Implementation method of magnetic field auxiliary electrostatic quadrupole trap for evaporative cooling

Abstract

The invention discloses an implementation method of a magnetic field-assisted electrostatic quadrupole trap for evaporative cooling. The implementation method comprises the following steps: S1, preparing CaF molecules on an X1 [sigma]-state hyperfine energy level; s2, preparing an electrostatic quadrupole trap by adopting a magnetic field-assisted electrostatic quadrupole trap device, enabling the device to generate a uniform magnetic field at the centers of coils through two electrified Helmholtz coils, and adjusting the magnetic field intensity through current; s3, CaF molecules are loaded in an electrostatic quadrupole trap, and the potential well depth is adjusted by adjusting the current in a Helmholtz electrified coil; and S4, after the molecules in the trap reach heat balance, reducing the depth of the potential trap, enabling the molecules with higher temperature to escape out of the trap, and realizing CaF molecule evaporative cooling through multiple times of heat balance. According to the invention, the current in the coil is changed, and the depth of the potential well is changed by cutting the well wall without changing the geometrical shape of the potential well, so that cold molecules with higher concentration are obtained finally.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of molecular cooling technology, and particularly relates to a magnetic field assisted electrostatic quadrupole trap implementation method for evaporative cooling. BACKGROUND

[0002] Compared with atoms, cold molecules have more abundant energy level structures and significantly enhanced electric dipole moments, which enable cold molecules to exhibit novel physical and chemical phenomena in low-temperature environments, thereby giving cold molecules more extensive application prospects. Two types of cold molecules that are currently studied more are alkali metal cold molecules and molecules with high Franck-Condon factors. For Franck-Condon molecules, people usually adopt direct laser cooling combined with magneto-optical trap (MOT) technology, and have successfully prepared various super-cooled molecules including AlCl, YO, CaF, etc. Among them, the Doyle group has successfully reduced the temperature of CaF molecules to about 340 muK in 2018. Through a pair of Helmholtz coils with reverse current, the magnetic field generated thereby provides an additional and position-dependent force, forming a trapping potential well, i.e., a magnetic trap, and then six beams of laser are used to slow down the molecules. The molecules are continuously pushed back to the center and slowed down in the magneto-optical trap, and finally the molecules are trapped and cooled. However, this scheme will cause molecular loss due to the introduction of multiple laser beams, resulting in fewer molecules, which is contrary to the actual demand. SUMMARY

[0003] The purpose of the present application is to provide a magnetic field assisted electrostatic quadrupole trap implementation method for evaporative cooling. In the process of molecular evaporative cooling, the electric field and the magnetic field are combined, the current intensity in the coil is adjusted (i.e., the magnetic induction intensity is changed), the depth of the electrostatic quadrupole trap is adjusted, the purpose of evaporative cooling is achieved, and cold molecules with high concentration are obtained.

[0004] Technical scheme: A magnetic field assisted electrostatic quadrupole trap implementation method for evaporative cooling, comprising the following steps: S1, preparing CaF molecules on X 1 Σ state hyperfine energy level N =1, J =1 / 2, F =0, M F =0) will appear a special structure of mutual transformation between "strong field searching state-weak field searching state-strong field searching state" due to perturbation interaction under the action of electric field and magnetic field. S2, the magnetic field assisted electrostatic quadrupole trap device is used to prepare the electrostatic quadrupole trap, the device constructs the linearly changed electric field which is left-right symmetrical through a ring electrode and two end cap electrodes, the device makes the uniform magnetic field generated at the center of two powered Helmholtz coils, and the magnetic field intensity can be adjusted through the current; S3, the CaF molecules are loaded in the electrostatic quadrupole trap, and the potential well depth is adjusted by adjusting the current in the powered Helmholtz coil; S4, after the molecules in the well reach thermal equilibrium, the potential well depth is reduced, so that the molecules with higher temperature escape from the well, and after multiple thermal equilibrium, the CaF molecules are evaporated and cooled.

[0005] Further, the X 1 The hyperfine energy level parameters of the Σ state are as follows: N =1, J =1 / 2, F =0, M F =0, J = N + S, F = J + I ; Wherein, N is the rotational angular momentum, S is the electron spin, J is the rotational angular momentum N and the electron spin S is coupled into the angular momentum of the molecule except the nuclear spin, I is the nuclear spin of the fluorine atom, F is J is coupled with I into the total angular momentum, M F is the projection quantum number of the total angular momentum under the external field.

