阅读说明：本技术 一种混合离子体系的双射频囚禁与势场匹配方法 (Double-radio-frequency trapping and potential field matching method for mixed ion system ) 是由 杜丽军 蒙艳松 贺玉玲 张立新 谢军 于 2021-06-25 设计创作，主要内容包括：本发明涉及一种混合离子体系的双射频普适性囚禁与势场匹配方法,属于冷离子频率标准技术领域。建立离子阱双射频动态束缚模型,量化分析了双射频势场下单组份离子体系的等效赝势模型、稳定束缚条件、微运动与久期运动的三维关联耦合特征,通过分析离子的微运动瞬态过程,界定第二囚禁频率的临界绝热束缚强度。匹配轻离子的高频囚禁势频率及幅度,实现轻离子的准绝热稳定囚禁。匹配重离子的低频囚禁势频率,有效抑制低频势对轻离子的谐振激发效应和微运动加热效应。在维持重离子准绝热外态操控的同时,通过提升低频势场强度,改善大质荷比差异混合三维离子体系的空间耦合强度和动力学模式匹配效率,实现外态高效协同作用、甚至振动基态冷却。(The invention relates to a double-radio-frequency universal trapping and potential field matching method for a mixed ion system, and belongs to the technical field of cold ion frequency standards. Establishing an ion trap dual-radio-frequency dynamic constraint model, quantitatively analyzing an equivalent pseudopotential model, a stable constraint condition and three-dimensional correlation coupling characteristics of micro-motion and long-term motion of a single-component ion system in a dual-radio-frequency potential field, and defining the critical adiabatic constraint strength of the second trapping frequency by analyzing the micro-motion transient process of ions. And matching the high-frequency trapping frequency and amplitude of the light ions to realize quasi-adiabatic stable trapping of the light ions. The low-frequency trapping potential frequency of the heavy ions is matched, and the resonance excitation effect and the micromotion heating effect of the low-frequency potential on the light ions are effectively inhibited. The space coupling strength and the dynamic mode matching efficiency of a large mass-to-charge ratio difference mixed three-dimensional ion system are improved by improving the low-frequency potential field strength while maintaining the quasi-adiabatic external state control of heavy ions, and the efficient synergistic effect of the external state and even the vibration ground state cooling are realized.)

1. A method for dual radio frequency trapping and potential field matching for mixed ionic systems, the method comprising the steps of:

firstly, establishing an ion trap double-radio-frequency trapping model;

and secondly, evaluating the influence of the low-frequency trapping field on stable trapping parameters and dynamic coupling characteristics of an ion system based on the ion trap dual-radio-frequency trapping model established in the first step, wherein the specific steps are as follows:

when used to trap ions, a low frequency trapping field (Ω)_rf2，U_rf2) At the mostSimultaneous high-frequency confinement of a well-stabilized confinement region_rf1，U_rf1) When the ion system is in an extremely weak confinement parameter area, the dual-radio-frequency confinement dynamic characteristic of the ion system is represented by using a low-frequency confinement potential field;

when used to trap ions, a high frequency trapping field (Ω)_rf1，U_rf1) Prolonged frequency of motion (ω) under high frequency trapping field while in the optimal stable trapping region_rf1) Meets omega with the frequency of the low-frequency trapping potential field_rf1＝mΩ_rf2When m is an integer and is less than n, the frequency of the low-frequency trapping field needs to be far away from the long-term motion frequency under the high-frequency trapping field of the ions;

thirdly, coupling and matching the light ion high-frequency trapping field and the heavy ion low-frequency trapping field;

fourthly, optimizing and inhibiting the radio frequency heating effect;

fifthly, carrying out mode matching on the dynamics of the two-component ions;

sixthly, evaluating the cooperative cooling efficiency;

and inverting the ion temperature based on the fluorescence line type of the ions or inverting the equilibrium state temperature of the ions based on the comparison between the time-containing position vector and the fluorescence imaging.

2. The method of claim 1, wherein the method comprises:

in the first step, an ion trap dual-radio-frequency trapping model is established based on simulation software such as Comsol and the like, and the steps are as follows:

the high-frequency trapping potential field in the double-radio-frequency trapping field is (omega)_rf1，U_rf1) The low frequency trapping potential field is (omega)_rf2，U_rf2) The ratio of the frequency in the high frequency trapping field to the frequency in the low frequency trapping field is Ω_rf1/Ω_rf2＝n；

Potential field experienced by ions trapped in a quadrupole linear ion trapComprises the following steps:

wherein omega_rf1The frequency of the high frequency trapping potential field; u shape_rf1The amplitude of the high frequency trapping potential field; omega_rf2The frequency of the low frequency trapping field; u shape_rf2The amplitude of the low frequency trapping potential field; t is the time of day and t is,radial distribution coordinates of the potential field in the ion trap; r is₀The minimum distance from the radial geometric center of the ion trap to the surface of the electrode; kappa_zAs an axial geometry factor parameter, U, of the ion trap_endFor static DC bias voltage applied to the end electrode of the ion trap, 2z₀Is an axial trapping region of the ion trap; z is an axial distribution coordinate of the potential field in the ion trap;

the Mathieu equation for the radial motion of ions in the above-mentioned potential field is:

where r ═ (x, y), a, q, p, and ξ are four dimensionless parameters, each of which is

Wherein, κ_rAs a parameter of the radial geometry factor, U, of the ion trap_dcFor a static dc bias voltage applied to the RF potential, Q and M are the charge and mass, respectively, of the trapped ions.

