω Be-r = 501.648 kHz. The relative matching errors between the characteristic peaks of the spectrum and the secular motion frequencies in the axial and radial directions under the equivalent pseudopotential approximation reach 2.3653% and 2.648% respectively (mainly limited by the measurement error of the harmonic motion spectrum). This shows that the three-dimensional harmonic mode of the single-ion system in the linear trap is very pure, and the high-order harmonic modes can be ignored, and it can be well approximated by the harmonic pseudopotential model.

[0071] Preferably, the establishment process of the steady-state harmonic trapping system of the HCIs-SCIs hybrid ion system is as follows: optimize and correct the electromagnetic field for trapping the SCIs ion ensemble to make it further compatible with the stable trapping conditions of the HCIs, inject the HCIs into the SCIs ion ensemble, evaluate the influence of the HCIs on the dynamic characteristics of the SCIs, achieve the steady-state trapping with a low heating rate of the HCIs-SCIs hybrid ion ensemble, and establish a steady-state dynamic harmonic trapping model for the HCIs-SCIs hybrid ion system.

[0072] The method for optimizing the compatible trapping field of the SCIs and HCIs hybrid ion ensemble is as follows: For the limiting factors such as the non-closed energy level structure of the ion system or the inability to generate the required wavelength laser, currently only 9 Be + , 24 Mg + , 40 Ca + , 87 Sr + , 113 Cd + , 137 Ba + , 171 Yb + and other ion systems with relatively simple energy level structures can be laser cooled. The equivalent pseudopotential, Coulomb coupling, and RF heating effects of the HCIs-SCIs two-ion system vary due to different mass numbers. First, adjust the compatible electromagnetic fields of the two types of ions so that both meet the conditions of the stable trapping region; on this basis, accurately match the stable trapping parameters of the two-ion systems under the same electromagnetic field, so that |q HCI - 0.3| + |q SCI - 0.3| takes the minimum value overall.

[0073] The steady-state kinetic resonance trapping model of the HCIs-SCIs mixed ion system is as follows: In the steady state, the HCIs-SCIs mixed two-ion system performs three-dimensional resonant motion near their respective equilibrium positions, and there is a certain coupling effect. Ignoring the high-order resonance effect, the external state coupling characteristics of the two-ion system can be decomposed into two modes: in-phase and anti-phase, which are represented by the following Hamiltonian:

[0074]

[0075] where are the standard harmonic oscillator ladder operators for the in-phase and anti-phase vibration modes respectively, is the reduced Planck constant. The coupled vibration displacements of HCI and SCI are q HCI , q SCI :

[0076] q HCI ≈z i b 1 sin(ω i t + φ i ) + z o b 2 cos(ω o t + φ o )

[0077]

[0078] where ω i , ω o and φ i , φ o are the eigenfrequencies and phases of the in-phase and anti-phase modes respectively. b 1 and b 2 are the two components of the normalized eigenvector of the in-phase vibration mode. The specific dimension satisfies: z i and z o are the amplitudes of the in-phase and anti-phase vibration modes of the ions. The mass ratio of the single-charge ion pair is μ = m SCI / m HCI . Based on simulation software such as Comsol, an ion trap radio frequency dynamic trapping model and an equivalent pseudopotential model are established.

[0079] Step 102, according to the cooperative action kinetics quantization model of the HCIs-SCIs mixed ion system, determine the logarithmic dependence relationship between the relative spatial distribution of HCIs-SCIs and the charge state of HCIs.

[0080] In this embodiment, based on the fast FFT method, the motion spectrum of the HCIs-SCIs mixed ion ensemble is extracted to verify whether the motion spectrum of the HCIs-SCIs mixed ion ensemble is consistent with the resonant frequency points of the low-order mode coupling theory; if not, the order of the high-order anharmonic potential of the HCIs-SCIs mixed ion ensemble is increased until precise matching; if matched, the characteristic temperature of the HCIs-SCIs mixed ion ensemble under different charge states is further extracted to obtain the influence of the charge state on the dynamic coupling relationship of HCIs-SCIs, and the logarithmic dependence relationship between the relative spatial distribution of HCIs-SCIs and the charge state of HCIs is determined.

[0081] The method and steps for extracting the motion spectrum of the HCIs-SCIs mixed ion ensemble are similar to those for extracting the motion spectrum of the SCIs ion system in step 101, with the only difference being that sequence codes are classified and compiled for HCIs and SCIs ions, and the motion spectrum characteristics of HCIs and SCIs ions are extracted separately.

