Generation of high-energy-resolved NH_3 molecular beam by a Stark decelerator with 179 stages

We demonstrate the production of cold, slow NH_3 molecules from a supersonic NH_3 molecular beam using our electrostatic Stark decelerator consisting of 179 slowing stages. By using this long Stark decelerator, a supersonic NH_3 molecular beam can be easily decelerated to trappable velocities. Here we present two modes for operating the Stark decelerator to slow the supersonic NH_3 molecules. The first is the normal mode, where all 179 stages are used to decelerate molecules, and it allows decelerating the NH_3 molecular beam from 333 m/s to 18 m/s, with a final temperature of 29.2 mK.The second is the deceleration-bunch mode, which allows us to decelerate the supersonic NH_3 beam from 333 m/s to 24 m/s,with a final temperature of 2.9 m K. It is clear that the second mode promises to produce colder(high-energy-resolution)molecular samples than the normal mode. Three-dimensional Monte Carlo simulations are also performed for the experiments and they show a good agreement with the observed results. The deceleration-bunch operation mode presented here can find applications in the fields of cold collisions, high-resolution spectroscopy, and precision measurements.     

亚声速NH3分子束静电Stark减速的理论研究

本文基于自行研制的第二代(180级)静电Stark减速器, 展开了对NH₃的有效减速与冷却的理论研究. 首先, 计算了NH₃分子在|J=1, K=1>量子态的Stark分裂, 研究了不同的同步相位角下, 减速器中NH₃分子的纵向相空间稳定区域; 接着, 采用Monte-Carlo方法研究了该分子在传统工作模式下的减速效果, 并讨论了该减速模式下多个参数(包括每级损失动能、分子波包末速度和相对减速效率)与同步相位角的依赖关系, 以及减速波包末速度与减速电压的关系, 研究发现: 采用传统的Stark减速模式, 当减速电压为±13 kV、同步相位角φ₀=26.08°时, 即可实现NH₃从280 m/s到6.7 m/s的有效减速, 对应平动动能减少了99.9%, 其波包温度由1.34 K降至80 mK; 最后, 研究了先聚束后减速模式下NH₃分子的减速效果, 以及该减速模式下减速波包末速度与同步相位角的依赖关系, 结果表明: 当减速电压为± 6.5 kV, 采用前15级电极作为聚束电极, 后165级作为减速电极时, 可将NH₃分子波包的中心速度由280 m/s减至20.7 m/s, 平动动能减少了99.4%, 温度由1.34 K降至1.6 mK, 与传统减速模式相比, 冷分子波包温度降低至1/50. 由此可见, 采用180级的传统Stark减速器完全可以实现具有较低Stark势能的NH₃分子的有效减速与冷却, 并获得温度约为1 mK的冷分子波包, 为进一步的实验研究提供了可靠的理论依据.     

Theoretical study of slowing supersonic CH3F molecular beams using electrostatic Stark decelerator

We have calculated the Stark effect of CH3F molecules in external electrical fields,the rotational population of supersonic CH3F molecules in different quantum states,and analyse the motion of weak-field-seeking CH3F molecules in a state |J = 1,KM = 1 inside the electrical field of a Stark decelerator by using a simple analytical model.Threedimensional Monte Carlo simulation is performed to simulate the dynamical slowing process of molecules through the decelerator,and the results are compared with those obtained from the analytical model,including the phase stability,slowing efficiency as well as the translational temperature of the slowed molecular packet.Our study shows that with a modest dipole moment(～1.85 Debye) and a relatively slight molecular weight(～34.03),CH3F molecules in a state |J = 1,KM = 1 are a good candidate for slowing with electrostatic field.With high voltages of ±10 kV applied on the decelerator,molecules of 370 m/s can be brought to a standstill within 200 slowing stages.     

A quasi-analytic model of a linear Stark accelerator/decelerator for polar molecules

This article describes a quasi-analytic model of a linear Stark accelerator/decelerator for polar molecules in both their low- and high-field seeking states, and examines the dynamics of the acceleration/deceleration process and its phase stability. The requisite time-dependent inhomogeneous Stark fields, used in current experiments, are Fourier-analyzed and found to consist of a superposition of partial waves with well-defined phase velocities. The kinematics of the interaction of molecules with the partial waves is discussed and the notion of a phase of a molecule in a travelling field is introduced. Next, the net potential and the net force that act on the molecules are derived. A special case, the first-harmonic accelerator/decelerator, is introduced. This represents a model system many of whose properties can be obtained analytically. The first-harmonic accelerator/decelerator dynamics is presented and discussed along with that of the isomorphic biased-pendulum problem. Finally, the general properties of the velocity of the molecules in a phase-stable accelerator/decelerator are examined.Received: 11 August 2004, Published online: 23 November 2004PACS: 32.60. + i Zeeman and Stark effects - 39.10. + j Atomic and molecular beam sources and techniques - 45.50.-j Dynamics and kinematics of a particle and a system of particles - 29.17. + w Electrostatic, collective, and linear accelerators     

Optical stark decelerator for molecules

We demonstrate a single stage optical Stark decelerator for neutral molecules which is capable of reducing the translational energy of benzene molecules within a molecular beam by 15% in a single pulsed Gaussian optical field of 15 ns duration. The change in velocity induced by the optical potential is measured by the change in the time of flight of benzene molecules ionized by a second optical field after the slowing field is turned off. A maximum reduction in the velocity of 25 m/s was measured using a single Gaussian beam with a peak intensity of 1.6 x 10(12) W/cm(2) corresponding to a maximum well depth of 253 K.     