3. The method of claim 1, wherein the method comprises:

in the third step, the coupling matching method for the light ion high-frequency trapping field and the heavy ion low-frequency trapping field is as follows:

high frequency field omega_rf1The light ions are imprisoned, and the low-frequency field omega is_rf2The heavy ions are trapped, and the low-frequency trapping field frequency omega is required_rf2Is far less than the high-frequency trapping field frequency omega_rf1And far away from the long-term motion frequency of the light ions and requiring the low-frequency field amplitude U_rf2Much smaller than the high-frequency field amplitude U_rf1And the low-frequency excitation intensity is suppressed.

4. The method of claim 1, wherein the method comprises:

in the fourth step, the method for optimizing and inhibiting the radio frequency heating effect comprises the following steps:

on the premise that the ionic system meets the quasi-adiabatic interaction, the radio frequency binding strength of the outer ionic system is improved, so that the relative distance between the inner ionic system and the outer ionic system is favorably compressed, the interaction between the inner ionic system and the outer ionic system is enhanced, and the energy exchange efficiency of the mixed ionic system is improved.

5. The method of claim 1, wherein the method comprises:

in the fifth step, the method for performing pattern matching on the dynamics of the two-component ions comprises the following steps:

the three-dimensional low-temperature ion system presents a body-centered cubic structure, in the process of injecting low-mass-to-charge-ratio ions, light ions are distributed in the inner layer of the mixed ion system, heavy ions are distributed in the outer layer of the mixed ion system, the radial distance between the heavy ions and the light ion system is regulated and controlled by changing parameters of a dual radio frequency potential field, when the radial distance between the heavy ions and the light ions is larger than the lattice size of the heavy ions, the equivalent resonance behaviors of the heavy ions and the light ions are relatively independent, the degree of motion and energy coupling between the inner layer ions and the outer layer ions is lower, the cooperative cooling is not facilitated, when the radial relative distance between the heavy ions and the light ions is smaller than the lattice size of the heavy ions, the equivalent resonance behaviors of the inner layer ions and the outer layer ions are mutually influenced, the motion and energy characteristics of the heavy ions and the light ions are tightly coupled together, and the radio frequency heating effect of the heavy ions is transmitted to the light ions through the strong coupling effect between the inner layer ions and the outer layer ions because the confinement strength of the heavy ions exceeds the quasi-adiabatic interaction range, and when the radial distance between the light ions and the heavy ions is matched with the size of the crystal lattice, the light ions fill the crystal lattice vacancies of the heavy ion crystal and are stably bound by the three-dimensional coulomb crystal lattice of the heavy ions, and the cooperative cooling efficiency between the light ions and the heavy ions reaches the maximum.

6. The method of claim 1, wherein the method comprises:

in the second step, the optimal stable confinement region means that p is more than or equal to 0.08 and less than or equal to 0.35, and the extremely weak confinement parameter region means that q is less than or equal to 0.08.

7. The method of claim 1, wherein the method comprises:

in the second step, a dual radio frequency field (Ω)_rf1＝3.7148MHz，U_rf1＝200V)、(Ω_rf2＝2.6268MHz，U_rf2100V) and simultaneously in an optimal stable trapping parameter (q is p is 0.15), the plasma system is spatially distributed on a radio frequency (x-y) potential section in a single micro-motion period time scale, the micro-motion of the ion system is regarded as a result of the mutual modulation of high-frequency small-amplitude fast micro-motion and low-frequency large-amplitude slow micro-motion, the long-term motion frequency of the ions under high-frequency trapping is higher, and the profile characteristic of the ion system is further dominated; under the influence of a low-frequency modulation field, the radial profile of an ion system extends, the three-dimensional ion system still follows a relatively fixed evolution track, and the evolution process comprises dynamic coupling information of high-frequency trapping and low-frequency trapping.

8. The method of claim 1, wherein the method comprises:

in the third step, the double radio-frequency trapping mixed ion system is analyzedThe potential field matching method comprises the following steps: aiming at double-frequency trapping of a double-ion system with a mass-to-charge ratio difference of 40 times, firstly, a group of high-frequency trapping potential fields are arranged to enable light ions to stably trap q_L,rf10.14 long-term exercise frequency of ω_L,rf14.598MHz, the high frequency trapping field contains heavy ions q_H,rf1The equivalent pseudopotential depth is shallower at 0.0035, on the basis of which a set of low-frequency trapping fields is matched, the frequency of which is Ω_rf2Much less than omega_L,rf1Light ions can not be excited to generate resonance, and low-frequency trapping potential amplitude U is regulated and controlled_rf2The heavy ion trapping intensity is changed relatively independently.

9. The method of claim 1, wherein the method comprises:

in the fifth step, the first step is carried out,

fifthly, the method for carrying out pattern matching on the dynamics of the two-component ions comprises the following steps: the position sequences of the 12 light ions from left to right are respectively L₁,L₂,……，L₁₂，(L₄,L₉) Simultaneously meets the requirements of ion trap confinement and three-dimensional coulomb lattice confinement, is stably bound in the vacancy of the heavy ion crystal and other light ions (L)₁～L₃,L₅～L₈,L₁₀～L₁₂) The high-frequency trapping effect and the strong coulomb repulsion effect of the heavy ions perform axial one-dimensional simple harmonic vibration, the axial resonance motion of the light ions is generated by the radial micro motion of the heavy ions through the synergistic effect excitation between the double-ion systems, and high-efficiency mode resonance is realized.