[0082] The method for determining the resonant frequency points of the low-order mode coupling theory of the HCIs-SCIs mixed ion ensemble is as follows: in the equilibrium ion system, the trapping potential and the Coulomb interaction potential between ions acting on each ion are expanded at its vibration equilibrium position, and the lowest-order effect of the coupled motion equation is solved, from which the three-dimensional resonant mode frequencies and eigenvectors of the ions are obtained as:

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089] Among them,

[0090]

[0091]

[0092] ω z is the axial secular motion frequency of HCIs ions, and ω rf is the radial secular motion frequency of HCIs ions.

[0093] Examples of the extraction of the motion spectrum of the HCIs-SCIs mixed ion ensemble and the verification of its resonant frequency points of the low-order mode coupling theory are as follows: When trapping a single 9Be + Inject a single 58 Ni 12+ into the system, and then 1 9 Be + -1 58 Ni 12+ The double-ion system is chain-distributed along the axis of the linear ion trap. The long-range Coulomb interaction between ions causes the coupling of their respective harmonic vibration characteristics, forming new resonant dynamic behaviors. Figure 3 gives the three-dimensional resonant motion spectrum of a single 9 Be + synergistically cooling a single 58 Ni 12+ to form 1 9 Be + -1 58 Ni 12+ ion pair crystal. In Figure 3 (a), for the synergistic cooling of 1 9 Be + -1 58 Ni 12+ ion pair crystal's axial resonant motion spectrum, 9 Be + , 58 Ni 12+ two sets of resonant frequency points appear simultaneously, ω 1z : (ω Ni-z ≈ω Be-z =261.026 kHz), ω 2z : (ω Ni-z ≈ω Be-z =511.851 kHz). The axial resonant motion modes are tightly coupled together, which is conducive to efficient energy exchange and synergistic cooling. According to the approximate theory of the equilibrium state double-ion mode coupling, for 1 9 Be + -1 58 Ni 12+ the frequency of the axial reverse mode of the ion pair is higher than that of the co-directional mode, which are ω i-z =273.296 kHz and ω o-z =517.924 kHz respectively; in the reverse mode, the resonant intensity of 58 Ni 12+ with a relatively smaller mass number dominates, and the reverse mode amplitude ratio is I(Ni out ) / I(Be out ) = b 2z ×√μ / b 1z =2.484624027; in the co-directional mode, the resonant intensity of 9 Be + with a relatively larger mass number dominates, and the co-directional mode amplitude ratio is I(Niin ) / I(Be in ) = b 1z ×√μ / b 2z = 0.751287932. In contrast, the coupling strength of the axial in-phase mode is higher than that of the anti-phase mode. It can be identified that Figure 3 (a) in the ion pair resonant motion spectrum, the first group of frequencies ω 1z is the in-phase motion mode, and the second group of frequencies ω 2z is the anti-phase motion mode, and the relative matching accuracies reach 4.70082% and 1.18640897% respectively. Figure 3 (a) The relative intensity of the axial resonant motion spectrum is basically consistent with the conclusion of the relative mode amplitude calculated theoretically. In Figure 3 (b) of 1 9 Be + -1 58 Ni 12+ ion pair radial resonant motion spectrum, 9 Be + and 58 Ni 12+ only have resonance at the frequency point of ω 1r :(ω Ni-r ≈ω Be-r = 469.338 kHz). 58 Ni 12+ 's radial resonant motion mode is richer than 9 Be + , with an additional obvious high-frequency resonant mode ω 2r (ω Ni-r = 959.933 kHz). According to the approximate theory of equilibrium state two-ion mode coupling, 1 9 Be + -1 58 Ni 12+ the radial in-phase mode frequency of the ion pair is higher than the anti-phase mode frequency, which are ω i-r = 958.838 kHz, ω o-r = 482.636 kHz respectively. In the in-phase mode, the resonant intensity of the ion with a relatively smaller relative mass number 58 Ni 12+ dominates, and the in-phase amplitude ratio is I( 58 Ni 12+ in ) / I( 9 Be + in ) = 22.8705; in the anti-phase mode, the resonant intensity of the ion with a relatively larger relative mass number 9 Be + dominates, and the anti-phase amplitude ratio is I( 58 Ni12+ out ) / I( 9 Be + out ) = 0.081618976. Theoretical analysis shows that there are weak coupling effects in both the radial in-phase mode and the anti-phase mode of the two ions, and the coupling strength of the in-phase mode is much lower than that of the anti-phase mode. It can be identified that Figure 3 (b) in the radial resonance motion spectrum of the ion pair, the frequency ω 1r is the anti-phase motion mode, 58 Ni 12+ the frequency ω 2r is the in-phase motion mode, and the relative matching accuracies reach 2.755202% and 0.11418% respectively. Figure 3 (b) In 9 Be + the amplitude of the in-phase mode is too weak and is submerged in the spectral noise. The relative intensity of the radial resonance motion spectrum is basically consistent with the conclusion of the relative mode amplitude in the theoretical calculation.

