METHOD, SYSTEM, ION TRAP, COMPUTER PROGRAM AND COMPUTER-READABLE STORAGE MEDIUM FOR DETECTING A FORM OF TWO PERMANENT MAGNETS BUILT INTO AN ION TRAP

Abstract

Method for determining a shape of two permanent magnets (2) installed in an ion trap (1), comprising - Providing a first function that is characteristic of any shape of the two permanent magnets (2) in lateral directions and with a predetermined thickness (6) in the vertical direction, and - Providing a second function dependent on the first function, which is characteristic of a magnetic field generated by the two permanent magnets (2), - Providing a first constraint characteristic of a predetermined point (7) in the lateral and vertical directions at which the magnetic field must vanish, - Determining an extremum of a functional that depends on the first constraint, where the function depends on the second function, and - Determining the shape of the two permanent magnets (2) as a function of the extremum, such that a gradient of quantities of the magnetic field over the two permanent magnets (2) is maximized, with the magnetic field vanishing at the predetermined point (7). Furthermore, a system, an ion trap (1), a computer program and a computer-readable storage medium are provided.

Description

[0001] The present disclosure relates to a method, a system, a computer program and a computer-readable storage medium for determining a shape of two permanent magnets incorporated in an ion trap and an ion trap.

[0002] Document DE 10 2020 116 096 A1 describes a device and a method for generating an inhomogeneous magnetic field. Document US 2008 / 0 296 494 A1 describes an ion trap with a longitudinal permanent magnet and a mass spectrometer using this ion trap. Document US 10 290 485 B2 describes a Fourier transform ion cyclotron resonance mass spectrometer.

[0003] One problem to be solved is to provide a method for optimizing the shape of two magnets of an ion trap with respect to their magnetic field. Furthermore, an ion trap with such magnets, as well as a system, a computer program, and a computer-readable storage medium for implementing such a method, are to be provided.

[0004] The problem is solved by the subject matter of the independent claims. Advantageous embodiments, implementations, and further developments are the subject matter of the respective dependent claims.

[0005] A method is described for determining the shape of two permanent magnets incorporated in an ion trap. In particular, the ion trap is designed to confine at least one ion and / or change an electronic state of the at least one ion, in particular to perform a quantum calculation with at least two ions. The ion trap can be a Paul trap, a linear ion trap, a surface ion trap, and / or a multilayer ion trap. For example, the ion trap comprises a set of electrodes. For example, a radio-frequency voltage is applied to the electrodes, thereby providing a time-varying electric field designed to confine and / or change the ion. In particular, the ion or ions are localized along a trapping axis. For example, the ion, in particular each of the ions, overlaps the trapping axis and / or oscillates around the trapping axis.For example, the ions in an ion chain are arranged along the capture axis.

[0006] The two permanent magnets are spaced apart from the capture axis. The two permanent magnets are designed to generate a magnetic field, particularly in a region around the capture axis that is spaced apart from the two permanent magnets.

[0007] A first function is provided that is characteristic of an arbitrary shape of the two permanent magnets in lateral directions, wherein the two permanent magnets have a predetermined thickness in the vertical direction. The first function comprises variables and / or parameters that are characteristic of the arbitrary shape, wherein the arbitrary shape in particular has a continuous and closed outer edge in lateral directions. The first function is defined in a three-dimensional Euclidean space with an x-axis, a y-axis, and a z-axis that are orthogonal to each other. The lateral directions are formed by the x-axis and the y-axis, and the vertical direction is formed by the z-axis.

[0008] In particular, the two permanent magnets are formed by a first permanent magnet and a second permanent magnet, which are spaced apart from each other in lateral directions. A first subfunction is, for example, characteristic of a shape of the first permanent magnet in lateral directions. A second subfunction is, for example, characteristic of a shape of the second permanent magnet that is, in particular, mirror-symmetrical to the shape of the first permanent magnet. The first subfunction and the second subfunction form the first function.

[0009] The permanent magnets each have a top surface and a bottom surface opposite the top surface. The top surface and the bottom surface extend, for example, exclusively in lateral directions. The top surface and the bottom surface are connected by a side surface arranged perpendicular to the top surface and the bottom surface. The side surfaces are formed in lateral directions according to the arbitrary shape. In particular, the permanent magnets are planar permanent magnets.

[0010] In particular, the predetermined thickness of the first permanent magnet is equal to the predetermined thickness of the second permanent magnet. The predetermined thickness is at least 1 micrometer and at most 500 micrometers, approximately 10 micrometers.

[0011] A second function dependent on the first function is provided, wherein the second function is characteristic of a magnetic field generated by the two permanent magnets. For example, the second function comprises further variables and / or further parameters that are characteristic of the magnetic field generated by the permanent magnets with the arbitrary shape according to the first function.

[0012] Permanent magnets, for example, exhibit homogeneous magnetization. The magnetic field is generated depending on the shape of the permanent magnets. For example, a gradient of magnetic field magnitudes for different positions on the capture axis is characteristic of a magnetic field gradient along the capture axis, particularly depending on the shape.