10. The method of claim 1, wherein the method comprises:

in the sixth step, the step of evaluating the cooperative cooling efficiency is as follows: l is₄And L₉Ions are stably trapped in a three-dimensional heavy ion lattice, a high-frequency trapping effect and a two-component ion synergistic effect realize better matching, the long-term motion energy of the equilibrium state is similar to that of heavy ions, and the mK magnitude is lowWen, three groups L⁺Ion (L)₁～L₃,L₅～L₈,L₁₀～L₁₂) Under the synergistic action of heavy ions, the heavy ions do axial resonance motion, and the energy ratio L of long-term motion of the equilibrium state₄、L₉The ion is obviously higher by one order of magnitude, (L)₃，L₅)、(L₈，L₁₀) Two groups of ions are respectively connected with L₄、L₉The ions are adjacent in position, and the cooperative cooling efficiency is far stronger than L₁、L₂、L₆、L₇、L₁₁、L₁₂The integral temperature of the ionic system for ion and cooperative cooling can be controlled within 0.1K, and efficient cooperative cooling of the mixed ionic system is realized.

Technical Field

The invention relates to an ion system radio frequency trapping method, in particular to a double radio frequency universal trapping and potential field matching method for a mixed ion system, and belongs to the technical field of cold ion frequency standards.

Background

The realization of high stability, low heating trapping and precise quantum state control of a specific ion system is the key for developing a high-performance ion clock, preparing a precise measurement quantum system, constructing a high-fidelity quantum logic gate and developing a mass spectrometer with an ultra-large detection range. Currently, ion trapping technology can achieve dynamic confinement of light to electrons and heavy to macro cluster ions.

The method is limited by factors such as an ion trap structure and potential field parameters, the optimal trapping frequencies of different types of ions are greatly different, the radio frequency trapping frequency of the ultra-light ions such as electrons is in the GHz level, the trapping frequency of common atomic ions is in the MHz level, the trapping frequency of heavy molecular ions is in the kHz level, and the trapping frequency of a macro charged particle cluster is in the ten Hz level. When the size of the ion trap is fixed, the optimal trapping frequency of a charged particle system is reduced along with the increase of the mass-to-charge ratio of trapped ions. The method is used for stably trapping mixed ion systems with different mass-to-charge ratios based on the radio frequency ion trap, and has important application in the fields of quantum logic spectroscopy, ion optical clocks, anti-substance preparation, dark ion detection, cold molecular ion precision measurement and the like. However, the difference in mass-to-charge ratios between the constituent ions in a mixed ionic system results in a large difference in the respective optimum trapping frequencies. In the trapping and collaborative cooling experiment of the mixed ion system based on a single radio frequency potential field, the binding strength of high-mass-to-charge-ratio (heavy) ions is far weaker than that of low-mass-to-charge-ratio (light) ions, and whether the two ions can realize collaborative cooling depends on the mass-to-charge ratio difference between the ions. When the mass-to-charge ratio difference of the mixed ion system exceeds a specific critical value, the mixed ion system escapes from the trapping region due to too low binding strength of heavy ions, or the mixed ion system escapes from the trapping region due to the fact that the light ion trapping parameter exceeds the stable region, and finally the simultaneous stable trapping of two ions is difficult to realize by optimizing a single radio frequency potential field. When the mass-to-charge ratio difference of the mixed ion system does not exceed a specific critical value, the heavy ions are distributed on the periphery of the light ions and are trapped together in a ring-packed configuration, and the interaction between the ion systems with different mass-to-charge ratios is far weaker than the interaction in the same ion system. The strong repulsion potential of the inner layer light ions can push the outer layer heavy ions to be far away from the center of the weak binding potential, and the radio frequency heating effect is further intensified, so that the outer layer ions are continuously escaped from the trapping restricted area. This current situation limits the application range and efficiency of cooperative cooling between heavy ions and light ions, and is not favorable for detection and control of cooperative cooling ions (dark ions).

In the study of anti-species trapping, the professor Dehmelt firstly proposes that differential ions with large mass-to-charge ratios can be trapped simultaneously based on a double radio frequency field, but because the efficient cooling method of the ions at that time is not mature, the double-frequency trapping method cannot be systematically analyzed and verified.

The scheme in the literature can realize the simultaneous trapping and cooling of the mixed ion system with similar mass-to-charge ratio. However, there are the following problems:

1) in the trapping and collaborative cooling experiment of the mixed ion system based on a single radio frequency potential field, the binding strength of high-mass-to-charge-ratio (heavy) ions is far weaker than that of low-mass-to-charge-ratio (light) ions, and whether the two ions can realize collaborative cooling depends on the mass-to-charge ratio difference between the ions. When the mass-to-charge ratio difference of the mixed ion system exceeds a specific critical value, the mixed ion system escapes from the trapping region due to too low binding strength of heavy ions, or the mixed ion system escapes from the trapping region due to the fact that the light ion trapping parameter exceeds the stable region, and finally the simultaneous stable trapping of two ions is difficult to realize by optimizing a single radio frequency potential field. The maximum mass-to-charge ratio difference of the mixed ionic systems in the literature does not exceed 7, and the caging applicability is limited.

2) In the literature, for a three-dimensional ion system with the mass-to-charge ratio difference of a mixed ion system not exceeding a specific critical value, heavy ions are distributed on the periphery of light ions and commonly trapped in a ring-packed configuration, and the interaction between ion systems with different mass-to-charge ratios is far weaker than the interaction between the ion systems with the same mass-to-charge ratio. The strong repulsion potential of the inner layer light ions can push the outer layer heavy ions away from the center of the weak binding potential to be far away, the radio frequency heating effect is further intensified, the outer layer ions are caused to continuously escape out of the trapping zone, and long-term stable trapping and application are difficult to realize. This current situation limits the application range and efficiency of cooperative cooling between heavy ions and light ions, and is not favorable for detection and control of cooperative cooling ions (dark ions).