[0094] 1 9 Be + -1 58 Ni 12+ The radial resonance coupling strength of the ion pair is generally weaker than that of the axial direction, and the cooperative cooling efficiency is mainly dominated by the axial resonance coupling effect. The three-dimensional resonance motion spectrum analysis method of the ion pair is in good agreement with the resonance characteristics predicted by the equilibrium two-ion mode coupling theory. The frequency point error mainly comes from the influence of the high-order coupling effect not considered in the mode coupling theory and the measurement error in the simple harmonic motion spectrum analysis. The relative intensity error of the vibration mode mainly comes from the background noise in the simple harmonic motion spectrum.

[0095] The process of extracting the characteristic temperature of the HCIs-SCIs mixed ion ensemble with different charge states is as follows: First, the temperature of each HCI and SCI ion under a specific charge state is precisely extracted. For details, please refer to the patent "A Method for Quantitative Evaluation of the Temperature and Energy of a Three-Dimensional Ion Ensemble". Then, starting from the single charge state, the number of charge states is increased in turn, the kinetic model of the HCIs-SCIs mixed ion ensemble under each charge state is reconstructed, and the characteristic temperature of the HCIs-SCIs mixed ion ensemble under each charge state is obtained in turn. Finally, the quantitative kinetic coupling relationship between the charge state and the HCIs-SCIs is obtained.

[0096] An example of verifying the relationship between the extraction of the characteristic temperature of the HCIs-SCIs mixed ion ensemble with different charge states and the kinetic coupling of cooperative cooling is as follows: Cooperative cooling 1 9 Be + -1 58 Ni 12+ In the ion pair system, 9 Be +The equilibrium three-dimensional secular motion energy of the ion is slightly increased due to the 58 Ni 12+ heating effect compared to single trapping. 58 Ni 12+ has a lower sympathetic cooling efficiency than 9 Be + system's direct cooling efficiency. Therefore, 58 Ni 12+ 's equilibrium three-dimensional secular motion energy is slightly higher than 9 Be + system. Figure 4 shows the three-dimensional energy distribution characteristics of the ion pair at equilibrium for laser cooling 9 Be + sympathetic cooling of different charge states 58 Ni Q+ (Q HCI = +1 to 28e). The solid line of black-square points (red-circle points) is 9 Be + ( 58 Ni Q+ )'s axial secular motion energy, and the solid line of black-up triangles (red-down triangles) is 9 Be + ( 58 Ni Q+ )'s radial secular motion energy. The dashed line of black-up triangles (red-down triangles) is 9 Be + ( 58 Ni Q+ )'s radial micromotion energy. The axial residual micromotion effect of the chain ion system in the linear trap is small enough to be ignored and is not shown in the figure.