[0013] For example, a portion of the magnetic field of a small (dx, dy) segment of the permanent magnets can be calculated as the field of a magnetic dipole. The total magnetic field of the permanent magnets at any point in x, y, and z space is calculated, for example, as an integral over all small segments of the permanent magnets. The magnetic field gradient can be calculated as an integral in a similar way.

[0014] A first constraint is provided which is characteristic of a predetermined point in lateral and vertical directions at which the magnetic field must vanish.

[0015] In particular, the predetermined point is arranged vertically above the top surfaces of the permanent magnets. For example, the predetermined point is arranged laterally between the two permanent magnets. This predetermined point does not overlap with the permanent magnets in lateral directions in plan view. In particular, the magnetic field has a magnitude that is zero at the predetermined point.

[0016] A predetermined distance in the vertical direction between the predetermined point and the cover surfaces is, for example, at least three times the predetermined thickness of the permanent magnets. For example, the predetermined distance of the predetermined point is at least 20 micrometers and at most 1 mm, approximately 100 micrometers.

[0017] An extremum of a functional is determined depending on the first constraint, where the functional depends on the second function.

[0018] For example, a Lagrange function is defined that depends on the functional and the first constraint. Specifically, Euler-Lagrange equations, which are a set of differential equations, are calculated based on the Lagrange function. The Euler-Lagrange equations are used to find a result function characteristic of the shape of the permanent magnets, which extremizes the functional while taking the first constraint into account. This means that the extremum, for example, is characteristic of the result function.

[0019] The first constraint is included, for example, using a method of Lagrange multipliers.

[0020] For example, the Euler-Lagrange equation can be solved analytically, and the result function is obtained in implicit form, represented by f(x,y) = 0.

[0021] The shape of the two permanent magnets is determined as a function of the extremum such that the gradient of the magnetic field magnitudes across the two permanent magnets is maximized, with the magnetic field vanishing at the predetermined point. Specifically, the shape is determined based on the result function that extremizes the functional. With such a shape of the two permanent magnets, the gradient of the magnetic field magnitudes along the capture axis is maximized.

[0022] For example, the method described here is performed in the order specified. The method described here is, for example, a computer-implemented method.

[0023] Magnetic field gradients are used in particular in certain types of quantum computers and in other fields, such as quantum metrology.

[0024] One idea behind the method described here is to determine the shape of the permanent magnets in such a way that a maximum gradient is achieved at a distance across the permanent magnets. Advantageously, the method works for any magnetization direction of the permanent magnets. The method also works advantageously to optimize the gradient of a specific magnetic field component or the gradient of a projection of the magnetic field in any direction.

[0025] According to at least one embodiment of the method, the two permanent magnets with the determined shape are installed in the ion trap. This means that the gradient of magnetic field magnitudes along the capture axis is maximized. Advantageously, a resonance frequency of each of the ions along the capture axis, which is subject to the magnetic field gradient, is unique for each trapped ion due to the gradient.

[0026] According to at least one embodiment of the method, the magnetization directions of the permanent magnets are identical to one another. The magnetization direction is characteristic of a predominant orientation of magnetic moments of a material of the permanent magnets. For example, the material of the permanent magnets is identical to one another and the material is uniformly magnetized. In particular, the magnetization directions point in the same direction.

[0027] For example, the magnetization direction of the first permanent magnet and the magnetization direction of the second permanent magnet are perpendicular to lateral directions, i.e., aligned along the vertical direction. For example, the magnetization direction points away from the permanent magnets toward the capture axis.

[0028] According to at least one embodiment of the method, a second constraint is provided that is characteristic of a predetermined maximum extension of the at least two permanent magnets in lateral directions, and the extremum of the functional is determined as a function of the first constraint and the second constraint. In particular, if the second constraint is a predetermined maximum surface area of ​​the permanent magnets and the predetermined thickness of the permanent magnets, the second constraint represents an additional condition of a limited volume of the permanent magnets.

[0029] The predetermined maximum dimension is, for example, at least 10 micrometers and at most 2 mm, about 300 micrometers.

[0030] Advantageously, a maximum gradient of magnetic field magnitudes is achieved for a predetermined amount of magnetic material at a predetermined distance.

[0031] According to at least one embodiment of the method, the extremum is characteristic of a result function which depends on at least one coefficient, and to determine the coefficient, the result function is substituted into the first constraint and / or the second constraint.

[0032] According to at least one embodiment of the method, the shape of the at least two permanent magnets depends on the result function and the at least one coefficient.

[0033] Furthermore, a system for determining the shape of at least two permanent magnets installed in an ion trap is described. The system is configured to carry out the method described here. Therefore, all features and embodiments disclosed in connection with the method are also disclosed in connection with the system, and vice versa. The system can, in particular, be a personal computer with a graphical user interface (GUI). The GUI is configured to receive inputs, such as at least one of the predetermined thickness of the permanent magnets, the predetermined distance of the predetermined point, and material parameters of the permanent magnets.