3) The current mixed ionic system cooperative cooling application only realizes mode quantization matching in a dual ionic system with low mass-to-charge ratio difference. For more complex ion systems, the spatial coupling strength of the mixed ion system can be improved only to a limited extent, the resonance coefficient and the resonance frequency of the mixed ions are not changed, and the precise coupling matching of the modes is difficult to realize.

Disclosure of Invention

The technical problem solved by the invention is as follows: the method aims to develop a universal high-stability low-heating trapping and control method of a large-mass-to-charge-ratio difference mixed ion system, which can be used in the fields of ion clocks, precise measurement and measurement, quantum calculation, mass spectrometry and the like, and solves the problems that the optimal trapping frequency difference is too large due to different mass-to-charge ratios of all component ions in the conventional mixed ion system, and the mixed ion system is difficult to realize stable trapping by optimizing a single radio-frequency potential field; on the other hand, the problems that simple harmonic vibration modes of ions of all components in the existing mixed ion system are separated, the spatial and dynamic coupling is too weak, and efficient collaborative cooling is difficult to realize are solved. The feasibility of realizing simultaneous optimal radio frequency trapping of ions with different mass-to-charge ratios based on a dual-frequency trapping method is quantitatively researched, the constraint strength of heavy ions is improved, the dynamic coupling effect of the heavy ions and light ions is enhanced, and the method has universality for improving the cooperative cooling efficiency of a mixed ion system.

The technical scheme adopted by the invention is as follows:

a method of dual radio frequency trapping and potential field matching for a mixed ion system, the method comprising the steps of:

firstly, establishing an ion trap dual-radio-frequency trapping model based on simulation software such as Comsol and the like;

the high-frequency trapping potential field in the double-radio-frequency trapping field is (omega)_rf1，U_rf1) The low frequency trapping potential field is (omega)_rf2，U_rf2) The ratio of the frequency in the high frequency trapping field to the frequency in the low frequency trapping field is Ω_rf1/Ω_rf2＝n；

Potential field experienced by ions trapped in a quadrupole linear ion trapComprises the following steps:

wherein omega_rf1The frequency of the high frequency trapping potential field; u shape_rf1The amplitude of the high frequency trapping potential field; omega_rf2The frequency of the low frequency trapping field; u shape_rf2The amplitude of the low frequency trapping potential field; t is the time of day and t is,radial distribution coordinates of the potential field in the ion trap; r is₀The minimum distance from the radial geometric center of the ion trap to the surface of the electrode; kappa_zAs an axial geometry factor parameter, U, of the ion trap_endFor static DC bias voltage applied to the end electrode of the ion trap, 2z₀Is an axial trapping region of the ion trap; z is an axial distribution coordinate of the potential field in the ion trap;

the Mathieu equation for the radial motion of ions in the above-mentioned potential field is:

where r ═ (x, y), a, q, p, and ξ are four dimensionless parameters, each of which is

Wherein, κ_rAs a parameter of the radial geometry factor, U, of the ion trap_dcFor a static dc bias voltage applied to the RF potential, Q and M are the charge and mass, respectively, of the trapped ions;

secondly, evaluating the influence of the low-frequency trapping field on stable trapping parameters and dynamic coupling characteristics of an ion system based on the ion trap dual-radio-frequency trapping model established in the first step;

the high-frequency trapping field and the low-frequency trapping field trapping kinetic effect of the double-radio-frequency trapping medium ion system are coupled together, the coupling strength is enhanced along with the approach of two groups of radio-frequency frequencies, and the low-frequency trapping field (omega) for trapping ions is used_rf2，U_rf2) High-frequency trapping potential field (omega) in the optimal stable trapping region (satisfying that p is more than or equal to 0.08 and less than or equal to 0.35)_rf1，U_rf1) When the ion system is in an extremely weak constraint (q is less than 0.08), the dual-radio-frequency trapping kinetic characteristic of the ion system is characterized by using a low-frequency trapping potential field;

when used to trap ions, a high frequency trapping field (Ω)_rf1，U_rf1) Prolonged frequency of motion (ω) under high frequency trapping field while in the optimal stable trapping region_rf1) Meets omega with the frequency of the low-frequency trapping potential field_rf1＝mΩ_rf2When the ion trapping frequency is/2 (m is an integer and m is less than n), the low-frequency trapping field can cause a resonance excitation heating effect on the ions, so that the ions cannot be stably trapped, and therefore the frequency of the low-frequency trapping field is far away from the long-term motion frequency under the high-frequency trapping field of the ions;

except for the two special cases, the trapping effect of the two groups of radio frequency fields on the ions is tightly coupled and must be considered simultaneously;

in a dual radio frequency field (omega)_rf1＝3.7148MHz，U_rf1＝200V)、(Ω_rf2＝2.6268MHz，U_rf2100V) while being in the optimal stable confinement parameter (q p 0.15), the plasma system is spatially distributed on a radio frequency (x-y) potential cross section within a single micro-motion period time scale, and the micro-motion of the ion system can be regarded as a result of inter-modulation of high-frequency small-amplitude fast micro-motion and low-frequency large-amplitude slow micro-motion. The secular motion frequency of the ions under high-frequency trapping is higher, and the profile characteristics of an ion system are further led. But the radial profile of the ion system is extended to some extent under the influence of the low frequency modulation field. The three-dimensional ion system still follows a relatively fixed evolution track, only the evolution process contains the dynamic coupling information of high-frequency trapping and low-frequency trapping, the micromotion mode is more complex, and the ruleThe law coupling relationship does not introduce new random modes, so the additive heating effect is negligible in the adiabatic steering range.

