A trapped-ion-based rotational angular-velocity sensing system and method

Abstract

The application discloses a kind of based on the rotational angular velocity sensing measurement system and method of trapped ion, the system includes permanent magnet, ion trap, ion trapping electrode, constant voltage power supply and dipole force light source;Permanent magnet is used to generate the magnetic field in z direction, for trapping ion in xy plane;Ion trapping electrode includes four electrodes, when measuring, constant voltage power supply is applied alternating voltage to form rotating electromagnetic field, the polarity of voltage applied to opposite two electrodes is same, the polarity of voltage applied to adjacent two electrodes is opposite;The dipole force light source is used to emit dipole force light beam, and the dipole force light beam is used to entangle the electron spin of ion and the z direction simple harmonic quantum mechanical oscillator of ion;The ion group rotates centric motion around z direction, when there is rotational angular velocity input outside, the ion group and coriolis force coupling, produce simple harmonic motion in z direction.In rotational measurement accuracy aspect, it has reached new height.

Description

Technical Field

[0001] This invention belongs to the field of quantum gyroscopes, and particularly relates to a rotation sensing measurement method based on a Penning ion trap. Background Technology

[0002] In the field of inertial measurement, the gyroscope is a core sensor, capable of measuring the angular motion of an object to achieve functions such as navigation and positioning. The core component of a traditional gyroscope is a rotor with a certain mass rotating at extremely high angular velocity. This component has the motion characteristics of a mechanical structure, thus suffering from drawbacks such as short lifespan, low accuracy, and large size. Subsequent gyroscopes, such as MEMS gyroscopes, laser gyroscopes, and atomic interferometer gyroscopes, all have certain limitations. MEMS gyroscopes have lower measurement accuracy than laser gyroscopes. The fiber optic gyroscope is a representative example of a laser gyroscope. The optical medium material used in fiber optic gyroscopes is affected by ambient temperature and light radiation absorption, thus affecting light propagation and limiting the accuracy of fiber optic gyroscopes. Atomic interferometer gyroscopes rely on atomic ensembles for measurement, inevitably introducing certain systematic errors. Therefore, achieving higher accuracy and integrable, compact, high-sensitivity gyroscopes for more precise rotational measurements has significant theoretical and practical value. Summary of the Invention

[0003] This invention provides a rotational angular velocity sensing and measurement system and method based on trapped ions, which enables higher precision rotational measurement and reduces the complexity of the device for measuring rotation.

[0004] To achieve the above objectives, the present invention provides a rotational angular velocity sensing and measurement system based on trapped ions, comprising a permanent magnet, an ion trap, an ion trapping electrode, a constant voltage power supply, and a dipole force light source; the permanent magnet is used to generate a magnetic field in the z-direction to trap ions in the ion trap within the xy plane; the ion trap includes a container and an ion cluster within the container, the ion cluster comprising several ions; the ion cluster rotates around its center of mass in the z-direction, and when there is an external rotational angular velocity input, the ion cluster couples with the Coriolis force, generating simple harmonic motion in the z-direction; the ion trapping electrode comprises four electrodes, and during measurement, the constant voltage power supply applies an alternating voltage to the ion trapping electrode (4) to form a rotating electromagnetic field, the voltage polarity of two opposite electrodes is the same, and the voltage polarity of two adjacent electrodes is opposite; the dipole force light source is used to emit a dipole force beam, the dipole force beam being used to entangle the electron spin of the ions and the z-direction simple harmonic quantum mechanical oscillator of the ions.

[0005] Furthermore, the ion is a Ca or Be ion.

[0006] Furthermore, the ion trap is a Penning ion trap.

