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Physical Review A

Phase stability in a multistage Zeeman decelerator

A. W. Wiederkehr, S. D. Hogan, Frédéric Merkt

Published Oct 25, 2010• 34 citations
Publisher

Abstract

The phase stability of a multistage Zeeman decelerator is analyzed by numerical particle-trajectory simulations and experimental measurements. A one-dimensional model of the phase stability in multistage Stark deceleration [Bethlem et al., Phys. Rev. Lett. 84, 5744 (2000)] has been adapted to multistage Zeeman deceleration and compared with one- and three-dimensional particle-trajectory simulations, including the analysis of the effect of finite switch-on and -off times of the deceleration pulses. The comparison reveals that transverse effects in the decelerator lead to a considerable reduction of the phase-space acceptance at low values of the phase angle and an enhancement at high values. The optimal combinations of phase angles and currents with which a preset amount of kinetic energy can be removed from atoms and molecules in a pulsed supersonic beam using a multistage decelerator are determined by simulation. Quantitative analysis of the phase-space acceptance within a given volume reveals that for our decelerator (8 $\mathrm{\ensuremath{\mu}}\mathrm{s}$ switch-off time) optimal conditions are achieved for values of the phase angle between ${45}^{\ifmmode^\circ\else\textdegree\fi{}}$ and ${55}^{\ifmmode^\circ\else\textdegree\fi{}}$. This conclusion is examined and confirmed by experimental measurements using deuterium atoms. Alternative approaches to generate optimal deceleration pulse sequences, such as the implementation of evolutionary algorithms or the use of higher-order modes of the decelerator, are discussed.