Thirdly, coupling and matching the light ion high-frequency trapping field and the heavy ion low-frequency trapping field;

in the process of carrying out relatively independent regulation and control of each component ion system based on different frequency radio frequency potential fields, high frequency field omega_rf1The trapping effect on light ions is mainly realized, and the trapping effect on heavy ions can be ignored; low frequency field omega_rf2Mainly plays a role in trapping heavy ions, and because the low-frequency trapping frequency is close to the high-frequency trapping long-term motion frequency magnitude of light ions, the low-frequency field omega_rf2The trapping effect on light ions can be ignored, but the light ions can be excited to generate resonance, so that on one hand, the low-frequency trapping field frequency omega is required_rf2Is far less than the high-frequency trapping field frequency omega_rf1And far away from the long-term motion frequency of light ions, and on the other hand, requires a low-frequency field amplitude U_rf2Much smaller than the high-frequency field amplitude U_rf1Suppressing the low-frequency excitation intensity;

the potential field matching method of the dual radio frequency trapping hybrid ionic system is analyzed by taking dual frequency trapping of the dual ionic system with the mass-to-charge ratio difference of 40 times as an example. Firstly, a group of high-frequency trapping potential fields is set to stably trap q light ions_L,rf10.14 long-term exercise frequency of ω_L,rf14.598MHz, the high frequency trapping field contains heavy ions q_H,rf1The equivalent pseudopotential depth of 0.0035 is shallow, and the trapping effect is negligible. On the basis of which a group of low-frequency trapping fields is matched, the frequency omega of which_rf2Much less than omega_L,rf1Light ions are not excited to generate resonance. By regulating and controlling low-frequency imprisoning potential amplitude U_rf2The heavy ion trapping intensity can be changed relatively independently;

fourthly, optimizing and inhibiting the radio frequency heating effect;

an optimal matching relationship exists between the cooperative cooling efficiency of the mixed ionic system and the double-radio-frequency trapping potential field, the too-weak or too-strong equivalent potential field is not beneficial to improving the cooperative cooling efficiency, on the premise that the ionic system meets the quasi-adiabatic interaction, the radio frequency binding strength of the outer ionic system is properly improved, the relative distance between the inner ionic system and the outer ionic system is favorably compressed, the interaction between the inner ionic system and the outer ionic system is enhanced, the energy exchange efficiency of the mixed ionic system is improved, but the quasi-adiabatic evolution characteristic of the heavy ionic system is prevented from being damaged due to the too-high low-frequency trapping potential strength, and the mixed ionic system cannot be cooled; the too weak equivalent potential field means that P is less than 0.08, and the too strong equivalent potential field means that P is more than 0.35;

fifthly, carrying out mode matching on the dynamics of the two-component ions;

the three-dimensional low-temperature ionic system presents a body-centered cubic structure. During the injection of low mass to charge ratio ions therein, light ions are distributed in the inner layer of the mixed ionic system and heavy ions are distributed in the outer layer of the mixed ionic system. The radial distance between the heavy ion and the light ion system can be regulated and controlled by changing the parameters of the dual radio frequency potential field. When the radial distance between the heavy ions and the light ions is larger than the size of the heavy ion lattice, the equivalent resonance behaviors of the heavy ions and the light ions are relatively independent, and the degree of motion and energy coupling between the inner layer ions and the outer layer ions is low, so that the cooperative cooling is not facilitated. When the radial relative distance between the heavy ions and the light ions is smaller than the size of the heavy ion lattice, the equivalent resonance behaviors of the inner layer ions and the outer layer ions are mutually influenced, and the motion and energy characteristics of the heavy ions and the light ions are closely coupled together. However, since the trapping strength of the heavy ions exceeds the quasi-adiabatic interaction range, the radio frequency heating effect of the heavy ions is transmitted to the light ions through the strong coupling effect between the inner and outer layer ions, so that the light ions cannot be efficiently and synergistically cooled. Only when the radial distance between the light ions and the heavy ions is matched with the size of the crystal lattice, the light ions can fill the crystal lattice vacancies of the heavy ion crystal and are stably bound by the three-dimensional coulomb crystal lattice of the heavy ions, and the synergistic cooling efficiency between the light ions and the heavy ions is extremely high.

The spatial distribution and the motion mode of a mixed ion system in efficient cooperative cooling have L position sequences of 12 light ions from left to right₁,L₂,……，L₁₂。(L₄,L₉) The ion trap trapping and three-dimensional coulomb lattice trapping requirements can be met simultaneously, and the ion trap is stably bound in the heavy ion crystal vacancy. Other light ions (L)₁～L₃,L₅～L₈,L₁₀～L₁₂) And carrying out axial one-dimensional simple harmonic vibration under the combined action of the high-frequency trapping effect and the strong coulomb repulsion effect of the heavy ions. The axial resonance motion of the light ions is generated by the radial micro motion of the heavy ions through the synergistic effect excitation between the double ion systems, and high-efficiency mode resonance is realized.

