Stark-potential evaporative cooling of polar molecules in a novel optical-access opened electrostatic trap

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 r0= 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 ND3 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 m K. 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.     

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

We propose a versatile electrostatic trap scheme using several charged spherical electrodes and a bias electric held.We hrst give the two-ball scheme and derive the analytical solution of the electric held.In order to make a comparison,we also give the numerical solution calculated by the hnite element software(Ansoft Maxwell).Considering the loading of cold polar molecules into the trap,we give the three-ball scheme.We hrst give the analytical and numerical solutions of the distribution of the electric held.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 held or decreasing the voltages applied to the spherical electrodes.     

可操控二种冷原子或冷分子样品的光学双阱新方案及其实验研究

提出了一种构建可囚禁与操控二种冷原子或冷分子样品的光学双阱的新方案,该方案采用常用的液晶空间光调制器作为分光器件,分光调制函数类似二元相位光栅;对提出的方案进行了模拟实验研究,并研究了从光学双阱到单阱的双向演化过程,该光学双阱的模拟实验结果表明与理论方案相符,双阱的操控性好,有利于二种不同的冷原子或冷分子样品的装载与操控等相关实验研究. 关键词： 原子光学 原子分子囚禁 液晶空间光相位调制器 光学双阱     

芯片表面的冷极性分子静电阱与微阱阵列

提出一种利用三根载荷金属杆来实现在芯片表面陷俘冷极性分子的静电阱.给出空间静电场等高线分布.通过调节电极电压操控阱中心距离芯片表面的高度.用经典的蒙特卡罗方法模拟冷分子被装载和囚禁的动力学过程.方案对中心速度为11 m·s^-1的冷分子束,最大装载效率可以达到40%,阱中分子的温度大约为25 mK.方案可以进一步微型化、集成化,形成一维和二维静电微阱阵列,在量子计算、低维物理等方面有应用价值.     

Novel electrostatic trap for cold polar molecules

We propose a novel scheme in which cold polar molecules are trapped by an electrostatic field generated by the combination of a pair of parallel transparent electrodes (i.e., two infinite transparent plates) and a ring electrode (i.e., a ring wire). The spatial distributions of the electrostatic fields from the above charged wire and the charged plates and the corresponding Stark potentials for cold CO molecules are calculated; the dependences of the trap centre position on the geometric parameters of the electrode are analysed. We also discuss the loading process of cold molecules from a cold molecular beam into our trap. This study shows that the proposed scheme is not only simple and convenient to trap, manipulate and control cold polar molecules in weak-field-seeking states, but also provides an opportunity to study cold collisions and collective quantum effects in a variety of cold molecular systems, etc.     

A versatile electrostatic trap with open optical access

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 ND₃ 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.     

一种新颖的表面空心微光阱阵列

提出了采用四台阶相位光栅与微透镜阵列组合产生一种新颖的表面空心微光阱阵列的方案，研究了表面空心微光阱阵列的光强分布，计算了相应的光学囚禁势，并讨论了该微光阱阵列在原子分子光学中的潜在应用.研究表明当用1W的YAG激光照射时，在1cm²面积上可产生近10⁴个空心光阱，每个光阱具有较小的囚禁体积和较大的有效光强及其强度梯度，对⁸⁵Rb原子的光学囚禁势可达190μK.如此深的光阱足以囚禁冷原子或冷分子，并可用于实现全光型原子或分子玻色-爱因斯坦凝聚，甚至制备新颖的光学晶格等. 关键词： 空心光阱 冷原子或冷分子 光学晶格     

ac electric trap for ground-state molecules

We here report on the realization of an electrodynamic trap, capable of trapping neutral atoms and molecules in both low-field and high-field seeking states. Confinement in three dimensions is achieved by switching between two electric field configurations that have a saddle point at the center of the trap, i.e., by alternating a focusing and a defocusing force in each direction. The ac trapping of 15ND(3) molecules is experimentally demonstrated, and the stability of the trap is studied as a function of the switching frequency. A 1 mK sample of 15ND(3) molecules in the high-field seeking component of the |J,K=|1,1 level, the ground state of para-ammonia, is trapped in a volume of about 1 mm(3).     

Two types of highly efficient electrostatic traps for single loading or multi-loading of polar molecules

Two novel electrostatic traps named octopole-based disk electrostatic trap(ODET)and tubular-based disk electrostatic trap(TDET)are proposed for trapping cold polar molecules in low-field-seeking states.Using MgF as the target molecule,single loading and multi-loading methods are numerically simulated with varied incident velocities of slow molecular beams in the two types of traps,respectively.In ODET,with an incident velocity of 10 m/s,a highest loading efficiency of 78.4% or 99.9% has been achieved under the single loading or multi-loading operation mode.In TDET,with an incident velocity of 11 m/s,a highest loading efficiency of 81.6% or 106.5% has been achieved using the two loading methods,respectively.With such high loading efficiencies,the trapped cold molecules can be applied in the researches of cold collisions,high precision spectroscopy,and precision measurements.Especially,together with a blue-detuned hollow beam,the new electrostatic traps proposed here offer a new platform for the following gradient-intensity cooling of MgF molecules,which may provide a new way to produce high density ultracold molecules.     