[0007] A rotational angular velocity sensing and measurement method based on trapped ions, based on the above-mentioned rotational angular velocity sensing and measurement system, includes the following steps:

[0008] S1: Set the ion trap magnetic field and trap voltage, and calculate the axial frequency ω of the ion cluster motion. z Controlling the frequency ω of the rotating electromagnetic field of the rotating wall w Equal to the axial frequency ω of the ion cluster z And to stabilize the ions in the ion trap into a cold atom trapped state;

[0009] S2: Calculate the strength β of the radial constraint relative to the axial constraint of the ion cluster;

[0010] S3: The shape of the ion cluster is controlled by adjusting the trap voltage and the frequency of the rotating electromagnetic field of the rotating wall. The aspect ratio α of the ion cluster is calculated based on the strength β of the radial constraint relative to the axial constraint. The trap voltage and the frequency ω of the rotating electromagnetic field of the rotating wall corresponding to the minimum value of α are then determined. w As a parameter that ultimately controls the shape of ion clusters;

[0011] S4: Fix the sensing and measurement system to the rotating target, so that the sensing and measurement system rotates with it. Let the direction of the rotation axis of the target be the z-direction, and let the plane perpendicular to the z-direction be the xy-plane. Then, the target rotates in the xy-plane. Calculate the radius r of the ion cluster on the z=0 plane based on α and β. cl This value is also the amplitude y of the i-th ion in the outermost layer along the y direction. i Therefore, the average amplitude is the amplitude of the entire ion cluster in the y-direction. c ;

[0012] S5: The axial amplitude Z of the ion cluster induced by the Coriolis force was measured according to the Hamiltonian formula provided by the optical dipole method. c According to Z c The frequency ω of the rotating electromagnetic field of the rotating wall w And the amplitude of the entire ion cluster in the y-direction. c The rotational angular velocity Ω of the target under test was calculated. x This means that the angular velocity can be measured.

[0013] Furthermore, in step 1, the magnetic field of the ion trap is set to 1T, and the trap voltage is between 10-100V.

[0014] Furthermore, in step 3, the aspect ratio α of the ion cluster is calculated according to the following formula:

[0015]

[0016] Where k1 and k0 are both intermediate variables; k0 = [1-α] 2] 1 / 2 r cl r cl As an intermediate variable,

[0017] The calculation formula is:

[0018]

[0019] Where a0 is an intermediate variable, e is the charge of an electron, ∈0 is the vacuum permittivity, and N is the number of ions in the ion trap.

[0020] Furthermore, in step 5, the rotational angular velocity Ω is calculated according to the following formula. x :

[0021]

[0022] Where Q is the quality factor of the Penning trap harmonic oscillator in the z-direction.

[0023] Furthermore, after step S5 is completed, the amplitude sensitivity is calculated according to the limiting sensitivity formula of amplitude sensing, and the limit of rotation sensing measurement sensitivity is obtained by using the proportional relationship between amplitude sensitivity and rotation measurement sensitivity.

[0024] Compared with the prior art, the present invention has at least the following beneficial technical effects:

[0025] The rotational angular velocity sensing and measurement system proposed in this invention is based on a Penning ion trap gyroscope, achieving ultra-high precision in rotational angular velocity measurement. It utilizes multiple ions for measurement, with each ion acting as a mechanical oscillator possessing an extremely high quality factor. In principle, a mechanical oscillator system with a high quality factor has significant potential for measuring rotational angular velocity. Compared to uncharged neutral atoms, ion trap systems suspended in an ultra-high vacuum environment are more suitable for quantum precision measurements because continuous pump light and correlated fluorescence detection can perfectly initialize and detect quantum states. Furthermore, almost arbitrary quantum state evolution operations can be achieved through microwaves, ultra-narrow linewidth lasers, or ultra-stable pulsed lasers. Therefore, it achieves a new level of precision in rotational measurement.

[0026] This invention proposes a rotational sensing measurement method based on a Penning ion trap. Calcium ions are cooled by laser, and a radio frequency electromagnetic field drives the calcium ion cluster to vibrate. The simple harmonic vibration induced by the Coriolis force in the orthogonal direction couples with the vibration of the ion cluster to form a quantum harmonic oscillator. The induced amplitude and rotational sensitivity are measured using the optical dipole force method (ODF), successfully realizing amplitude and rotational sensing measurement based on a Penning ion trap. Ion traps are one of the more suitable systems for quantum precision measurement. The trapped ions, as carriers of quantum states, have a long coherence time, and the optical path structure of the ion trap is relatively simple, which is beneficial for chip-based implementation.

