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Chinese Physics B

Theoretical derivation and simulation of a versatile electrostatic trap for cold polar molecules

Shengqiang Li

Published Nov 1, 2016• 2 citations
Publisher

Abstract

We propose a versatile electrostatic trap scheme using several charged spherical electrodes and a bias electric field. We first give the two-ball scheme and derive the analytical solution of the electric field. In order to make a comparison, we also give the numerical solution calculated by the finite element software (Ansoft Maxwell). Considering the loading of cold polar molecules into the trap, we give the three-ball scheme. We first give the analytical and numerical solutions of the distribution of the electric field. Then we simulate the dynamic process of the loading and trapping cold molecules using the classical Monte Carlo method. We analyze the influence of the velocity of the incident molecular beam and the loading time on the loading efficiency. After that, we give the temperature of the trapped cold molecules. Our study shows that the loading efficiency can reach 82%, and the corresponding temperature of the trapped molecules is about 24.6 mK. At last, we show that the single well divides into two ones by increasing the bias electric field or decreasing the voltages applied to the spherical electrodes.

DOI
10.1088/1674-1056/25/11/113702

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We propose a versatile electrostatic trap scheme using several charged spherical electrodes and a bias electric field. We first give the two-ball scheme and derive the analytical solution of the electric field. In order to make a comparison, we also give the numerical solution calculated by the finite element software (Ansoft Maxwell). Considering the loading of cold polar molecules into the trap, we give the three-ball scheme. We first give the analytical and numerical solutions of the distribution of the electric field. Then we simulate the dynamic process of the loading and trapping cold molecules using the classical Monte Carlo method. We analyze the influence of the velocity of the incident molecular beam and the loading time on the loading efficiency. After that, we give the temperature of the trapped cold molecules. Our study shows that the loading efficiency can reach 82%, and the corresponding temperature of the trapped molecules is about 24.6 mK. At last, we show that the single well divides into two ones by increasing the bias electric field or decreasing the voltages applied to the spherical electrodes.
A versatile electrostatic trap with open optical access for cold polar molecules in weak-field-seeking state is proposed in this paper. The trap is composed of a pair of disk electrodes and a hexapole. With the help of a finite element software, the spatial distribution of the electrostatic field is calculated. The results indicate that a three-dimensional closed electrostatic trap is formed. Taking ND 3 molecules as an example, the dynamic process of loading and trapping is simulated. The results show that when the velocity of the molecular beam is 10 m/s and the loading time is 0.9964 ms, the maximum loading efficiency reaches 94.25% and the temperature of the trapped molecules reaches about 30.3 mK. A single well can be split into two wells, which is of significant importance to the precision measurement and interference of matter waves. This scheme, in addition, can be further miniaturized to construct one-dimensional, two-dimensional, and three-dimensional spatial electrostatic lattices.
We propose a novel optical-access opened electrostatic trap to study the Stark-potential evaporative cooling of polar molecules by using two charged disk electrodes with a central hole of radius r 0 =1.5 mm, and derive a set of new analytical equations to calculate the spatial distributions of the electrostatic field in the above charged-disk layout. Afterwards, we calculate the electric-field distributions of our electrostatic trap and the Stark potential for cold ND 3 molecules, and analyze the dependences of both the electric field and the Stark potential on the geometric parameters of our charged-disk scheme, and find an optimal condition to form a desirable trap with the same trap depth in the x , y , and z directions. Also, we propose a desirable scheme to realize an efficient loading of cold polar molecules in the weak-field-seeking states, and investigate the dependences of the loading efficiency on both the initial forward velocity of the incident molecular beam and the loading time by Monte Carlo simulations. Our study shows that the maximal loading efficiency of our trap scheme can reach about 95%, and the corresponding temperature of the trapped cold molecules is about 28.8 mK. Finally, we study the Stark-potential evaporative cooling for cold polar molecules in our trap by the Monte Carlo method, and find that our simulated evaporative cooling results are consistent with our developed analytical model based on trapping-potential evaporative cooling.
We propose an optically accessible electrostatic trap scheme to confine cold polar molecules by using two charged spherical electrodes, and we calculate the corresponding electric field distribution and the Stark trapping potential for ND3 molecules. We also propose a desirable scheme to realize an efficient loading of cold polar molecules in weak-field-seeking states, and our simulated results show that the maximal loading efficiency can reach ∼14%. In addition, we briefly discuss some potential applications of our proposed trap scheme in the studies of optical-potential evaporative cooling and electrostatic surface traps for cold polar molecules.
An electrostatic beam splitter composed of three charged poles for polar molecules in weak-field-seeking states is proposed. First, the schematic diagram is given. Then we calculate the spatial distribution of the electrical field using the finite element software. We simulate the dynamic process of the loading and splitting polar molecules using the classical Monte Carlo method. We investigate the influences of the longitudinal velocity of the incident molecular beam and the voltages on the performance of our beam splitter. In order to alter the splitting ratio of the molecular beam conveniently, we cut off the two output arms of beam splitter at a certain position. Then we study the influences of the voltages and cutting positions on the splitting ratio. At last, we discuss two methods of keeping the height of guiding center nearly unchanged.
We propose a simple scheme for trapping cold polar molecules in low-field seeking states on the surface of a chip by using a grounded metal plate and two finite-length charged wires that half embanked in an insulating substrate, calculate the electric field distributions generated by our charged-wire layout in free space and the corresponding Stark potentials for ND3 molecules, and analyze the dependence of the trapping center position on the geometric parameters. Moreover, the loading and trapping processes of cold ND3 molecules are studied by using the Monte Carlo method. Our study shows that the loading efficiency of the trap scheme can reach 11.5%, and the corresponding temperature of the trapped cold molecules is about 26.4 mK.
An electrostatic trap for polar molecules is proposed. Loading and trapping of polar molecules can be realized by applying different voltages to the two electrodes of the trap. For ND 3 molecular beams centered at ∼10 m/s, a high loading efficiency of ∼67% can be obtained, as confirmed by our Monte Carlo simulations. The volume of our trap is as large as ∼3.6 cm 3 , suitable for study of the adiabatic cooling of trapped molecules. Our simulations indicate that trapped ND 3 molecules can be cooled from ∼23.3 mK to 1.47 mK by reducing the trapping voltages on the electrodes from 50.0 kV to 1.00 kV.