[0097] 9 Be + ion's equilibrium energy is mainly dominated by the laser cooling effect and is less affected by 58 Ni Q+ 's charge state. 9 Be + ion's axial secular motion energy is slightly lower than the total radial two-dimensional secular motion energy, and both can be maintained at the order of 1 mK. 58 Ni Q+ ion's equilibrium energy is mainly determined by 9 Be + - 58 Ni Q+ sympathetic cooling efficiency. 58 Ni Q+ 's charge state affects 9 Be + - 58 Ni Q+ The interaction strength between them, thus affecting 58 Ni Q+ the equilibrium state energy. 58 Ni Q+ and 9 Be + the interaction is axially dominant. As 58 Ni Q+ the charge state increases, 9 Be + - 58 Ni Q+ the axial spacing continuously increases, and the axial in-phase and anti-phase mode frequencies of the two ions also increase accordingly, and the axial interaction strength does not decrease significantly. 58 Ni Q+ the axial secular motion energy of Ni can always be maintained at a level comparable to 9 Be + the axial secular motion energy of the Be ion. However, 9 Be + - 58 Ni Q+ the positive correlation of the ion spacing with the increase of the charge state Q reduces the radial coupling strength of the ion system. Therefore 9 Be + - 58 Ni Q+ the radial resonant coupling effect between the ions is much weaker than that in a single-charge ion system with the same mass-to-charge ratio difference. 58 Ni Q+ the radial resonant mode frequency of Ni changes positively with the charge state Q. When 58 Ni Q+ the Q of Ni < +3e, 58 Ni Q+ the too high mass-to-charge ratio of Ni leads to too shallow a radial effective pseudopotential, 9 Be + - 58 Ni Q+ the radial coupling effect between them is extremely low, 58 Ni Q+ the radial dominant resonant frequency of Ni is much lower than 9 Be + the radial dominant resonant frequency, which is not conducive to 58 Ni Q+ the radial sympathetic cooling of Ni, 58 Ni Q+ the radial secular motion energy of Ni increases sharply with the decrease of Q. When 58 Ni Q+ the Q of Ni is in the range of +(3 - 12)e, 58 Ni Q+ the radial effective pseudopotential of Ni increases accordingly,9 Be + - 58 Ni Q+ The coupling effect of the radial motion modes between them is significantly enhanced. 58 Ni Q+ The co-cooling efficiency reaches the optimum. When 58 Ni Q+ has Q > +12e, 58 Ni Q + the radial equivalent pseudopotential of 58 Ni Q+ exceeds the adiabatic confinement region of the ions, 58 Ni Q+ and 9 Be + it is difficult to achieve strong resonance in the radial motion mode of 58 Ni Q+ and the energy of the radial secular motion of 58 Ni Q+ increases accordingly. The radial micromotion effect of the 58 Ni Q+ ions is positively correlated with the amplitude of the radial secular motion and increases with the increase of the energy of the radial secular motion. Since 58 Ni Q+ the radial secular motion of 58 Ni 12+ is much stronger than the axial one, the equilibrium state characteristics of

[0098] Step 103: Establish a charge state-ion relative spacing scale for the trapped HCIs-SCIs hybrid ion system according to the logarithmic dependence between the relative spatial distribution of HCIs-SCIs and the charge state of HCIs.

[0099] In this embodiment, taking the actual trapping potential and the parameters of the HCIs-SCIs mixed ion ensemble as the initial values, the ion dynamics trajectory tracking method is used to obtain the three-dimensional time-dependent position vectors of the entire dynamic steady-state process of the mixed ion ensemble. By inverting the time-dependent position vectors, the equilibrium state spatial distribution maps of the HCIs-SCIs mixed ion ensemble with different charge states are determined. The relative positions of SCIs and HCIs in the equilibrium state spatial distribution of the HCIs-SCIs mixed ion ensemble under each charge state are statistically calibrated, and the logarithmic dependence relationship between the relative spatial distribution of the chain-like HCIs-SCIs ion ensemble and the charge state of HCIs is fitted. Experimentally, through a high-magnification imaging system, the fluorescence of SCIs ions is collected and imaged at the single-photon level in a specific dimension. Then, the fitting resolution of the mixed ion ensemble in the same dimension is adjusted to exactly match the imaging resolution of the trapped ion experimental detection system, and thus a charge state-ion relative spacing scale of the trapped HCIs-SCIs mixed ion system corrected by the imaging resolution of the trapped ion experimental detection system is established.

[0100] Among them, the method for obtaining the relative spatial distribution map of the equilibrium state of the HCIs-SCIs mixed ion ensemble is as follows: The time evolution information of the full-time domain position vectors of all ions in the ion ensemble in S1 is sampled by time-delayed exposure according to the time scale in the Leap Frog kinematic algorithm, and multiple sampled values are weighted averaged and three-dimensionally graphically displayed. For the imaging plane consistent with the experimental detection system, the fluorescence intensity projection is accumulated, and the time-delayed fluorescence broadening information of the ions on the preset projection plane can be obtained. The time-delayed fluorescence broadening information is the full width at half maximum of the normalized intensity distribution of the radiation fluorescence of the ions, and the full width at half maximum refers to the emission width when the emission intensity of the ions decreases to half of the peak value.