[0006] Further, the magnetic field assisted electrostatic quadrupole trap device includes a circular ring electrode, two hyperbolic end cap electrodes and a powered Helmholtz coil, one powered Helmholtz coil is arranged on one side of the two hyperbolic end cap electrodes, the radius of the powered Helmholtz coil is equal to the distance between the two powered Helmholtz coils; the two hyperbolic end cap electrodes are grounded, and the circular ring electrode is arranged between the two hyperbolic end cap electrodes; the circular ring electrode is provided with a cold molecule detection hole; After the direct current is turned on, the magnetic induction intensity generated by the powered Helmholtz coil is B 0 and the current i The relationship is: , Wherein, is the vacuum permeability, N is the number of turns, R is the coil radius.

[0007] Further, the magnetic induction intensity of the space is changed by the current size in the Helmholtz coil, and then the position of the perturbation point between the mutual transformation of the "strong field searching state-weak field searching state-strong field searching state" is changed, so that the potential well depth is changed.

[0008] Further, the evaporation cooling process is as follows: when the molecules are evaporatively cooled in the trap, the magnetic field is gradually reduced by adjusting the current in the Helmholtz coil, the potential well depth is reduced, and the molecules with higher energy in the potential well escape from the trap; after the remaining molecules reach a new thermal equilibrium through collision, the magnetic induction intensity in the Helmholtz coil is changed to continue adjusting the magnetic induction intensity, and the potential well depth is reduced again to further reduce the system temperature.

[0009] Compared with the prior art, the present application has the following remarkable effects: 1. The present application utilizes the perturbation interaction of hyperfine energy levels in the electric and magnetic mixed field, and changes the electrostatic quadrupole well depth by adjusting the magnetic induction intensity; the traditional magnetic well not only utilizes the interaction of electric field and magnetic field to generate perturbation, but also needs to utilize microwave field or light field, so that the device is complex, and the molecular loss is increased, resulting in fewer final molecules; compared with the existing magnetic well for evaporation cooling, the present application can directly change the depth of the electrostatic quadrupole well by changing the current in the coil, so that the operation is simpler, and the molecular loss is low. 2. In the present application, the current in the coil (i.e. the magnetic induction intensity) is changed, the potential well depth is changed by cutting the well wall without changing the potential well geometry, and the potential well volume is further reduced, so that the final concentration of the cold molecules is greater, and the further trapping or loading is facilitated. BRIEF DESCRIPTION OF DRAWINGS

[0010] Figure 1 The flowchart of the present application; Figure 2 X is the hyperfine energy level of CaF cold molecules in the magnetic field of 50G; 1 Sigma state N =1 and N =0 mixed field effect, wherein the solid line corresponds to N= 1, J =1 / 2, F =0, M F =0 hyperfine energy level; Figure 3 The structure schematic diagram of the magnetic auxiliary electrostatic quadrupole well device, wherein 1 is a circular ring electrode, the inner side is a hyperboloid; 2 is a hyperbolic end cover electrode, 3 is a group of Helmholtz coils, and 4 is a small hole for detecting cold molecules.

[0011] Figure 4(a) is the spatial electric field distribution in the electrostatic quadrupole trap, (b) is the magnetic field assisted electrostatic quadrupole trap and the electric field distribution profile in the trap; Figure 5 CaF cold molecular X 1 Σ state hyperfine energy level N= 1, J =1 / 2, F =0, M F =0 mixed field effect under different magnetic fields, reflecting the change rule of the depth of the electrostatic quadrupole trap with the magnetic field. DETAILED DESCRIPTION

[0012] The application will be described in further detail below with reference to the accompanying drawings and specific embodiments.

[0013] In order to further reduce the temperature of the molecules to achieve deep cooling, evaporation cooling is an effective scheme. The principle is that by repeatedly removing molecules with energy higher than the average value in the trapped molecular sample (evaporation), the remaining molecules reach thermal equilibrium through elastic collision, so that the average energy of the molecules continues to decrease, and the goal of deep cooling is finally achieved. Therefore, the application provides a magnetic field assisted electrostatic quadrupole trap implementation method.