[0027] The ion cluster shape control method based on ion trap proposed in this invention can improve the sensitivity of ion trap rotation measurement. Because the ion cluster is a flat circle, the amplitude of ion movement in the axial direction of the ion cluster can be enhanced, thereby increasing the coupling strength of the Coriolis force, thus increasing the vibration amplitude in the z-direction, and further improving the measurement sensitivity. Therefore, the ion cluster shape control method is the key point, providing a new idea for ion trap gyroscope design, which is beneficial to improving the rotation sensing accuracy of the gyroscope. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the principle of measuring rotational angular velocity based on the Penning ion trap, and a schematic diagram of the rotation of the ion cluster in the xy plane when it senses AC driving voltage, constant electric quadrupole voltage and magnetic field, where the direction of B is the positive z-axis.

[0029] Figure 2 When the trap voltage is 100V, the aspect ratio α of the ion cluster and the rotational angular frequency ω of the ion cluster are... r The relationship, due to the axial frequency ω z Given a fixed trap voltage, the x-axis is represented by ω. r / ω z express.

[0030] In the attached diagram: 1. Permanent magnet, 2. Ion, 3. Electron spin of the outermost layer of the ion, 4. Ion trapping electrode, 5. Rotating electromagnetic field, 6. Dipole force beam. Detailed Implementation

[0031] To make the objectives and technical solutions of this invention clearer and easier to understand, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. The specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention.

[0032] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientation or positional relationships based on the orientation or positional relationships shown in the accompanying drawings, are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined with "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more. In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0033] This invention discloses a rotational angular velocity sensing and measurement method based on trapped ions. Calcium ions are cooled by laser and driven by a radio frequency electromagnetic field to rotate around their center of mass. The rotational motion around the center of mass, coupled with the Coriolis force, induces simple harmonic motion in the vertical direction. Ultra-precise measurement of this vertical harmonic motion enables a rotational angular velocity measurement method based on a quantum harmonic oscillator. The invention also proposes using the optical dipole force (ODF) method to measure the vertical amplitude of the ion cluster. This rotational sensing method based on Penning ion traps provides a new approach for the development of high-precision quantum gyroscopes and has broad application prospects in navigation, positioning, and other fields.

[0034] Example 1

[0035] Reference Figure 1 A rotational angular velocity sensing and measurement system based on trapped ions includes a permanent magnet 1, an ion trap, an ion trapping electrode 4, a constant voltage power supply, a laser, and a dipole force light source. The ion trap includes a container and an ion cluster within the container, the ion cluster comprising a plurality of ions 2.

[0036] Permanent magnet 1 generates a magnetic field B in the z-direction, with a magnitude between 0.5 and 1 T, used to confine ions within the xy-plane. The ions are typically Ca, Be, or similar ions. The outermost electron spin 3 of the ion is the electron remaining after one electron has been stripped from the atom.

[0037] Two permanent magnets 1 are located directly above and below the ion trapping electrode 4, respectively. The ion trap is located inside the ion trapping electrode 4. The ion trapping electrode 4 is a ring electrode and is cut into four electrodes for light transmission. Alternating voltages applied to the four cut electrodes form a rotating electromagnetic field 5. The voltages applied to opposite electrodes have the same polarity, while the voltages applied to adjacent electrodes have opposite polarities. A dipole force light source is used to generate a dipole force beam 6 to entangle the z-direction harmonic quantum mechanical oscillator of the electron spin 3 and the ion 2.

[0038] The ion cluster undergoes a centroidal motion around the z-axis, with an angular frequency of rotation ω. r When an external rotational angular velocity is input, the rotational center of mass motion of the calcium ion cluster and the Coriolis force cause simple harmonic motion coupling in the z-direction. When the characteristic frequency ω of the trapped ion in the z-direction... z equal to ω r When the conditions for coupled resonance are met, the sensitivity for measuring rotational angular velocity is highest. Specifically, under external rotational input, ion clusters rotating in the xy-plane are affected by the Coriolis force.