DOI
10.1103/physreva.82.043428

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The phase stability of a multistage Zeeman decelerator is analyzed by numerical particle-trajectory simulations and experimental measurements. A one-dimensional model of the phase stability in multistage Stark deceleration [Bethlem et al., Phys. Rev. Lett. 84, 5744 (2000)] has been adapted to multistage Zeeman deceleration and compared with one- and three-dimensional particle-trajectory simulations, including the analysis of the effect of finite switch-on and -off times of the deceleration pulses. The comparison reveals that transverse effects in the decelerator lead to a considerable reduction of the phase-space acceptance at low values of the phase angle and an enhancement at high values. The optimal combinations of phase angles and currents with which a preset amount of kinetic energy can be removed from atoms and molecules in a pulsed supersonic beam using a multistage decelerator are determined by simulation. Quantitative analysis of the phase-space acceptance within a given volume reveals that for our decelerator (8 \ensuremathμs\mathrm{\ensuremath{\mu}}\mathrm{s}\ensuremathμs switch-off time) optimal conditions are achieved for values of the phase angle between 45\ifmmode∘\else\textdegree\fi{45}^{\ifmmode^\circ\else\textdegree\fi{}}45\ifmmode∘\else\textdegree\fi and 55\ifmmode∘\else\textdegree\fi{55}^{\ifmmode^\circ\else\textdegree\fi{}}55\ifmmode∘\else\textdegree\fi. This conclusion is examined and confirmed by experimental measurements using deuterium atoms. Alternative approaches to generate optimal deceleration pulse sequences, such as the implementation of evolutionary algorithms or the use of higher-order modes of the decelerator, are discussed.
A modular multistage Zeeman decelerator consisting of an array of solenoids has been developed to control the velocity of cold, paramagnetic atoms and molecules in supersonic beams. The translational motion these atoms and molecules was manipulated with high precision by exploiting the interaction between their magnetic moments and timedependent inhomogeneous magnetic elds. Deceleration was achieved by pulsing high currents (up to 300 A) through the solenoids of the decelerator with pulse sequences calculated to preserve the phase-space density of the atomic and molecular samples while removing a preset amount of kinetic energy. For the operation of the multistage Zeeman decelerator, solenoids and electronic units were developed to generate strong magneticeld pulses (> 2 T) with rise and fall times of only a few microseconds. An accurate three-dimensional particle-trajectory simulation program has been developed to analyze the deceleration process and optimize its e ciency. This software was thoroughly tested by systematic comparison with experimental results and enabled, in combination with measurements, the complete characterization of the spatial and velocity distributions of the decelerated and trapped atoms for di erent sets of experimental conditions. The program was essential to achieve a complete interpretation of the dynamics of the deceleration process and to devise a strategy to e ciently load the decelerated atoms and molecules into magnetic quadrupole traps. In a rst experiment, hydrogen atoms seeded in a supersonic expansion of Kr have been decelerated from an initial velocity of 435 m/s to nal velocities as low as 107 m/s in a 12-stage Zeeman decelerator. The operation of the decelerator has been analyzed by comparing the results of numerical particle-trajectory simulations with those of independent measurements of the velocity distribution by ion time-ofight mass spectrometry following photoionization of the decelerated atoms. The velocity distribution of the decelerated atom cloud was found to have a half width at half maximum of 25± 12 m/s corresponding to a temperature of ∼ 40 mK. The phase stability of the multistage-Zeeman-deceleration process has been investigated by numerical particle-trajectory simulations and experimental measurements on deuterium atoms in a 24-stage Zeeman decelerator. A one-dimensional analytical model of the phase stability in a multistage Zeeman decelerator was adapted from a one-dimensional model of phase stability in a multistage Stark decelerator and compared with the results of oneand three-dimensional particle-trajectory simulations. The comparison, which included the analysis of the e ects of nite switch-on and switch-o times of the deceleration pulses, revealed that transverse e ects in the decelerator lead to a considerable reduction of the
We present a formalism to calculate phase-space acceptance in a Zeeman decelerator. Using parameters closely mimicking previous Zeeman deceleration experiments, this approach reveals a velocity dependence of the phase stability which we ascribe to the finite rise and fall times of the current pulses that generate the magnetic fields inside the deceleration coils. It is shown that changing the current switch-off times (characterized by the reduced position of the synchronous particle ${\ensuremath{\kappa}}_{0}$) as the sequence progresses, so as to maintain a constant mean acceleration per pulse, can lead to a constant phase stability and hence a beam with well-defined characteristics. We also find that the time overlap between fields of adjacent coils has an influence on the phase-space acceptance. Previous theoretical and experimental results [A. W. Wiederkehr et al., Phys. Rev. A 82, 043428 (2010); J. Chem. Phys. 135, 214202 (2011).] suggested unfilled regions in phase space that influence particle transmission through the decelerator. Our model provides a means to directly identify the origin of these effects due to coupling between longitudinal and transverse dynamics. Since optimum phase stability is restricted to a rather small parameter range in terms of the reduced position of the synchronous particle ${\ensuremath{\kappa}}_{0}$, only a limited range of final velocities can be attained using a given number of coils. We evaluate phase stability for different Zeeman deceleration sequences, and by comparison with numerical three-dimensional particle-trajectory simulations, we demonstrate that our model provides a valuable tool to find optimum parameter sets for improved Zeeman deceleration schemes. An acceleration-deceleration scheme is shown to be a useful approach to generating beams with well-defined properties for variable-energy collision experiments. More generally, the model provides significant physical insights that are applicable to other types of particle decelerators with finite rise and fall time fields.
A supersonic beam of metastable neon atoms has been decelerated by exploiting the interaction between the magnetic moment of the atoms and time-dependent inhomogeneous magnetic fields in a multistage Zeeman decelerator. Using 91 deceleration solenoids, the atoms were decelerated from an initial velocity of 580m/s to final velocities as low as 105m/s, corresponding to a removal of more than 95% of their initial kinetic energy. The phase-space distribution of the cold, decelerated atoms was characterized by time-of-flight and imaging measurements, from which a temperature of 10mK was obtained in the moving frame of the decelerated sample. In combination with particle-trajectory simulations, these measurements allowed the phase-space acceptance of the decelerator to be quantified. The degree of isotope separation that can be achieved by multistage Zeeman deceleration was also studied by performing experiments with pulse sequences generated for ²⁰Ne and ²²Ne. © 2011 American Institute of Physics.
We present a concept for a multistage Zeeman decelerator that is optimized particularly for applications in molecular beam scattering experiments. The decelerator consists of a series of alternating hexapoles and solenoids, that effectively decouple the transverse focusing and longitudinal deceleration properties of the decelerator. It can be operated in a deceleration and acceleration mode, as well as in a hybrid mode that makes it possible to guide a particle beam through the decelerator at constant speed. The deceleration features phase stability, with a relatively large six-dimensional phase-space acceptance. The separated focusing and deceleration elements result in an unequal partitioning of this acceptance between the longitudinal and transverse directions. This is ideal in scattering experiments, which typically benefit from a large longitudinal acceptance combined with narrow transverse distributions. We demonstrate the successful experimental implementation of this concept using a Zeeman decelerator consisting of an array of 25 hexapoles and 24 solenoids. The performance of the decelerator in acceleration, deceleration, and guiding modes is characterized using beams of metastable helium (3S^{3}S3S) atoms. Up to 60% of the kinetic energy was removed for He atoms that have an initial velocity of 520 m/s. The hexapoles consist of permanent magnets, whereas the solenoids are produced from a single hollow copper capillary through which cooling liquid is passed. The solenoid design allows for excellent thermal properties and enables the use of readily available and cheap electronics components to pulse high currents through the solenoids. The Zeeman decelerator demonstrated here is mechanically easy to build, can be operated with cost-effective electronics, and can run at repetition rates up to 10 Hz.
The concept of phase stability in a Stark decelerator ensures that polar molecules can be accelerated, guided, or decelerated without loss; molecules within a certain position and velocity interval are kept together throughout the deceleration process. In this paper the influence of the transverse motion on phase stability in a Stark decelerator is investigated. For typical deceleration experiments---i.e., for high values of the phase angle ${\ensuremath{\phi}}_{0}$---the transverse motion considerably enhances the region in phase space for which phase stable deceleration occurs. For low values of ${\ensuremath{\phi}}_{0}$, however, the transverse motion reduces the acceptance of a Stark decelerator and unstable regions in phase space appear. These effects are quantitatively explained in terms of a coupling between the longitudinal and transverse motion. The predicted longitudinal acceptance of a Stark decelerator is verified by measurements on a beam of OH $(X\phantom{\rule{0.2em}{0ex}}^{2}\ensuremath{\Pi}_{3∕2},J=3∕2)$ radicals passing through a Stark decelerator.
Hydrogen and deuterium atoms in supersonic jet expansions have been decelerated using a multistage Zeeman decelerator. The properties of the decelerator have been completely characterized in a series of experiments in which (i) the initial longitudinal velocities of the decelerated atoms, (ii) the maximum magnetic field strength, and (iii) the duration of zero-field intervals between successive field pulses in neighboring deceleration stages were systematically varied. Experiments using Ar and Kr as carrier gases have clearly revealed that the H atoms are located at the surface of the jet expansion cone in each case. Comparison of the results of these experiments with numerical simulations of the atom trajectories through the decelerator provides a full description of the phase-space distribution of the decelerated atoms. Evidence is presented of transverse guiding of the beam and of a partial redistribution of the H atom population among the MF{M}_{F}MF​ components of the F=1F=1F=1 manifold at times when the magnetic field strength approaches zero.