[0014] As Figure 1 shown, it is a flow chart of the magnetic field assisted electrostatic quadrupole trap implementation method for evaporation cooling of the application, and the specific steps are as follows: Step 1, preparation of molecular state; When the molecules are cooled to a certain extent, the hyperfine structure of the molecules cannot be ignored, and when they interact with external electric field and external magnetic field, the hyperfine energy level will produce Stark effect and Zeeman effect, and when the hyperfine energy level of the cold molecules interacts with the electric field and the magnetic field at the same time, some special energy level structures will be produced due to perturbation interaction, such as Figure 2 shown, the solid line corresponds to the hyperfine energy level of CaF cold molecular X 1 Σ state N =1, J =1 / 2, F =0, M F =0, this hyperfine energy level will produce the condition that the energy level is transformed between "strong field searching state-weak field searching state-strong field searching state" under the action of the mixed field, and the inflection point of the strong field-weak field (weak field-strong field) mutual conversion caused by the perturbation interaction can be called perturbation point, the energy level between two perturbation points constitutes a potential well, and the depth of the potential well will change accordingly with the change of the magnetic field, so in the process of molecular evaporation cooling, the depth of the potential well can be reduced by adjusting the size of the magnetic field, thereby realizing the reduction of the temperature of the molecules.

[0015] Therefore, first of all, CaF molecule is prepared in X 1 Σ state hyperfine level N =1, J =1 / 2, F =0, M F =0, wherein J = N +S , the rotational angular momentum N and the electron spin S are coupled into the angular momentum of the molecule except the nuclear spin J , J is coupled with the nuclear spin I of the fluorine atom into the total angular momentum F , that is F = J + I , M F , represents the projection quantum number of the total angular momentum under the external field.

[0016] Step 2, preparation of electrostatic quadrupole trap; A set of specially designed electrodes are used, such as Figure 3 The magnetic field assisted electrostatic quadrupole trap device is shown in the figure, the inner side of the hyperbolic end cap electrode 2 on the left and right sides is a hyperboloid, the distance between the two hyperbolic end cap electrodes 2 at the top is 5 mm, and the two electrodes are grounded; the inner side of the middle ring electrode 1 is also a hyperboloid, the inner radius is 5 mm, and a +15 kV voltage is applied. At this time, the spatial electric field E distribution expression is: , wherein, the center of the middle ring electrode 1 is taken as the coordinate origin, z is the axial distance from the coordinate origin, r is the radial distance from the coordinate origin, R is the inner radius of the ring electrode 1, V is the voltage difference between the hyperbolic end cap electrode 2 and the ring electrode 1, and the spatial electric field distribution formed is shown in Figure 4 (a).

[0017] The potential well formed by the hyperfine level structure of the molecule is evaporatively cooled under the spatial electric field formed by the electrostatic quadrupole, so it is also called electrostatic quadrupole trap, and the cross-sectional view of the electrostatic quadrupole trap and the spatial electric field distribution is shown in Figure 4 (b).

[0018] A Helmholtz coil 3 is placed on one side of the two hyperbolic end cap electrodes 2, the radius of the Helmholtz coil is equal to the distance between the two Helmholtz coils, and a uniform magnetic field is generated at the center of the axis of the Helmholtz coil 3 after a direct current is applied, and the magnetic induction intensity B 0 is related to the current i as , where, is the vacuum permeability, N is the number of turns of the coil, and R is the radius of the coil.

[0019] Figure 3 In the middle, the small hole 4 on the circular ring electrode 1 is used for late cold molecular detection.

[0020] Step 3, adjustment of the well depth; Due to the perturbation interaction under the mixed field, the CaF molecule X 1 The position of the perturbation point between the "strong field search state-weak field search state-strong field search state" of the Σ state hyperfine level N =1, J =1 / 2, F =0, M F Changes with the magnetic induction intensity (equivalent to the change of the well depth), so by adjusting the Figure 3 The size of the current in the Helmholtz coil 3 changes the magnetic induction intensity in space, thereby changing the depth of the electrostatic quadrupole well. As shown in Figure 5 When the direct current field and the magnetic field are in the same direction, the applied magnetic field B =50G, the energy level interval between the two perturbation points, i.e. the potential well depth, is 65.8MHz, and the temperature of the potential well at this time can be calculated to be about 3.158mK. If the applied magnetic field B =25G, the energy level interval between the two perturbation points, i.e. the potential well depth, is 21.8MHz, and the temperature of the potential well at this time can be calculated to be about 1.046mK.

[0021] As can be seen from Figure 5 After the CaF molecule is prepared to this special hyperfine level X 1 Σ state N =1, J =1 / 2, F =0, M F =0), when the current of the Helmholtz coil is adjusted (i.e. the magnetic induction intensity is changed), the potential well depth can be changed. This means that when the magnetic induction intensity gradually decreases, the potential well depth gradually decreases, and therefore the magnetic field is like a "knife" that can cut the well wall, thereby changing the depth of the potential well.