[0039] Calcium ion crystals are trapped using Penning ion traps, and the motion characteristics of the ion clusters are controlled by a rotating electromagnetic field driven by the electrode walls, ensuring that the ion clusters meet stable trapping conditions. Specifically, ellipsoidal ion clusters are controlled to achieve a specific shape. The z-axis of the zx or zy section of the ellipsoidal ion cluster is calculated. cl and the radius r of the x(y) direction axis of the ellipse cl The ratio α, and by adjusting the frequency ω of the rotating electromagnetic field of the rotating wall. w (and the rotation frequency ω of ion clusters) r The shape of the ion cluster is controlled by the trapping voltage V (which controls the simple harmonic vibration frequency in the z-direction of the ion) applied to the trapping electrode.

[0040] The ion cluster is formed by multiple calcium ions, because the motion characteristics of a single ion cannot meet the resonance conditions of the coupled oscillator.

[0041] The rotating electromagnetic field driving method uses a frequency of ω w The four-electrode rotating electric field (QRF) drives the ion cluster rotation frequency ω r It needs to be synchronized (identical) with it and needs to meet the resonance condition of the coupled oscillator to improve the sensitivity of the gyroscope.

[0042] The aspect ratio α is the z-axis length 2z of the ion cluster. cl Diameter 2r on the plane z=0 clThe ratio of β to ω represents the shape of the ion cluster in the ion trap, calculated from the strength β of the radial constraint relative to the axial constraint, while β is related to the rotation frequency ω of the ion cluster. r cyclotron frequency ω c and axial frequency ω z related.

[0043] The condition for coupled resonance is an important condition for achieving high-sensitivity detection, when the axial frequency ω z Equal to the rotational frequency ω of the ion cluster r The conditions for resonant coupling are reached at that time.

[0044] The aspect ratio α is affected by the rotating electromagnetic field frequency ω of the rotating wall. w The effect of α on ω under a specific trap voltage. r / ω z First increase then decrease, when ω r / ω z When z = 1, cl / r cl Below 10%, the ion clusters become flat and round, which provides high sensitivity for Coriolis force measurement.

[0045] Synchronization condition between the rotating electric field of the four electrodes and the rotation of the ion cluster, frequency ω of the rotating electromagnetic field of the rotating wall. w Equal to the ion cluster rotation frequency ω r .

[0046] The trap voltage range used for controlling the shape of ion clusters is between 10 and 100 V, and the aspect ratio α is between 0.1 and 0.2.

[0047] The stable trapping condition for an ion trap is: the magnetron rotation frequency ω m <Ion cluster rotation frequency ω r <Corrected cyclotron frequency Ω m .

[0048] Controlling the shape of the ion cluster to a flat disk can improve the sensitivity of rotation measurement, which requires that the aspect ratio α and the strength of the radial constraint relative to the axial constraint β be much less than 1.

[0049] Example 2

[0050] The rotation sensing measurement method based on the Penning ion trap proposed in this invention includes two parts: ion cluster shape control and rotation measurement. The specific operation steps are as follows:

[0051] Step 1: Apply a uniform trap magnetic field B = 1T through a constant permanent magnet 1 to cause the ion cluster to move; apply an initial trap voltage V0 = 100V through a constant voltage power supply; the axial distance between the upper and lower end caps of the ion trap is 2Z0 = 2cm; the ions in the ion trap are calcium ions; and the number of ions in the ion trap is N = 1000.

[0052] Step 2: Turn on the laser and use a 397nm wavelength laser to perform Doppler cooling on the calcium ions in the ion trap, causing them to absorb photons and thus slow down, achieving a stable cold atom trapping state.

[0053] Step 3: Calculate the axial frequency ω of the ion cluster motion according to formula (2). z In this example, ω z =247kHz; Adjust the frequency ω of the rotating electromagnetic field of the rotating wall. w Make it consistent with the axial frequency ω z The equations are equal, which strongly couples the simple harmonic motion in the z-direction with the motion of the magnetron coil in the xy-plane, resulting in the maximum amplitude response.

[0054] Step 4: Calculate the strength β of the radial constraint relative to the axial constraint of the ion cluster according to formula (4). In this example, β = 0.05.

[0055] Step 5: Adjust the trap voltage V0 and the frequency ω of the rotating electromagnetic field of the rotating wall. w The shape of the ion clusters is controlled, and α is calculated according to formula (5). The trap voltage V and the frequency ω of the rotating electromagnetic field of the rotating wall are minimized. w As the parameter that ultimately controls the shape of the ion cluster, α = 0.16 in this example, which satisfies the requirement of a flat, round shape.