[0101] An example of fitting and verifying the logarithmic dependence relationship between the relative spatial distribution of the HCIs-SCIs mixed ion ensemble and the charge state of HCIs is as follows: A chain-like 2 9 Be + +1 58 Ni Q+ ion system stably trapped in a linear ion trap. According to 58 Ni Q+ the different positions, there are three distribution structures in total: right (R) type, left (L) type, and middle (M) type. The centroids of the three types of distributions always remain the same. Among them, the R type and the L type have lower potential energy and are stable structures; the M type is an unstable structure. Both the R type and the L type can be used as highly sensitive sensing systems for the HCI charge state and relative spatial distribution. Figure 5 Two 9 Be + cooperatively cooled single different charge states 58 Ni Q+ to the steady state (R type), the axial relative distribution of the ion system and the ion charge state QHCI The corresponding relationship between them. When Q HCI = +1e, d Be-Ni = d Be-Be . As Q increases, d Be-Be basically remains unchanged, d Be-Ni increases in a logarithmic trend. By fitting, d Be-Ni / d Be-Be and Q satisfy the following logarithmic function relationship:

[0102] d Be-Ni / d Be-Be = ln(m + nQ)

[0103] where the fitting parameters are m = 1.628(0.074) and n = 1.045(0.020).

[0104] Step 104: According to the charge state-ion relative spacing scale of the trapped HCIs-SCIs mixed ion system, calibrate the charge state and relative spatial distribution of the trapped ions, and give a scheme for realizing real-time and non-destructive precise inversion of the relative position and charge state of HCIs.

[0105] In this embodiment, the relative spatial distribution of the HCIs-SCIs ion composition chain-like ion system is not affected by the trapping potential field and the ion mass number, and is only related to the ionization charge number of the HCIs ions; the dHCIs-SCIs / dSCIs-SCIs of the chain-like mixed ion system satisfies a logarithmic transformation function relationship with the ionization charge number of the HCIs ions; based on the charge state-ion relative spacing scale of the trapped HCIs-SCIs mixed ion system, a visual precision inversion scale map of the charge state and spatial distribution of HCIs that can be accurately compared by the experimental system is reconstructed in sequence; in the reconstructed visual precision inversion scale map of the charge state and spatial distribution of HCIs, by accurately identifying the maximum probability position distribution and fluorescence broadening of SCIs, the relative position and accurate charge state characteristics of HCIs can be accurately inverted, and the charge state and relative spatial distribution of the trapped ions can be calibrated.

[0106] The verification example of the real-time, accurate and non-destructive inversion of the relative spatial distribution of the HCIs-SCIs mixed ion ensemble and the accurate charge state of HCIs based on the logarithmic dependence relationship is as follows: The charge state and relative position scale map of HCIs inverted based on the sub-micron single-photon imaging spatial distribution information of all charge state ions established in step 103 is as Figure 6 shown. The coordinate resolution is 0.3 microns, and the coordinate error is less than 1.5 microns. Since the coordinate change of the mixed ion ensemble caused by the integer charge state difference is greater than 4 microns, the HCIs ion charge state identification method can meet the integer charge resolution requirement.

[0107] In summary, in order to accurately evaluate and calibrate the charge state and relative spatial position of trapped ions, the method of the present invention first evaluates the original parameters of the trapped SCI ion ensemble, determines the initial trapped electromagnetic field parameters, and establishes a model of the trapped SCI ion ensemble; then optimizes and corrects the electromagnetic field of the trapped SCI ion ensemble so that it can further match the stable trapping conditions of HCIs, injects HCIs into the SCI ion ensemble, evaluates the influence of HCIs on the dynamic coupling characteristics of SCIs, realizes the steady-state cooling of the HCI-SCI hybrid ion ensemble, and establishes the steady-state resonant dynamics of the HCI-SCI hybrid ion system; on this basis, evaluates the (resonant and cooling) dynamic coupling relationship between HCIs and SCIs; then, determines the logarithmic dependence relationship between the relative spatial distribution of chain-like HCIs-SCIs and the charge state of HCIs according to the actual trapping potential and the parameters of the HCI-SCI hybrid ions, and establishes a charge state-ion relative spacing scale for the trapped hybrid ion system; finally, based on the charge state-ion relative spacing scale of the trapped hybrid ion system in the determined coordinate system, inversely calculates the relative position and charge state of HCIs.

