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New Journal of Physics

Zeeman deceleration beyond periodic phase space stability

Jutta Toscano, Atreju Tauschinsky, Katrin Dulitz, Chris Rennick, Brianna R. Heazlewood, T. P. Softley

Published Aug 16, 2017• 12 citations
Publisher

Abstract

In Zeeman deceleration, time-varying spatially inhomogeneous magnetic fields are used to create packets of translationally cold, quantum-state-selected paramagnetic particles with a tuneable forward velocity, which are ideal for cold reaction dynamics studies. Here, the covariance matrix adaptation evolutionary strategy is adopted in order to optimise deceleration switching sequences for the operation of a Zeeman decelerator. Using the optimised sequences, a 40% increase in the number of decelerated particles is observed compared to standard sequences for the same final velocity, imposing the same experimental boundary conditions. Furthermore, we demonstrate that it is possible to remove up to 98% of the initial kinetic energy of particles in the incoming beam, compared to the removal of a maximum of 83% of kinetic energy with standard sequences. Three-dimensional particle trajectory simulations are employed to reproduce the experimental results and to investigate differences in the deceleration mechanism adopted by standard and optimised sequences. It is experimentally verified that the optimal solution uncovered by the evolutionary algorithm is not merely a local optimisation of the experimental parameters—it is a novel mode of operation that goes beyond the standard periodic phase stability approach typically adopted.

DOI
10.1088/1367-2630/aa7ef5

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Generating a controllable and pure source of molecular free-radicals or open-shell atoms has been one of the primary barriers hindering the detailed study of radical processes in the laboratory. In this thesis, a novel source of state-selected radicals -- composed of a Zeeman decelerator interfaced with a newly-designed magnetic guide -- is introduced. This tuneable source generates a pure beam of velocity-selected hydrogen atoms that will enable the study of radical interactions with exceptional control over the properties of the radical species. In Zeeman deceleration, time-varying spatially inhomogeneous magnetic fields are used to create packets of translationally cold, quantum-state-selected paramagnetic particles with a tuneable forward velocity, which are ideal for cold reaction dynamics studies. In a proof-of-principle experiment, the Zeeman deceleration of nitrogen atoms in the metastable 2D5/2 state from 460 to 410 m/s is demonstrated for the first time. The covariance matrix adaptation evolutionary strategy (CMA-ES) is adopted in order to optimise deceleration switching sequences for the operation of a 12-stage Zeeman decelerator. Using the optimised sequences, a 40% increase in the number of decelerated H(2S1/2) atoms is observed compared to standard sequences for the same final velocity, imposing the same experimental boundary conditions. Furthermore, up to 98% of the initial kinetic energy of particles in the incoming beam is removed by the optimised sequences, compared to the removal of a maximum of 83% of kinetic energy with standard sequences. Three-dimensional particle-trajectory simulations show that the optimal solution uncovered by the evolutionary algorithm is not merely a local optimisation of the experimental parameters -- it is a new mode of operation that goes beyond the standard periodic phase stability approach typically adopted. A novel magnetic guide is designed and constructed to purify the post-deceleration beam. Only radicals with a selected velocity are transmitted through the guide; all other components of the incoming beam (radical species travelling at other velocities, precursor molecules and seed gases) are removed. The guide is composed of four Halbach arrays -- hexapolar focusing elements -- and two skimming blades. The relative positions of these components can be adjusted to tune the properties of the resulting beam and to optimise transmission for a given velocity. Experimental measurements of Zeeman-decelerated H atoms transmitted through the guide, combined with extensive simulations, show that the magnetic guide successfully removes 99% of H atoms travelling outside the narrow target velocity range.

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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.

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Zeeman deceleration is an experimental technique which allows for the manipulation of open-shell atoms and molecules in a supersonic beam thus producing mK-cold, velocity-tunable beams of particles in selected quantum states. The method relies on the Zeeman interaction between paramagnetic particles and time-varying, inhomogeneous magnetic fields generated by pulsing high currents through an array of solenoid coils. This thesis describes the construction and implementation of a supersonic beam setup including a 12-stage Zeeman decelerator. The Zeeman decelerator follows an original design that makes it possible to replace individual deceleration coils. Using ground-state hydrogen atoms as a test system, it is shown that the transverse acceptance in a Zeeman decelerator can be significantly increased by generating a rather low, temporally varying quadrupole field in one of the solenoid coils. An electron-impact source was constructed and optimised enabling, for the first time, the Zeeman deceleration of metastable helium atoms in the 23S1 state, with an up to 40 % decrease in the kinetic energy of the beam. It is shown that the pulse duration for electron-impact excitation needs to be matched to the acceptance of the decelerator in order to attain a good contrast between the decelerated and undecelerated parts of the beam. Experimental results are rigorously analysed and interpreted using three-dimensional numerical particle trajectory simulations. A phase-space model provides, for the first time, a means to estimate the six-dimensional phase-space acceptance in a Zeeman decelerator and to find optimum parameter sets for improved Zeeman deceleration schemes. The approach also reveals a hitherto unconsidered velocity dependence of the phase stability which is ascribed mainly to the rise and fall times of the current pulses that generate the magnetic fields inside the deceleration coils. In the future, it is planned to combine the Zeeman decelerator with a source of cold atomic and molecular ions to study chemical collisions at low temperatures. A hybrid magnetic guide consisting of permanent magnet assemblies (Halbach arrays) in hexapole configuration and a set of current-carrying wires is proposed and simulated as an interface between these setups. The design promises very efficient velocity selection, a high degree of quantum-state selection and a nearly complete removal of residual carrier gas. Prospects for using magnetic hexapole focusing in front of the Zeeman decelerator are discussed. The work represents a major step towards the study and control of chemical reactivity of paramagnetic species in the low-temperature regime and it will help in the testing of fundamental chemical reaction theories.