Sixthly, evaluating the cooperative cooling efficiency;

temperature is one of the most important characterization methods reflecting synergistic cooling efficiency. There are two main methods for obtaining the temperature of the ionic system at present, which are respectively: inverting the ion temperature based on the fluorescence line of the ion; and inverting the equilibrium state temperature of the ions based on the comparison of the time-bearing position vector and the fluorescence imaging. For a multi-ion system, because ions have temperature distribution, and the fluorescence lines of ions with different temperature distributions are overlapped, the finally obtained temperature is the integral contribution of the multi-ions, and the temperature of specific ions and the temperature distribution of three-dimensional ion crystals cannot be reflected. Based on the ion temperature distribution obtained by the time-containing position vector and fluorescence imaging comparison method, the temperature characteristics of each ion can be more accurately reflected.

Equilibrium state energy distribution, L, of cooperative cooling ions obtained based on numerical analysis method₄And L₉Ions are stably trapped in a three-dimensional heavy ion lattice, a high-frequency trapping effect and two-component ions have synergistic effect to realize better matching, and the long-term motion energy of the equilibrium state is similar to that of the heavy ions, so that the low temperature of the mK magnitude is achieved. Three groups L⁺Ion (L)₁～L₃,L₅～L₈,L₁₀～L₁₂) Under the synergistic action of heavy ions, the heavy ions do axial resonance motion, and the energy ratio L of long-term motion of the equilibrium state₄、L₉The ions are significantly higher by one order of magnitude. (L)₃，L₅)、(L₈，L₁₀) Two groups of ions are respectively connected with L₄、L₉The ions are adjacent in position, and the cooperative cooling efficiency is far stronger than L₁、L₂、L₆、L₇、L₁₁、L₁₂Ions. The integral temperature of the cooperative cooling ionic system can be controlled within 0.1K, and the high temperature of the mixed ionic system is realizedThe effect is synergistic cooling.

Compared with the prior art, the method has the following advantages:

(1) according to the scheme, two groups of radio-frequency potentials are introduced to realize simultaneous optimal resonance-free radio-frequency trapping of ions with different mass-to-charge ratios, and an optimal adiabatic control area is achieved while stable trapping parameters of a mixed ion system are improved. Compared with the traditional single-frequency weak binding scheme, the method has the characteristics that the trapping frequency can be independently regulated and controlled, the mass-to-charge ratio application range is greatly expanded, and the like.

(2) According to the scheme, the optimal matching of the resonance coefficient, the spatial coupling and the dynamic mode is realized by independently regulating and controlling the strength of the two groups of trapping potential fields, the binding strength of heavy ions is improved, the dynamic coupling effect of the heavy ions and the light ions is greatly enhanced, the regulation and control mode is compatible with the mode in the single-frequency trapping scheme and is converted into mode customization in double-frequency trapping, the regulation and control mode is more essential, the efficiency is higher, and the universality is realized on the cooperative cooling efficiency of a mixed ion system.

(3) The scheme system provides stable constraint conditions and transient dynamic characteristics of a double-frequency trapping ion system, three-dimensional correlation coupling characteristics of long-term motion and micro-motion, energy coupling relations and other dynamic characteristics. And establishing a cooperative cooling dynamic mode coupling relation and a cooperative cooling efficiency influence factor of the dual-frequency trapping mixed ion system and a promoting method.

(4) The scheme definitely gives the function of the spatial configuration and the mode matching between the laser cooling ions and the cooperative cooling ions in improving the cooperative cooling efficiency of the two-component ion system, and indicates a parameter constraint method and dynamic process influence factors. The method has important instructive significance for promoting the engineering application process of the high-performance atomic clock.

(5) The method comprises the following processes of evaluating the influence of low trapping frequency on stable trapping parameters and dynamic coupling characteristics of a single-component ion system, matching of a light ion high-frequency trapping field, matching of heavy ion low-frequency trapping potential, restraining of light ion excitation effect, optimizing and restraining of radio frequency heating effect, matching of two-component ion space coupling and dynamic mode, evaluating and optimizing of cooperative cooling efficiency and the like.

In order to realize the stable restriction of double radio frequency of the mixed ion system and high-efficiency synergistic cooling. Firstly, establishing an ion trap dual-radio-frequency dynamic constraint model based on simulation software such as Matlab and Comsol, quantitatively analyzing an equivalent pseudopotential model, a stable constraint condition and three-dimensional correlation coupling characteristics of micro-motion and long-term motion of a single-component ion system in a dual-radio-frequency potential field, and defining the critical adiabatic constraint strength of the second trapping frequency by analyzing the micro-motion transient process of ions. And then, matching the high-frequency trapping frequency and amplitude of the light ions to realize quasi-adiabatic stable trapping of the light ions. On the basis, the low-frequency trapping potential frequency of the heavy ions is matched, and the resonant excitation effect and the micromotion heating effect of the low-frequency potential on the light ions are effectively inhibited. And finally, while maintaining the quasi-adiabatic external state control of the heavy ions, improving the space coupling strength and the dynamic mode matching efficiency of a large mass-to-charge ratio difference mixed three-dimensional ion system by improving the strength of a low-frequency potential field, and realizing the high-efficiency synergistic effect of the external state and even the vibration ground state cooling.

