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International Journal of Modern Physics B

Electrostatic lattice preventing the nonadiabatic transition for cold polar molecules based on a molecular chip

Sheng-Qiang Li, Nannan Zhang

Published Feb 1, 2023• 1 citation
Publisher

Abstract

An electrostatic lattice is composed of many micro-scale traps. It is a powerful tool for manipulating cold polar molecules on a chip with the help of the interaction between the dipole moment and the inhomogeneous electric field. To the best of our knowledge, the existing electrostatic lattice still suffers the nonadiabatic transition that will lead to the escape of molecules from the electrostatic trap. In the paper, we skillfully design the electrode structure to avoid the zero-field zone at the center of every single microtrap, and the nonadiabatic transitions can be prevented. First, we numerically calculate the distribution of the spatial electrostatic field. Then, the influences of voltages on the electric field intensity and the height of the trap center are investigated. We simulate of the trajectory of molecules using the Monte Carlo method and figure out the factors impacting the loading efficiency of our electrostatic lattice. At last, we discuss how the voltages and the loading positions affect the positional distribution of trapped molecules.

DOI
10.1142/s0217979223502405

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An electrostatic lattice is composed of many micro-scale traps. It is a powerful tool for manipulating cold polar molecules on a chip with the help of the interaction between the dipole moment and the inhomogeneous electric field. To the best of our knowledge, the existing electrostatic lattice still suffers the nonadiabatic transition that will lead to the escape of molecules from the electrostatic trap. In the paper, we skillfully design the electrode structure to avoid the zero-field zone at the center of every single microtrap, and the nonadiabatic transitions can be prevented. First, we numerically calculate the distribution of the spatial electrostatic field. Then, the influences of voltages on the electric field intensity and the height of the trap center are investigated. We simulate of the trajectory of molecules using the Monte Carlo method and figure out the factors impacting the loading efficiency of our electrostatic lattice. At last, we discuss how the voltages and the loading positions affect the positional distribution of trapped molecules.
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.
Trapping particles (atoms or molecules) allows long interaction time and therefore potentially high resolution in precision measurements. Moreover, the particles in the trap are thermally isolated from the outside world and can be cooled to very low temperatures. As a result, the atomic (or molecular) traps have been widely used in many research areas. However, the molecules in these traps exhibiting zero field in the trap center undergo nonadiabatic transitions, which is the major loss of particles. The loss of atoms in this type of trap seriously hinders the generation of the first BEC (Bose-Einstein condensates). In this paper, we propose a chip-based controllable Ioffe-type electrostatic mirotrap, in which nonadabatic loss can be avoided due to the non-zero electric field. The mirotrap is composed of a pair of L-typed gold wires, which is 1 m in height and deposited on a glass substrate. The non-zero potential well originated in the microsize electrodes offers a steep gradient enable to trap low-field-seeking state polar molecules. The electric field strength in the trap center can be changed in a wide range by adjusting the applied voltage or/and the widths of the electrodes. For instance, under the conditions in the paper, the electric field strength in the trap center can be changed from 0.15 to 5.5 kV/cm. The height of the potential well is about 10 m above the chip and can also be tuned in a large range by adjusting the parameters of the electrodes. Under the conditions in the paper, the height of the potential well can be adjusted from 6.0 to 17.0 m. The electric fields of the microtrap near the surface of the chip are calculated by using a finite element software. Monte-Carlo simulations of the loading and the trapping processes are also carried out in order to justify the feasibility of our scheme. Taking ND3 molecules for example, the loading efficiency of molecules as a function of longitudinal velocity of molecular packet is studied. Our proposed surface microtrap can be used not only for integrating the molecular chips but also for producing the quantum degenerate gas near the chip surface. It offers a platform for many research fields such as precision measurements, quantum computing, surface cold collisions and cold chemistry.
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.
We propose a controllable high-efficiency electrostatic surface trap for cold polar molecules on a chip by using two insulator-embedded charged rings and a grounded conductor plate. We calculate Stark energy structure pattern of ND3 molecules in an external electric field using the method of matrix diagonalization. We analyze how the voltages that are applied to the ring electrodes affect the depth of the efficient well and the controllability of the distance between the trap center and the surface of the chip. To obtain a better understanding, we simulate the dynamical loading and trapping processes of ND 3 molecules in a | J , KM 〉 = |1, − 1〉 state by using classical Monte—Carlo method. Our study shows that the loading efficiency of our trap can reach ∼ 88%. Finally, we study the adiabatic cooling of cold molecules in our surface trap by linearly lowering the potential-well depth (i.e., lowering the trapping voltage), and find that the temperature of the trapped ND3 molecules can be adiabatically cooled from 34.5 mK to ∼ 5.8 mK when the trapping voltage is reduced from −35 kV to −3 kV.
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 suhstrate, 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 inK.
Compared to the atomic chip, which has been a powerful platform to perform an astonishing range of applications from rapid Bose-Einstein condensate (BEC) production to the atomic clock, the molecular chip is only in its infant stages. Recently a one-dimensional electric lattice was demonstrated to trap polar molecules on a chip. This excellent work opens up the way to building a molecular chip laboratory. Here we propose a two-dimensional (2D) electric lattice on a chip with concise and robust structure, which is formed by arrays of squared gold wires. Arrays of microtraps that originate in the microsize electrodes offer a steep gradient and thus allow for confining both light and heavy polar molecules. Theoretical analysis and numerical calculations are performed using two types of sample molecules, ND3\mathrm{N}{\mathrm{D}}_{3}ND3​ and SrF, to justify the possibility of our proposal. The height of the minima of the potential wells is about 10 \ensuremath{\mu}m above the surface of the chip and can be easily adjusted in a wide range by changing the voltages applied on the electrodes. These microtraps offer intriguing perspectives for investigating cold molecules in periodic potentials, such as quantum computing science, low-dimensional physics, and some other possible applications amenable to magnetic or optical lattice. The 2D adjustable electric lattice is expected to act as a building block for a future gas-phase molecular chip laboratory.