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Multistage Zeeman deceleration of metastable neon

A. W. Wiederkehr, M. Motsch, S. D. Hogan +5 more

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.

•Dec 7, 2011•19 citations
In Zeeman deceleration, time-varying spatially inhomogeneous magnetic fields are used to create packets of translationally cold, quantum-state-selected paramagnetic particles with a tuneable forward velocity, which are ideal for cold reaction dynamics studies. Here, the covariance matrix adaptation evolutionary strategy is adopted in order to optimise deceleration switching sequences for the operation of a Zeeman decelerator. Using the optimised sequences, a 40% increase in the number of decelerated particles is observed compared to standard sequences for the same final velocity, imposing the same experimental boundary conditions. Furthermore, we demonstrate that it is possible to remove up to 98% of the initial kinetic energy of particles in the incoming beam, compared to the removal of a maximum of 83% of kinetic energy with standard sequences. Three-dimensional particle trajectory simulations are employed to reproduce the experimental results and to investigate differences in the deceleration mechanism adopted by standard and optimised sequences. It is experimentally verified that the optimal solution uncovered by the evolutionary algorithm is not merely a local optimisation of the experimental parameters—it is a novel mode of operation that goes beyond the standard periodic phase stability approach typically adopted.
Generating a controllable and pure source of molecular free-radicals or open-shell atoms has been one of the primary barriers hindering the detailed study of radical processes in the laboratory. In this thesis, a novel source of state-selected radicals -- composed of a Zeeman decelerator interfaced with a newly-designed magnetic guide -- is introduced. This tuneable source generates a pure beam of velocity-selected hydrogen atoms that will enable the study of radical interactions with exceptional control over the properties of the radical species. In Zeeman deceleration, time-varying spatially inhomogeneous magnetic fields are used to create packets of translationally cold, quantum-state-selected paramagnetic particles with a tuneable forward velocity, which are ideal for cold reaction dynamics studies. In a proof-of-principle experiment, the Zeeman deceleration of nitrogen atoms in the metastable 2D5/2 state from 460 to 410 m/s is demonstrated for the first time. The covariance matrix adaptation evolutionary strategy (CMA-ES) is adopted in order to optimise deceleration switching sequences for the operation of a 12-stage Zeeman decelerator. Using the optimised sequences, a 40% increase in the number of decelerated H(2S1/2) atoms is observed compared to standard sequences for the same final velocity, imposing the same experimental boundary conditions. Furthermore, up to 98% of the initial kinetic energy of particles in the incoming beam is removed by the optimised sequences, compared to the removal of a maximum of 83% of kinetic energy with standard sequences. Three-dimensional particle-trajectory simulations show that the optimal solution uncovered by the evolutionary algorithm is not merely a local optimisation of the experimental parameters -- it is a new mode of operation that goes beyond the standard periodic phase stability approach typically adopted. A novel magnetic guide is designed and constructed to purify the post-deceleration beam. Only radicals with a selected velocity are transmitted through the guide; all other components of the incoming beam (radical species travelling at other velocities, precursor molecules and seed gases) are removed. The guide is composed of four Halbach arrays -- hexapolar focusing elements -- and two skimming blades. The relative positions of these components can be adjusted to tune the properties of the resulting beam and to optimise transmission for a given velocity. Experimental measurements of Zeeman-decelerated H atoms transmitted through the guide, combined with extensive simulations, show that the magnetic guide successfully removes 99% of H atoms travelling outside the narrow target velocity range.
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.
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.
Zeeman deceleration is an experimental technique which allows for the manipulation of open-shell atoms and molecules in a supersonic beam thus producing mK-cold, velocity-tunable beams of particles in selected quantum states. The method relies on the Zeeman interaction between paramagnetic particles and time-varying, inhomogeneous magnetic fields generated by pulsing high currents through an array of solenoid coils. This thesis describes the construction and implementation of a supersonic beam setup including a 12-stage Zeeman decelerator. The Zeeman decelerator follows an original design that makes it possible to replace individual deceleration coils. Using ground-state hydrogen atoms as a test system, it is shown that the transverse acceptance in a Zeeman decelerator can be significantly increased by generating a rather low, temporally varying quadrupole field in one of the solenoid coils. An electron-impact source was constructed and optimised enabling, for the first time, the Zeeman deceleration of metastable helium atoms in the 23S1 state, with an up to 40 % decrease in the kinetic energy of the beam. It is shown that the pulse duration for electron-impact excitation needs to be matched to the acceptance of the decelerator in order to attain a good contrast between the decelerated and undecelerated parts of the beam. Experimental results are rigorously analysed and interpreted using three-dimensional numerical particle trajectory simulations. A phase-space model provides, for the first time, a means to estimate the six-dimensional phase-space acceptance in a Zeeman decelerator and to find optimum parameter sets for improved Zeeman deceleration schemes. The approach also reveals a hitherto unconsidered velocity dependence of the phase stability which is ascribed mainly to the rise and fall times of the current pulses that generate the magnetic fields inside the deceleration coils. In the future, it is planned to combine the Zeeman decelerator with a source of cold atomic and molecular ions to study chemical collisions at low temperatures. A hybrid magnetic guide consisting of permanent magnet assemblies (Halbach arrays) in hexapole configuration and a set of current-carrying wires is proposed and simulated as an interface between these setups. The design promises very efficient velocity selection, a high degree of quantum-state selection and a nearly complete removal of residual carrier gas. Prospects for using magnetic hexapole focusing in front of the Zeeman decelerator are discussed. The work represents a major step towards the study and control of chemical reactivity of paramagnetic species in the low-temperature regime and it will help in the testing of fundamental chemical reaction theories.
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
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.