基于调制光晶格的中性分子束光学Stark减速与囚禁的理论研究

本文基于分子束光学Stark减速理论,提出采用调制的红失谐光晶格来减速和囚禁任意脉冲超声分子束方案,并予以理论研究.以CH₄超声分子束为例,利用Monte-Carlo方法模拟了调制光晶格中的分子减速与囚禁的动力学过程,给出减速级数、同步分子初始位相角与减速效果的关系.研究结果表明：随着减速级数的增加,被减速的分子波包逐渐从原来的分子速度分布的大波包中分离开来,且减速级数越高,减速后的分子速度越小.在其他条件相同时同步分子初始位相角越大,减速波包内的分子数目越少,同时位相空间被压缩.与未调制的光晶格减速方案相比,本方案中无分子自由飞行过程,在相同的光晶格长度内完成了双倍的减速级数.当光晶格长度取3.71 mm时,模拟结果显示CH₄分子从280 m/s减速至172 m/s,而未调制光晶格只能将CH₄分子从280 m/s减速至232 m/s,减速效果提高了26%.本方案可以集分子的减速、囚禁于一体,是一种新型的分子光学功能器件,在冷分子光学、量子信息、冷化学等前沿研究领域中有潜在的应用.     

Mitigation of loss within a molecular Stark decelerator

The transverse motion inside a Stark decelerator plays a large role in the total efficiency of deceleration. We differentiate between two separate regimes of molecule loss during the slowing process. The first mechanism involves distributed loss due to coupling of transverse and longitudinal motion, while the second is a result of the rapid decrease of the molecular velocity within the final few stages. In this work, we describe these effects and present means for overcoming them. Solutions based on modified switching time sequences with the existing decelerator geometry lead to a large gain of stable molecules in the intermediate velocity regime, but fail to address the loss at very low final velocities. We propose a new decelerator design, the quadrupole-guiding decelerator, which eliminates distributed loss due to transverse/longitudinal couplings throughout the slowing process and also exhibits gain over normal deceleration to the lowest velocities.     

Cold SO<Subscript>2</Subscript> molecules by Stark deceleration

We produce SO₂ molecules with a centre of mass velocity near zero using a Stark decelerator. Since the initial kinetic energy of the supersonic SO₂ molecular beam is high, and the removed kinetic energy per stage is small, 326 deceleration stages are necessary to bring SO₂ to a complete standstill, significantly more than in other experiments. We show that in such a decelerator possible loss due to coupling between the motional degrees of freedom must be considered. Experimental results are compared with 3D Monte-Carlo simulations and the quantum state selectivity of the Stark decelerator is demonstrated.     

极性分子的激光冷却及囚禁技术

分子由于其不同于原子的特殊性质,在原子、分子和光物理研究中有其独特的地位.冷分子研究已经开展了二三十年,取得了很多重大的进展.但是以斯塔克减速器为代表的传统冷却方案遇到瓶颈,很难进一步提高分子的相空间密度.将原子中成熟的激光冷却技术拓展到极性分子中是本领域近年来的重大突破,使得冷却和囚禁分子的范围得以大大扩展,分子的相空间密度也得以提高.本文对国内外激光冷却极性分子的最新成果进行综述,并以BaF分子为例介绍激光冷却极性分子的相关理论和技术,包括分子能级结构分析及精密光谱测量,采用缓冲气体冷却进行态制备和预冷却,以及通过冷分子束研究激光与BaF分子间的相互作用.这些为后续开展激光冷却与囚禁实验研究奠定了基础,也为开展其他新的分子冷却实验提供了参考.     

Slowing polar molecules using a wire Stark decelerator

We have designed and implemented a new Stark decelerator based on wire electrodes, which is suitable for ultrahigh vacuum applications. The 100 deceleration stages are fashioned out of 0.6 mm diameter tantalum and the array's total length is 110 mm, approximately 10 times smaller than a conventional Stark decelerator with the same number of electrode pairs. Using the wire decelerator, we have removed more than 90% of the kinetic energy from metastable CO molecules in a beam.     

Formation of high-density cold molecules via electromagnetic trap

Preparation and control of cold molecules are advancing rapidly, motivated by many exciting applications ranging from tests of fundamental physics to quantum information processing. Here, we propose a trapping scheme to create high-density cold molecular samples by using a combination of electric and magnetic fields. In our theoretical analysis and numerical calculations, a typical alkaline-earth monofluoride, MgF, is used to test the feasibility of our proposal. A cold MgF molecular beam is first produced via an electrostatic Stark decelerator and then loaded into the proposed electromagnetic trap, which is composed of an anti-Helmholtz coil, an octupole, and two disk electrodes. Following that, a huge magnetic force is applied to the molecular sample at an appropriate time, which enables further compressing of the spatial distribution of the cold sample. Molecular samples with both higher number density and smaller volume are quite suitable for the laser confinement and other molecular experiments such as cold collisions in the next step.     