[0108] Based on the above embodiments, the present invention also discloses a system for calibrating the charge state and relative spatial distribution of trapped ions, including: a model construction module for establishing a quantitative model of the cooperative dynamics of the HCI-SCI hybrid ion system; a relationship determination module for determining the logarithmic dependence relationship between the relative spatial distribution of HCIs-SCIs and the charge state of HCIs according to the quantitative model of the cooperative dynamics of the HCI-SCI hybrid ion system; a scale establishment module for establishing a charge state-ion relative spacing scale for the trapped HCI-SCI hybrid ion system according to the logarithmic dependence relationship between the relative spatial distribution of HCIs-SCIs and the charge state of HCIs; a calibration module for calibrating the charge state and relative spatial distribution of trapped ions according to the charge state-ion relative spacing scale of the trapped HCI-SCI hybrid ion system, and providing a scheme for realizing real-time and non-destructive precise inversion of the relative position and charge state of HCIs.

[0109] For the system embodiment, since it corresponds to the method embodiment, the description is relatively simple. For related parts, please refer to the description in the method embodiment section.

[0110] Although the present invention has been disclosed above with preferred embodiments, it is not used to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention without departing from the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

[0111] The content not detailed in the specification of the present invention belongs to the well-known technology of those skilled in the art.

Claims

1. A method for calibrating the charge state and relative spatial distribution of trapped ions, characterized in that, it includes: establishing a kinetic quantization model for the synergistic effect of the HCIs-SCIs mixed ion system; determining the logarithmic dependence relationship between the relative spatial distribution of HCIs-SCIs and the charge state of HCIs according to the kinetic quantization model for the synergistic effect of the HCIs-SCIs mixed ion system; establishing a charge state-ion relative spacing scale for the trapped HCIs-SCIs mixed ion system according to the logarithmic dependence relationship between the relative spatial distribution of HCIs-SCIs and the charge state of HCIs; including: taking the actual trapping potential and the parameters of the HCIs-SCIs mixed ion ensemble as the initial values, using the ion kinetic trajectory tracking method to obtain the three-dimensional time-dependent position vector of the entire kinetic steady-state process of the mixed ion ensemble, and determining the equilibrium state spatial distribution diagram of the HCIs-SCIs mixed ion ensemble with different charge states through the inversion of the time-dependent position vector, statistically calibrating the relative positions of SCIs and HCIs in the equilibrium state spatial distribution of the HCIs-SCIs mixed ion ensemble with each charge state, and fitting the logarithmic dependence relationship between the relative spatial distribution of the chain-like HCIs-SCIs ion ensemble and the charge state of HCIs; experimentally, through a high magnification imaging system, collecting and imaging the fluorescence of SCIs ions at the single photon level in a specific dimension; then adjusting the fitting resolution of the mixed ion ensemble in the same dimension to accurately match the imaging resolution of the trapped ion experimental detection system, and further establishing a charge state-ion relative spacing scale for the trapped HCIs-SCIs mixed ion system corrected by the imaging resolution of the trapped ion experimental detection system; calibrating the charge state and relative spatial distribution of the trapped ions according to the charge state-ion relative spacing scale of the trapped HCIs-SCIs mixed ion system, and giving a scheme for realizing the real-time and non-destructive precise inversion of the relative position and charge state of HCIs.

2. The method for calibrating the charge state and relative spatial distribution of trapped ions according to claim 1, characterized in that, establishing a kinetic quantization model for the synergistic effect of the HCIs-SCIs mixed ion system includes: establishing a trapped SCIs ion ensemble model; establishing a steady-state resonant trapping system for the HCIs-SCIs mixed ion system.

3. The method for calibrating the charge state and relative spatial distribution of trapped ions according to claim 2, characterized in that, establishing a trapped SCIs ion ensemble model includes: Establish an electromagnetic field confinement test device for the ion ensemble. Taking the original parameters of the SCIs ion ensemble and the electromagnetic field parameters as the initial value conditions, according to the Mathieu dynamic equation of the ion ensemble, construct a radio frequency dynamic binding model for confining the SCIs ion ensemble, extract the motion spectrum of the SCIs ion ensemble, and achieve an accurate match with the secular motion excitation spectrum by improving the accuracy of the geometric factor; among them, the original parameters of the SCIs ion ensemble include: the mass M of the ion, the charge Q of the ion, and the number of ions N in the ion ensemble; the electromagnetic field parameters of the SCIs ion ensemble include: the frequency Ω of the radio frequency potential, the amplitude U of the radio frequency potential rf , the static DC bias voltage U applied to the radio frequency field dc , the radial geometric factor parameter κ of the ion trap r , the axial geometric factor parameter κ of the ion trap z , the minimum radial distance r from the geometric center of the ion trap to the surface of the ion trap 0 , the equivalent capacitance value C of the ion trap under resonance matching, and the potential well depth D.