[0022] Therefore, when the electrostatic field and the magnetic field are in the same direction, by adjusting the magnetic induction intensity, the two perturbation points of the energy level will move accordingly; when the magnetic field gradually decreases, the potential well depth gradually decreases, thereby reducing the temperature of the system and achieving the purpose of evaporation cooling.

[0023] Step 4, CaF molecules evaporative cooling; When CaF molecules are evaporatively cooled in the trap, by adjusting the current of the Helmholtz coil, the magnetic field is gradually reduced, the depth of the potential well is reduced, and the molecules with higher energy in the potential well (i.e. the molecules with higher temperature) escape from the well. After the remaining molecules reach a new thermal equilibrium through collisions, the magnetic induction strength is adjusted again by changing the current in the Helmholtz coil, and the depth of the potential well is reduced again, thereby further reducing the temperature of the system. Finally, through multiple adjustments of the depth of the magnetic field assisted electrostatic quadrupole well, the effect of evaporative cooling of molecules is achieved.

Claims

1. A magnetic field assisted electrostatic quadrupole trap implementation method for evaporative cooling, characterized in that, The steps include the following: S1, CaF molecules are prepared in X 1 Σ state hyperfine levels N =1, J =1 / 2, F =0, M F =0) will appear the special structure of energy level transformation between "strong field searching state-weak field searching state-strong field searching state" due to perturbation interaction under the action of electric field and magnetic field. S2, an electrostatic quadrupole trap is prepared by using a magnetic field assisted electrostatic quadrupole trap device, the device constructs a linearly changing electric field through a ring electrode and two end cap electrodes, the device generates a uniform magnetic field at the center of two energized Helmholtz coils, and the magnetic field intensity can be adjusted by current; S3, CaF molecules are loaded in the electrostatic quadrupole trap, and the potential well depth is adjusted by adjusting the current in the Helmholtz coil; S4, after the molecules in the trap reach thermal equilibrium, the potential well depth is reduced, so that the molecules with higher temperature escape from the trap, and after multiple thermal equilibrium, the CaF molecules are evaporatively cooled.

2. The method for magnetic field assisted electrostatic quadrupole trap implementation for evaporative cooling of claim 1, wherein, The X 1 The parameters of the Σ state hyperfine levels are respectively: N =1, J =1 / 2, F =0, M F =0, J=N+S, F=J+I ; wherein N is the rotational angular momentum, S is the electron spin, J is the rotational angular momentum N and the electron spin S coupled into the angular momentum of the molecule in addition to the nuclear spin I of the fluorine atom, F is J the total angular momentum coupled with I, M F is the projection quantum number of the total angular momentum in the external field.

3. The method for magnetic field assisted electrostatic quadrupole trap implementation for evaporative cooling of claim 1, wherein, The magnetic field assisted electrostatic quadrupole trap device includes a circular ring electrode (1), two hyperbolic end cap electrodes (2) and a Helmholtz coil (3), one Helmholtz coil (3) is placed on one side of the two hyperbolic end cap electrodes (2), the radius of the Helmholtz coil is equal to the distance between the two Helmholtz coils; the two hyperbolic end cap electrodes (2) are grounded, and the circular ring electrode (1) is arranged between the two hyperbolic end cap electrodes (2); the circular ring electrode (1) is provided with a cold molecule detection hole; After the direct current is applied, the magnetic induction intensity generated by the Helmholtz coil (3) B 0 and the current i relationship is: ， wherein is the vacuum permeability, N is the number of turns of the coil, R is the radius of the coil.

4. The method for magnetic field assisted electrostatic quadrupole trap implementation for evaporative cooling of claim 3, wherein, The magnetic induction intensity of the space is changed by the current in the Helmholtz coil (3), and then the position of the perturbation point between the "strong field searching state-weak field searching state-strong field searching state" is changed, so that the potential well depth is changed.

5. The method for magnetic field assisted electrostatic quadrupole trap implementation for evaporative cooling of claim 1, wherein, The process of evaporative cooling is as follows: when the molecules are trapped in the trap for evaporative cooling, the current in the Helmholtz coil is adjusted to gradually reduce the magnetic field and reduce the potential well depth, so that the molecules with higher energy in the potential well escape from the trap; after the remaining molecules reach a new thermal equilibrium through collision, the magnetic induction intensity is adjusted by changing the current in the Helmholtz coil, and the potential well depth is reduced again to further reduce the system temperature.

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