一种针对弱场搜寻态冷极性分子的可控静电表面囚禁方案

提出一种使用带电金属环和六个球电极和一个外加偏置电场实现对冷极性分子静电囚禁的新方案.计算装载和囚禁时空间电场分布.囚禁中心距离芯片表面的高度可以通过外电场和环形电极所加电压来操控.蒙特卡罗模拟表明对于中心速度为15 m·s^-1的ND₃分子束,装载效率可以达到70%,得到冷分子的温度大约为45 mK.当继续增加偏置电场强度时,单阱分裂为对称的两个阱.如果同时改变球形电极上所加电压,得到不对称的两个阱,可以借此来调节两个阱中所囚禁的冷分子数目的比例.为了易于理解,用蒙特卡罗方法模拟了装载、囚禁、分裂冷分子波包的动力学过程.     

Electrostatic Surface Trap for Cold Polar Molecules with a Charged Circular Wire

We propose a novel scheme to trap cold polar molecules on the surface of an insulating substrate （i.e. a chip） by using an inhomogeneous electrostatic field, which is generated by the combination of a circular charged wire （a ring electrode） and a grounded metal plate. The spatial distributions of the electrostatic field from the above charged wire layout and its Stark potentials for CO molecules are calculated. Our study shows that when the voltage applied to the wire is U = 15 kV, a ring radius is R = 5 mm, the thickness of the insulating substrate is b = 5 mm, and a wire radius is r = 1mm, the maximum efficient trapping potential （i.e., as equivalent temperature） for CO molecules is greater than 141.7mK, which is high enough to trap cold polar molecules with a temperature of 50 mK in the low-field-seeking states.     

Two-dimensional trapping of dipolar molecules in time-varying electric fields

Simultaneous two-dimensional trapping of neutral dipolar molecules in low- and high-field seeking states is analyzed. A trapping potential of the order of 20 mK can be produced for molecules such as ND3 with time-dependent electric fields. The analysis is in agreement with an experiment where slow molecules with longitudinal velocities of the order of 20 m/s are guided between four 50 cm long rods driven by an alternating electric potential at a frequency of a few kHz.     

一种实现冷分子囚禁的可控制静电双阱方案

提出了采用双环形载荷导线和两透明电极系统实现冷分子静电囚禁的可控制静电双阱的新方案,计算了带电圆导线和带电板所产生的静电场分布,从几个方面分析了这个囚禁方案的优点. 提出了一种有效的冷分子装载方法,并研究了双阱到单阱的演化过程. 研究表明,该可控制静电双阱方案不仅方便装载与操控弱场搜寻态的极性冷分子,而且在分子物质波的干涉、纠缠、冷碰撞,甚至进行双阱分子BEC研究等分子光学领域中有着广阔的应用前景. 关键词： 极性冷分子 静电囚禁 可控制静电双阱 分子光学     

Laser cooling and magnetic trapping at several tesla

Laser cooling and magnetic trapping of (85)Rb atoms have been performed in extremely strong and tunable magnetic fields, extending these techniques to a new regime and setting the stage for a variety of cold atom and plasma experiments. Using a superconducting Ioffe-Pritchard trap and an optical molasses, 2.4 x 10(7) atoms were laser cooled to the Doppler limit and magnetically trapped at bias fields up to 2.9 T. At magnetic fields up to 6 T, 3 x 10(6) cold atoms were laser cooled in a pulsed loading scheme. These bias fields are well beyond an order of magnitude larger than those in previous experiments. Loading rates, molasses lifetimes, magnetic-trapping times, and temperatures were measured using photoionization and electron detection.     

Electrostatic microtrap on the surface of the chip

As is well known in atomic optics, the nonadiabatic transitions induce the loss of atoms trapped in a magnetic well which seriously affects the formation of the Bose-Einstein condensates. Electrostatic traps have widespread applications in molecular optics. While, for most existing electrostatic traps, the electric field strength in the trap center is nearly zero which may cause the nonadiabatic transitions. Especially for a chip-based microtrap, ingenious design is need to overcome this problem. In the paper, we propose a novel electrostatic microtrap composed of four arc-shaped electrodes. The influences of the voltages and the geometrical parameters of the electrodes on the electric field strength as well as the height of the potential well are studied. The distributions of electrostatic field are numerically calculated. We firstly simulate the trajectory of one molecule in the processes of loading and trapping. After that, we simulate the movements of a large number of molecules using the method of Monte Carlo. Then we calculate the temperature of trapped cold molecules. After that, we analyze the impacts of voltages and the geometrical parameters on the efficiency of our microtrap. At last, we show that our scheme can evolve into electrostatic microtrap arrays which should be a powerful tool for a variety of basic research and applications.     