[0056] Step 6: Place the sensing and measurement system on the rotating target and fix it, so that the sensing and measurement system rotates with it. Assume that the rotation axis of the target is in the z direction, and the plane perpendicular to the z direction is set as the xy plane. Then it rotates in the xy plane. Substitute α and β into formula (6) to calculate the radius r of the ion cluster on the z=0 plane. cl This value is also the amplitude y of the i-th ion in the outermost layer along the y direction. i =0.022cm. Since the amplitude in the y-direction is related to the ion diameter, the amplitude of the innermost ion is 0, and the amplitude of the outermost ion is the largest, which is y. i Therefore, the middle position is taken as the amplitude y in the y direction of the entire ion cluster. c That is, the average amplitude y c =0.011cm.

[0057] Step 7: Using a dipole force light source, emit two laser beams with a specific frequency difference (the magnitude of the frequency difference depends on the atomic spectral lines used and is an empirical value; in this system, calcium ions are used, and the empirical value is 20 GHz). These beams are incident on the ion trap at a specific angle (an empirical value; in this system, it is 20°), forming an optical potential field around the ion cluster. The motion of the ions in the optical potential field is subject to the optical dipole force ODF. This force is related to the ion spin state, so ODF couples the ion position and spin. The coupling relationship is the Hamiltonian of the ion in the optical potential field. The axial amplitude Z of the ion cluster is calculated according to the Hamiltonian formula (9) provided by the optical dipole force method (ODF). c ;

[0058] The axial amplitude Z induced by the Coriolis force was obtained using the optical dipole method. c This involves entanglement of the ion's spin and z-direction vibrations using optical dipole forces, thereby detecting the z-direction amplitude. Changes in the z-direction amplitude lead to changes in the ion's spin projection in the z-direction. The magnitude of the z-direction spin projection is then detected by measuring the population in the z-direction of the conventional spin projection. The population detection is achieved through the absorption of a detection beam, ultimately reflected in the absorption of the detection beam and the z-direction harmonic motion amplitude Z. c In measuring size relationships.

[0059] Step 8: Based on the axial amplitude Z of the ion cluster c and rotational angular velocity Ω x The relation, i.e. formula (8), is used to calculate the rotational angular velocity Ω of the target being measured. x .

[0060] First, let's explain Z. c and Z i Relationship, Z c and Z i Both refer to the amplitude of ion motion in the z-direction caused by external rotational angular velocity input, simply called axial amplitude. However, they involve different objects, Z. i Z is the axial amplitude of the i-th ion along the radial direction in the z=0 plane. c It represents the axial amplitude of the entire ion cluster. Furthermore, Zi is a defined quantity and cannot be directly calculated. c It is a measurement quantity, used to calculate Ω. x Z cannot be used at this time i Instead, use Z. c Z c The axial amplitude is measured by the optical dipole method. The magnitude of the ion cluster motion amplitude can be obtained by the optical dipole method, i.e., equation (9). Then, according to Z... c and rotational angular velocity Ω x The relationship, i.e., formula (8), is used to calculate the rotational angular velocity Ω. xThis allows for the measurement of rotational angular velocity.

[0061] Step 9: Calculate the amplitude limiting sensitivity δZ according to the limiting sensitivity formula (10) for amplitude sensing. c In this example, when F0 = 100yN and N = 10000, the amplitude limiting sensitivity is 0.4 pm / Hz. 1 / 2 .

[0062] Step 10: Calculate the limiting measurement sensitivity δΩ of the rotation sensor according to equation (11). x In this example, the limiting measurement sensitivity of the rotation sensor is 3.0 × 10⁻⁶. -9 rad / s / Hz 1 / 2 .

[0063] The principle of this invention is as follows:

[0064] The motion of ions in a penning ion trap consists of three components: cyclotron motion, axial motion, and drift motion (also known as magnetron motion).