Phase space manipulation of cold free radical OH molecules

We report bunching, slowing, and acceleration of a supersonically cooled beam of diatomic hydroxyl radicals (OH). In situ observation of laser-induced fluorescence along the beam propagation path allows for detailed characterization of longitudinal phase-space manipulation of OH molecules through the Stark effect by precisely sequenced inhomogeneous electric fields.     

Measurement of the three-dimensional velocity distribution of Stark-decelerated Rydberg atoms

The full three-dimensional velocity distributions of decelerated and accelerated particles in a Stark decelerator for Rydberg atoms and molecules have been measured. In the experiment, argon atoms in a supersonic beam are excited to low-field and high-field seeking Stark states with principal quantum number in the range n=15 to 25 and are decelerated in a 3 mm long decelerator consisting of four electrodes on which time-dependent voltages are applied. The time dependence of the resulting inhomogeneous electric field is chosen such that the decelerating force acting on the high-field seeking states is maximized at each point along the trajectories. The three-dimensional velocity distribution of the atoms before and after the deceleration is determined by measuring times of flight and two-dimensional images of the atomic cloud on the detector. Under optimal deceleration conditions, the decrease in kinetic energy in the longitudinal dimension amounts to 1.0×10^-21 J and the increase in mean kinetic energy in the transverse dimensions is only 1.0×10^-23 J. The corresponding temperatures of 100 mK and 300 mK in the two transverse dimensions are sufficiently low that trapping can be envisaged. The possibility of focusing a Rydberg atom beam is demonstrated experimentally.     

Deceleration and electrostatic trapping of OH radicals

A pulsed beam of ground state OH radicals is slowed down using a Stark decelerator and is subsequently loaded into an electrostatic trap. Characterization of the molecular beam production, deceleration, and trap loading process is performed via laser induced fluorescence detection inside the quadrupole trap. Depending on the details of the trap loading sequence, typically 10(5) OH (X2Pi(3/2),J=3/2) radicals are trapped at a density of around 10(7) cm(-3) and at temperatures in the 50-500 mK range. The 1/e trap lifetime is around 1.0 s.     

Cold molecule spectroscopy for constraining the evolution of the fine structure constant

We report precise measurements of ground-state, Lambda-doublet microwave transitions in the hydroxyl radical molecule (OH). Utilizing slow, cold molecules produced by a Stark decelerator we have improved over the precision of the previous best measurement 25-fold for the F'=2-->F=2 transition, yielding (1 667 358 996 +/- 4)Hz, and by tenfold for the F'=1-->F=1 transition, yielding (1 665 401 803 +/-12)Hz. Comparing these laboratory frequencies to those from OH megamasers in interstellar space will allow a sensitivity of 1 ppm for Delta(alpha/alpha) over approximately 10(10) yr.     

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.     

Interaction of a supersonic beam of toluene with a resonant RF electric field

Deflection of a cold supersonic toluene beam seeded in He has been observed when these molecules interact with both a static and a resonant oscillating electric field. The toluene beam splits into two beams each one peaking at a deflection angle of 1 degree towards the positive and negative direction of the Stark field when the employed resonant frequency between the two Stark levels of the toluene molecule is 1411 kHz. This deflection angle is about four orders of magnitude higher than the value one would expect from the toluene dipole moment and the employed RF field gradient. Different hypothesis are suggested to explain the observed strong beam splitting including the possibility of transverse beam interferences induced by both the resonant RF field and the transverse uniform electric field. A theoretical model is presented based on molecular beam interferences induced by the resonant RF field which seems to account satisfactorily for the present observations.     

Intracavity coherent addition of single high-order modes

We report on efficient intracavity coherent addition of several single high-order mode distributions in a multichannel laser resonator. The phase locking and coherent addition is achieved by using an intracavity interferometric beam combiner. The principle, configuration, and experimental results with pulsed Nd:YAG Laguerre-Gaussian TEM01 and TEM02 laser beam distributions are presented. The results reveal more than 95% combining efficiency with a nearly pure high-order mode output beam distribution in both free-running and Q-switched operation.     

Laser radiation pressure slowing of a molecular beam

We demonstrate deceleration of a beam of neutral strontium monofluoride molecules using radiative forces. Under certain conditions, the deceleration results in a substantial flux of detected molecules with velocities ?50 m/s. Simulations and other data indicate that the detection of molecules below this velocity is greatly diminished by transverse divergence from the beam. The observed slowing, from ～140 m/s, corresponds to scattering ?10(4) photons. We also observe longitudinal velocity compression under different conditions. Combined with molecular laser cooling techniques, this lays the groundwork to create slow and cold molecular beams suitable for trap loading.