Drawings

FIG. 1 is a schematic flow diagram of the process of the present invention;

FIG. 2 shows a dual RF field (Ω)_rf1，U_rf1)、(Ω_rf2，U_rf2) Meanwhile, when the ion is in the optimal stable confinement parameter, the plasma system is distributed in the radial space in a single micromotion period, the (initial) 0 phase of the ion presents diagonal elliptical distribution, the pi/2 phase presents centrosymmetric circular distribution, and the pi phase presents another orthogonal diagonal elliptical distribution;

FIG. 3 is a schematic diagram of a body-centered cubic spatial configuration of a dual-frequency trapping two-component ionic system;

fig. 4 is a schematic diagram of energy distribution of a cooperative cooling ion system in a dual-frequency trapped two-component ion system.

Detailed Description

Referring to fig. 1, a schematic diagram of a dual-radio-frequency universal matching method for realizing high stability, low heating trapping and control of a large-mass-to-charge-ratio differential mixed ion system is shown. The technical scheme comprises the processes of establishing an ion trap dual-radio-frequency trapping model, evaluating the influence of a second trapping frequency on stable trapping parameters and dynamic coupling characteristics of an ion system, coupling and matching light ion high-frequency trapping potential and heavy ion low-frequency trapping potential, optimizing and inhibiting dual-radio-frequency modulation and heating effect, matching three-dimensional space configuration and dynamic mode of a mixed ion system, evaluating and optimizing cooperative cooling efficiency and the like.

(1) Establishment of ion trap double-radio-frequency trapping model

Two groups of radio frequency parameters (omega) are agreed in the double-frequency imprisoning field_rf1，U_rf1)，(Ω_rf2，U_rf2) Has a frequency ratio of omega_rf1/Ω_rf2N, ions trapped in a quadrupole linear ion trap experience a potential field of

Wherein, U_endFor a static DC bias voltage applied to the end electrode of the ion trap, κ_zIs an axial geometry factor parameter of the ion trap. The Mathieu equation describing the radial motion of ions in dual-frequency trapping is as follows:

wherein r is x, y. a, q, p and xi are four dimensionless parameters, respectively

Wherein κ_rAs a parameter of the radial geometry factor, U, of the ion trap_dcFor a static dc bias voltage applied to the RF potential, Q and M are the charge and mass, respectively, of the trapped ions. An ion trap dual-radio-frequency dynamic trapping model and an equivalent pseudopotential model are established based on simulation software such as Comsol and the like.

(2) Evaluation of influence of second trapping frequency on stable trapping parameters and dynamic coupling characteristics of ionic system

Two trapping kinetic effects of an ionic system in dual-frequency trapping are coupled together, with the coupling strength following the two groupsThe proximity of the radio frequency increases. When used to trap ions, a low frequency field (Ω)_rf2，U_rf2) In the optimum stable confinement region, while the high frequency field (omega)_rf1，U_rf1) In the very weakly bound parameter region, the dual-frequency trapping dynamics of the ion system can be approximately described using a single low-frequency trapping field theory. When used to trap ions, a high frequency field (Ω)_rf1，U_rf1) In the optimal stable imprisoning area, and the m omega is satisfied between the frequency of the low-frequency imprisoning field and the long-term motion frequency under high-frequency imprisoning_rf2/2＝ω_rf1When m is an integer and is less than n, the low-frequency trapping potential can cause resonance excitation heating effect on the ions, so that the ions cannot be stably trapped. The low frequency trapping frequency must therefore be far from the secular motion frequency under high frequency trapping of ions. In addition to the two special cases, the trapping effect of the two sets of rf fields on the ions must be considered simultaneously. As shown in fig. 2, a dual radio frequency field (Ω) is given_rf1＝3.7148MHz，U_rf1＝200V)、(Ω_rf2＝2.6268MHz，U_rf2100V) while being in the optimal stable confinement parameter (q p 0.15), the plasma system is spatially distributed on a radio frequency (x-y) potential cross section within a single micro-motion period time scale, and the micro-motion of the ion system can be regarded as a result of inter-modulation of high-frequency small-amplitude fast micro-motion and low-frequency large-amplitude slow micro-motion. The secular motion frequency of the ions under high-frequency trapping is higher, and the profile characteristics of an ion system are further led. But the radial profile of the ion system is extended to some extent under the influence of the low frequency modulation field. The three-dimensional ion system still follows a relatively fixed evolution track, only the evolution process contains the dynamic coupling information of high-frequency trapping and low-frequency trapping, the micromotion mode is more complex, and a new random mode cannot be introduced into the regular coupling relation, so that the additional heating effect in the adiabatic control range can be ignored.

(3) Coupling matching of light ion high-frequency trapping potential and heavy ion low-frequency trapping potential

In the process of carrying out relatively independent regulation and control of each component ion system based on different frequency radio frequency potential fields, high frequency field omega_nMainly has the functions of trapping light ions and trapping effect on heavy ionsCan be ignored; the low-frequency field omega mainly plays a role in trapping heavy ions, and as the low-frequency trapping frequency is close to the high-frequency trapping long-term motion frequency magnitude of the light ions, the trapping effect on the light ions can be ignored, but the light ions can be excited to resonate. On the one hand, therefore, the low-frequency trapping field frequency Ω is required to be much smaller than the high-frequency trapping field frequency Ω_nAnd far away from the long-term motion frequency of light ions, and on the other hand, requires a low-frequency field amplitude U_rfMuch smaller than the high-frequency field amplitude U_nrfAnd the low-frequency excitation intensity is suppressed. The potential field matching method of the dual radio frequency trapping hybrid ionic system is analyzed by taking dual frequency trapping of the dual ionic system with the mass-to-charge ratio difference of 40 times as an example. Firstly, a group of high-frequency trapping potential fields is set to stably trap light ions, and q_L,rf10.14, and a prolonged exercise frequency of ω_L,rf14.598 MHz. Heavy ions q in the high-frequency trapping potential field_H,rf1The equivalent pseudopotential depth is shallow, and the trapping effect can be ignored, namely 0.0035. On the basis of which a group of low-frequency trapping fields is matched, the frequency omega of which_rf2Much less than omega_L,rf1Light ions are not excited to generate resonance. By regulating and controlling low-frequency imprisoning potential amplitude U_rf2The intensity of heavy ion trapping can be varied relatively independently.