[0065] Rotational motion is a small-radius rotational motion about the direction of the magnetic field lines (which are parallel to the z-axis). The angular frequency of rotational motion is ω. C The calculation formula is:

[0066]

[0067] In the formula, q is the charge of the ion, B is the magnetic field strength, and m is the ion mass;

[0068] The axial motion is a simple harmonic motion along the z-axis of the ion trap's symmetry, with an angular frequency of ω. z The calculation formula is:

[0069]

[0070] In the formula, V0 is the trap voltage, and z0 is half the distance between the upper and lower end caps of the ion trap container;

[0071] The angular frequency of the drift motion is ω m The calculation formula is:

[0072]

[0073] In equation (3), to simplify the formula, the angular frequency ω of the cyclotron motion is... C and the angular frequency ω of axial motion z Converted to cyclotron frequency v c and axial motion frequency v z Perform the calculation.

[0074] The sensitivity of an ion trap gyroscope is related to the shape parameters of the ion cluster. A flat, disc-shaped cluster can provide greater response sensitivity. Therefore, the strength β of the radial constraint relative to the axial constraint should be as much less than 1 as possible. β is defined as:

[0075]

[0076] Calculate the aspect ratio α of the ion cluster shape, assuming the diameter of the ion cluster in the z = 0 plane is 2r. cl The axial length is 2z cl Then α = z cl / r cl The relationship between β and α is:

[0077]

[0078]

[0079] Among them, k1 and k0 are both intermediate variables;

[0080] k0=[1-α 2 ] 1 / 2 r cl r cl r is an intermediate variable cl The calculation formula is:

[0081]

[0082]

[0083] Where a0 is an intermediate variable, e is the charge of an electron, ∈0 is the vacuum permittivity, and N is the number of ions in the ion trap.

[0084] The key to controlling the shape of ion clusters is the frequency ω of the rotating electromagnetic field of the rotating wall. w That is, the rotational angular frequency ω of the ion cluster. r The frequency ω of the rotating electromagnetic field of the rotating wall is changed under different trap voltages. w Calculate the aspect ratio and fit the curve, such as Figure 2 The figure shows the shape of the ion cluster and the frequency ω of the rotating electromagnetic field of the rotating wall at a trap voltage of 100V. w The relationship diagram. Based on... Figure 2 It can be seen that when ω r / ω z When = 1, the ion cluster has a flattened oval shape, meaning the two oscillators are strongly coupled. For Coriolis force sensing, the response of the axial oscillator will be very large.

[0085] For the amplitude Z induced in the z-direction by the i-th ion from the inside to the outside on the z=0 plane... i Defined as:

[0086]

[0087] In the formula, Q is the quality factor of the Penning trap harmonic oscillator in the z-direction, which is approximately 10. 6 , and y i This is the input angular velocity Ω x The induced amplitude in the lower y direction is equal to the radius rcl of the ion cluster in the z=0 plane.

[0088] In the experiment, the amplitude Z induced by the i-th ion in the z-direction could not be measured. i However, the amplitude Z induced by the ion cluster in the z-direction can be measured by the optical dipole method. c Therefore, by transforming equation (7), we obtain the following equation:

[0089]

[0090] Among them, y c It is the average amplitude of the ion cluster in the y direction.

[0091] The optical dipole force applied to the ion causes entanglement between the ion's electron spin and the ion's z-direction harmonic phonon, and the ion's Hamiltonian... for:

[0092]

[0093] Where F0 is the magnitude of the optical dipole force sensed by the ion, and Z c σ is the axial amplitude of the ion cluster, Δμ is the frequency difference between the two beams of the optical dipole force and the difference between the frequency of the simple harmonic oscillation in the z-direction of the ion, δ is the phase difference between the optical dipole force and the simple harmonic oscillation in the z-direction of the ion, and σ is the axial amplitude of the ion cluster. i It is the electron spin Pauli operator.

[0094] The limiting sensitivity δZ of ​​the Z-direction simple harmonic motion amplitude sensing c for:

[0095]

[0096] In the formula, Z c Let τ be the amplitude in the z-direction and τ be the measurement time. is Planck's constant, e is the charge of electrons, and N is the number of ions.