磁光阱中超冷钠-铯原子碰撞的实验研究

研究了磁光阱中异核超冷钠铯原子的碰撞机理, 测量了超冷钠原子的碰撞损失率, 得到了钠-铯原子的碰撞损失系数β_Na-Cs与钠原子俘获光强度之间的关系. 利用多普勒模型计算了不同俘获光强度下的钠原子磁光阱的阱深, 得到了临界光强的理论值, 与实验结果符合得较好.     

通过圆孔衍射实现冷分子(或冷原子)囚禁的光学偶极阱

以单色标量波衍射理论为基础,研究单色平面波由圆孔衍射产生实现冷分子(或冷原子)光学囚禁的光阱。运用圆孔衍射理论分析讨论了光学偶极阱的光强分布、光学势及偶极力,并导出了有关光阱的几何参量、光强分布、强度梯度及其曲率与光学系统参量(如照明光波的波长、小孔的孔径)间的解析关系。研究表明,当激光功率与波长分别为P=500 W和λ=1.08μm,小孔半径a=20μm时,产生囚禁甲烷CH4分子的光阱光学势约为57.9μK。通过圆孔衍射可实现冷分子或冷原子囚禁,该方案不仅简单可行、操作方便,而且在冷分子物理、原子光学、分子光学和量子光学等领域中有着广阔的应用前景。     

一种可控的Ioffe型冷分子表面微电阱

囚禁于阱中的粒子(原子或分子)可获得更长的相互作用时间,因而在精密测量中可获得更高的分辨率.阱中的粒子与外界隔离,从而可以被冷却到更低的温度.因此原子(或分子)阱已广泛应用到许多研究领域.然而中心电场强度为零的势阱会导致粒子发生非绝热跃迁,这是原子或分子损失的主要来源.该损失曾是制备原子玻色-爱因斯坦凝聚的最后一道障碍.本文提出了一种可控的Ioffe型表面微电阱,其电场强度处处不为零,可有效避免分子的非绝热损失.另外,通过调节电压等参数,势阱中心电场强度以及势阱中心距芯片表面的高度可以在较大范围内调节,例如在本文参数下,势阱中心电场强度可在0.15—5.5 kV/cm变化,势阱中心高度可在6.0—17.0μm变化.本文通过有限元软件计算了芯片表面微电阱的电场分布,并用Monte Carlo模拟验证了该方案的可行性.该表面微电阱不仅可用于分子芯片的集成,而且可用于表面量子简并气体的制备.为精密测量、量子计算、表面冷碰撞和冷化学等领域提供了一个平台.     

Electrostatic surface guiding of cold polar molecules with a single charged wire

This paper proposes a scheme to guide cold polar molecules by using a single charged wire half embanked in an insulating substrate and a homogeneous bias electric field, which is generated by a plate capacitor composed of two infinite parallel metal plates. The spatial distributions of the electrostatic field produced by the combination of the charged wire and the plate capacitor and the corresponding Stark potentials (including dipole forces) for metastable CO molecules are calculated, the relationships between the electric field and the parameters of our charged-wire layout are analysed. It also studies the influences of the insulator on the electric field distribution and the discharge effect. This study shows that the proposed scheme can be used to guide cold polar molecules in the weak-field -- seeking states, and to form various molecule-optical elements, such as molecular funnel, molecular beam-splitters and molecule interferometer, even to construct a variety of integrated molecule-optical elements and their molecule chips.     

可控双空心光束的理论方案及实验研究

提出了一种利用双周期弧向非满额相位调制的方法产生双空心光束的方案. 当准直氦氖激光通过1.5 mm半径透光孔照射到该相位图样时, 在200 mm成像透镜像空间获得长30 mm, 间距57.6μm, 单管束宽度0.11–0.14 mm的双空心光束. 该方案结构简单, 产生的双空心光束具有较好的可控性, 双光管间距由相位调制因子p决定, 能够实现从双空心光束到单空心光束的双向演化. 对所提出的方案进行了实验研究并得到与理论相符的结果. 利用多种组合方式讨论了将该方案拓展到蓝失谐光学囚禁势阱, 可以实现可控的空心双光阱、四光阱与光学晶格等, 有望在冷原子、冷分子囚禁与操控等领域的实验研究中发挥重要作用.