[0034] Additionally, an ion trap is described. The ion trap comprises two permanent magnets, the shape of which is determined using the method described here. Therefore, all features and embodiments disclosed in connection with the method are also disclosed in connection with the ion trap, and vice versa. According to one embodiment, the at least two permanent magnets are arranged on a substrate of the ion trap.

[0035] Furthermore, a computer program is described which comprises instructions which, when the computer program is executed by a computer, cause the computer program to carry out the method described here.

[0036] Furthermore, a computer-readable storage medium is specified on which the computer program described here is stored.

[0037] In the following, the method and the ion trap are explained in more detail with reference to embodiments and the associated figures. Fig. 1 shows a flowchart of the method for determining the shape of two permanent magnets in an ion trap according to an embodiment. Fig. 2 shows an ion trap according to an embodiment.

[0038] Elements that are identical or similar, or have the same effect, are provided with the same reference numerals in the figures. The figures and the proportions of the elements depicted in the figures are not to be considered to scale. Rather, individual elements may be exaggerated for clarity and / or clarity.

[0039] The process stage S1 according to the embodiment of the Fig. 1 comprises providing a first function which is characteristic of any shape of two permanent magnets 2 in lateral directions and having a predetermined thickness 6 in the vertical direction.

[0040] In process step S2, a second function is provided as a function of the first function, wherein the second function is characteristic of a magnetic field generated by the two permanent magnets 2.

[0041] In process step S3, a first constraint is provided, wherein the first constraint is characteristic of a predetermined point 7 in the lateral direction and vertical direction at which the magnetic field must disappear.

[0042] An extremum of a functional is determined, whereby the functional depends on the second function in the process step S4, whereby the determination depends on the first constraint.

[0043] Finally, in process step S5, the shape of the two permanent magnets 2 is determined, the determination depending on the extremum such that a gradient of magnitudes of the magnetic field across the two permanent magnets is maximized, the magnetic field vanishing at the predetermined point 7.

[0044] The ion trap 1 in connection with the embodiment of Fig. 2 comprises two permanent magnets 2 with the shapes defined by the Fig.1. The two permanent magnets 2 comprise a first permanent magnet 3 and a second permanent magnet 4, which are two planar permanent magnets with a main extension plane in lateral directions x, y. The first permanent magnet 3 and the second permanent magnet 4 are arranged on a substrate 5 of the ion trap 1 and spaced apart from each other in lateral directions x, y. In particular, the two permanent magnets 2 have the same magnetization direction, which is indicated by the two arrows perpendicular to the main extension plane of the permanent magnets 2.

[0045] The predetermined point 7 is arranged above and between the first permanent magnet 3 and the second permanent magnet 4 at a predetermined distance in the vertical direction z. Information signs 1 ion trap 2 permanent magnets 3 first permanent magnet 4 second permanent magnet 5 Substrat 6 predetermined thickness 7 given point S1..S6 process steps

Claims

[1] Method for determining a shape of two permanent magnets (2) installed in an ion trap (1), comprising - providing a first function which is characteristic of any shape of the two permanent magnets (2) in lateral directions and having a predetermined thickness (6) in the vertical direction, and - providing a second function dependent on the first function, which is characteristic of a magnetic field generated by the two permanent magnets (2), - providing a first constraint characteristic of a predetermined point (7) in the lateral and vertical directions at which the magnetic field must disappear, - Determining an extremum of a functional depending on a first constraint, where the functional depends on the second function, and - Determining the shape of the two permanent magnets (2) as a function of the extremum, so that a gradient of magnitudes of the magnetic field across the two permanent magnets (2) is maximized, wherein the magnetic field disappears at the predetermined point (7). [2] The method according to claim 1, wherein - the two permanent magnets (2) with the determined shape are installed in the ion trap (1). [3] Method according to one of claims 1 or 2, wherein - a magnetization direction of the permanent magnets (2) is equal to each other. [4] Method according to one of claims 1 to 3, wherein - a second constraint is provided which is characteristic of a maximum extension of the at least two permanent magnets (2) in lateral directions, and - the extremum of the functional is determined depending on the first constraint and the second constraint. [5] Method according to claim 4, wherein - the extremum is characteristic of a result function that depends on at least one coefficient, and - to determine the coefficient, the result function is substituted into the first constraint and / or second constraint. [6] Method according to claim 5, wherein - the shape of the at least two permanent magnets (2) depends on the result function and the at least one coefficient. [7] System for determining a shape of at least two permanent magnets (2) installed in an ion trap (1), wherein the system is designed to carry out the method according to one of the preceding claims. [8] Ion trap (1), comprising - the at least two permanent magnets (2) with the determined shape according to one of claims 1 to 3, wherein - at least two permanent magnets (2) are mounted on a substrate (5) of the ion trap (1). [9] A computer program comprising instructions which, when the computer program is executed by a computer, cause the computer program to carry out the method according to any one of claims 1 to 6. [10] A computer-readable storage medium on which the computer program according to claim 9 is stored.

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