(4) Optimized suppression of RF heating effects

An optimal matching relation exists between the cooperative cooling efficiency of the mixed ion system and the double-frequency trapping potential field, and the equivalent potential field which is too weak or too strong is not beneficial to improving the cooperative cooling efficiency. On the premise that the ionic system meets the quasi-adiabatic interaction, the radio frequency binding strength of the outer layer ionic system is properly improved, so that the relative distance between the inner layer ionic system and the outer layer ionic system is favorably compressed, the interaction between the inner layer ion and the outer layer ion is enhanced, and the energy exchange efficiency of the mixed ionic system is improved. But it must be prevented that the quasi-adiabatic evolution characteristics of the heavy ion system are destroyed due to too high intensity of the low-frequency trapping potential, so that the mixed ion system cannot be cooled.

(5) Kinetic pattern matching of two-component ions

The three-dimensional low-temperature ionic system presents a body-centered cubic structure. During the injection of low mass to charge ratio ions therein, light ions are distributed in the inner layer of the mixed ionic system and heavy ions are distributed in the outer layer of the mixed ionic system. The radial distance between the heavy ion and the light ion system can be regulated and controlled by changing the parameters of the dual radio frequency potential field. When the radial distance between the heavy ions and the light ions is larger than the size of the heavy ion lattice, the equivalent resonance behaviors of the heavy ions and the light ions are relatively independent, and the degree of motion and energy coupling between the inner layer ions and the outer layer ions is low, so that the cooperative cooling is not facilitated. When the radial relative distance between the heavy ions and the light ions is smaller than the size of the heavy ion lattice, the equivalent resonance behaviors of the inner layer ions and the outer layer ions are mutually influenced, and the motion and energy characteristics of the heavy ions and the light ions are closely coupled together. However, since the trapping strength of the heavy ions exceeds the quasi-adiabatic interaction range, the radio frequency heating effect of the heavy ions is transmitted to the light ions through the strong coupling effect between the inner and outer layer ions, so that the light ions cannot be efficiently and synergistically cooled. Only when the radial distance between the light ions and the heavy ions is matched with the size of the crystal lattice, the light ions can fill the crystal lattice vacancies of the heavy ion crystal and are stably bound by the three-dimensional coulomb crystal lattice of the heavy ions, and the synergistic cooling efficiency between the light ions and the heavy ions is extremely high.

FIG. 3 shows the spatial distribution and motion pattern of the mixed ion system during efficient cooperative cooling, where the sequence of positions of 12 light ions from left to right is L₁,L₂,……，L₁₂。(L₄,L₉) The ion trap trapping and three-dimensional coulomb lattice trapping requirements can be met simultaneously, and the ion trap is stably bound in the heavy ion crystal vacancy. Other light ions (L)₁～L₃,L₅～L₈,L₁₀～L₁₂) And carrying out axial one-dimensional simple harmonic vibration under the combined action of the high-frequency trapping effect and the strong coulomb repulsion effect of the heavy ions. The axial resonance motion of the light ions is generated by the radial micro motion of the heavy ions through the synergistic effect excitation between the double ion systems, and high-efficiency mode resonance is realized.

(5) Evaluation of synergistic Cooling efficiency

Temperature is one of the most important characterization methods reflecting synergistic cooling efficiency. There are two main methods for obtaining the temperature of the ionic system at present, which are respectively: inverting the ion temperature based on the fluorescence line of the ion; and inverting the equilibrium state temperature of the ions based on the comparison of the time-bearing position vector and the fluorescence imaging. For a multi-ion system, because ions have temperature distribution, and the fluorescence lines of ions with different temperature distributions are overlapped, the finally obtained temperature is the integral contribution of the multi-ions, and the temperature of specific ions and the temperature distribution of three-dimensional ion crystals cannot be reflected. Based on the ion temperature distribution obtained by the time-containing position vector and fluorescence imaging comparison method, the temperature characteristics of each ion can be more accurately reflected.

Fig. 4 shows the equilibrium state energy distribution of the cooperative cooling ions obtained based on the numerical analysis method. L is₄And L₉Ions are stably trapped in a three-dimensional heavy ion lattice, a high-frequency trapping effect and two-component ions have synergistic effect to realize better matching, and the long-term motion energy of the equilibrium state is similar to that of the heavy ions, so that the low temperature of the mK magnitude is achieved. Three groups L⁺Ion (L)₁～L₃,L₅～L₈,L₁₀～L₁₂) Under the synergistic action of heavy ions, the heavy ions do axial resonance motion, and the energy ratio L of long-term motion of the equilibrium state₄、L₉The ions are significantly higher by one order of magnitude. (L)₃，L₅)、(L₈，L₁₀) Two groups of ions are respectively connected with L₄、L₉The ions are adjacent in position, and the cooperative cooling efficiency is far stronger than L₁、L₂、L₆、L₇、L₁₁、L₁₂Ions. The integral temperature of the cooperative cooling ionic system can be controlled within 0.1K, and the efficient cooperative cooling of the mixed ionic system is realized.