4. The method for calibrating the charge state and relative spatial distribution of trapped ions according to claim 3, characterized in that, establishing a steady-state resonant trapping system for the HCIs-SCIs mixed ion system includes: optimizing and correcting the electromagnetic field of the trapped SCIs ion ensemble so that it can further be compatible and match the stable trapping conditions of HCIs, injecting HCIs into the SCIs ion ensemble, evaluating the influence of HCIs on the kinetic characteristics of SCIs, realizing the steady-state trapping with a low heating rate of the HCIs-SCIs mixed ion ensemble, and establishing a steady-state kinetic resonant trapping model for the HCIs-SCIs mixed ion system.

5. The method for calibrating the charge state and relative spatial distribution of trapped ions according to claim 4, characterized in that, according to the kinetic quantization model of the cooperative effect of the HCIs-SCIs mixed ion system, to determine the logarithmic dependence relationship between the relative spatial distribution of HCIs-SCIs and the charge state of HCIs, including: extracting the motion spectrum of the HCIs-SCIs mixed ion ensemble based on the fast FFT method, and verifying whether the motion spectrum of the HCIs-SCIs mixed ion ensemble is consistent with the resonant frequency points of the low-order mode coupling theory; if not, increasing the order of the high-order anharmonic potential of the HCIs-SCIs mixed ion ensemble until precise matching; if matching, further extracting the characteristic temperature of the HCIs-SCIs mixed ion ensemble under different charge states, obtaining the influence of the charge state on the kinetic coupling relationship of HCIs-SCIs, and determining the logarithmic dependence relationship between the relative spatial distribution of HCIs-SCIs and the charge state of HCIs.

6. The method for calibrating the charge state and relative spatial distribution of trapped ions according to claim 5, characterized in that, according to the charge state-ion relative spacing scale of the trapped HCIs-SCIs mixed ion system, to calibrate the charge state and relative spatial distribution of trapped ions, including: the relative spatial distribution of the HCIs-SCIs ion composition chain-like ion system is not affected by the trapping potential field and the ion mass number, and is only related to the ionization charge number of the HCIs ions; the dHCIs-SCIs / dSCIs-SCIs of the chain-like mixed ion system satisfies a logarithmic transformation function relationship with the ionization charge number of the HCIs ions; based on the charge state-ion relative spacing scale of the trapped HCIs-SCIs mixed ion system, reconstructing in sequence the visual precision inversion scale map of the HCIs charge state and spatial distribution for precise comparison by the experimental system; in the reconstructed visual precision inversion scale map of the HCIs charge state and spatial distribution, by accurately identifying the maximum probability position distribution and fluorescence broadening of the SCIs, the relative position and precise charge state characteristics of the HCIs can be accurately inverted, and the charge state and relative spatial distribution of the trapped ions can be calibrated.

7. A system for calibrating the charge state and relative spatial distribution of trapped ions for implementing the method according to claim 1, characterized in that, comprising: a model construction module for establishing a kinetic quantization model of the cooperative effect of the HCIs-SCIs mixed ion system; a relationship determination module for determining the logarithmic dependence relationship between the relative spatial distribution of HCIs-SCIs and the charge state of HCIs according to the kinetic quantization model of the cooperative effect of the HCIs-SCIs mixed ion system; a scale establishment module for establishing a charge state-ion relative spacing scale of the trapped HCIs-SCIs mixed ion system according to the logarithmic dependence relationship between the relative spatial distribution of HCIs-SCIs and the charge state of HCIs. Calibration module, which is used to calibrate the charge state and relative spatial distribution of trapped ions according to the charge state-ion relative spacing scale for trapping the HCIs-SCIs mixed ion system, and gives a scheme for realizing real-time and non-destructive precise inversion of the relative position and charge state of HCIs.

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