[0097] The limiting measurement sensitivity of the rotation sensor can be calculated using the following formula:

[0098]

[0099] It will be understood by those skilled in the art that the above descriptions are merely preferred examples of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A method for sensing and measuring the rotational angular velocity based on trapped ions, characterized in that, Includes the following steps: S1: Set the ion trap magnetic field and trap voltage, and calculate the axial frequency ω of the ion cluster motion. z Controlling the frequency ω of the rotating electromagnetic field of the rotating wall w Equal to the axial frequency ω of the ion cluster z And to stabilize the ions in the ion trap into a cold atom trapped state; S2: Calculate the strength β of the radial constraint relative to the axial constraint of the ion cluster; S3: The shape of the ion cluster is controlled by adjusting the trap voltage and the frequency of the rotating electromagnetic field of the rotating wall. The aspect ratio α of the ion cluster is calculated based on the strength β of the radial constraint relative to the axial constraint. The trap voltage and the frequency ω of the rotating electromagnetic field of the rotating wall corresponding to the minimum value of α are then determined. w As a parameter that ultimately controls the shape of ion clusters; S4: Fix the sensing and measurement system to the rotating target, so that the sensing and measurement system rotates with it. Let the direction of the rotation axis of the target be the z-direction, and let the plane perpendicular to the z-direction be the xy-plane. Then, the target rotates in the xy-plane. Calculate the radius r of the ion cluster on the z=0 plane based on α and β. cl This value is also the amplitude y of the i-th ion in the outermost layer along the y direction. i Therefore, the average amplitude is the amplitude of the entire ion cluster in the y-direction. c ; S5: The axial amplitude Z of the ion cluster induced by the Coriolis force was measured according to the Hamiltonian formula provided by the optical dipole method. c According to Z c The frequency ω of the rotating electromagnetic field of the rotating wall w And the amplitude of the entire ion cluster in the y-direction. c The rotational angular velocity Ω of the target under test was calculated. x That is, to achieve the measurement of angular velocity; The sensing and measurement system includes a permanent magnet (1), an ion trap, an ion trapping electrode (4), a constant voltage power supply, and a dipole force light source; The permanent magnet (1) is used to generate a magnetic field in the z direction to trap ions in the ion trap in the xy plane; The ion trap includes a container and an ion cluster within the container, the ion cluster comprising a plurality of ions; the ion cluster rotates around its center of mass in the z-direction, and when an external angular velocity input is present, the ion cluster couples with the Coriolis force, generating simple harmonic motion in the z-direction; The ion trapping electrode (4) includes four electrodes. During measurement, a constant voltage power supply applies an alternating voltage to the ion trapping electrode (4) to form a rotating electromagnetic field. The voltages applied to two opposite electrodes have the same polarity, while the voltages applied to two adjacent electrodes have opposite polarities. The dipole force source is used to emit a dipole force beam (6), which is used to entangle the electron spin of the ion and the z-direction harmonic quantum mechanical oscillator of the ion.

2. The rotational angular velocity sensing and measurement method based on trapped ions according to claim 1, characterized in that, The ion is a Ca or Be ion.

3. The rotational angular velocity sensing and measurement method based on trapped ions according to claim 1, characterized in that, The ion trap is a Penning ion trap.

4. The rotational angular velocity sensing and measurement method based on trapped ions according to claim 1, characterized in that, In step 1, the magnetic field of the ion trap is set to 1T, and the trap voltage is between 10-100V.

5. The rotational angular velocity sensing and measurement method based on trapped ions according to claim 1, characterized in that, In step 3, the aspect ratio α of the ion cluster is calculated according to the following formula: Among them, k1 and k0 are both intermediate variables; r cl r cl As an intermediate variable, the calculation formula is: in, Here, e is an intermediate variable, representing the charge of an electron. is the vacuum permittivity, and N is the number of ions in the ion trap.

6. The rotational angular velocity sensing and measurement method based on trapped ions according to claim 1, characterized in that, In step 5, the rotational angular velocity Ω is calculated according to the following formula. x : Where Q is the quality factor of the Penning trap harmonic oscillator in the z-direction.

7. The rotational angular velocity sensing and measurement method based on trapped ions according to claim 1, characterized in that, After step S5 is completed, the amplitude sensitivity is calculated according to the limiting sensitivity formula of amplitude sensing, and the limit of rotation sensing measurement sensitivity is obtained by using the proportional relationship between amplitude sensitivity and rotation measurement sensitivity.

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