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International Journal of Modern Physics B

Trapping paramagnetic molecules in a dynamic magnetic trap

Sheng-Qiang Li, Jing Lin, Xue Chen, Nannan Zhang

Published Mar 8, 2024• 0 citations
Publisher

Abstract

Trapping molecules in strong-field-seeking states is particularly attractive to scientists in the field of molecular optics. If the external field is strong enough, all molecules are strong-field seekers. Contrary to the weak-field-seeking states, molecules trapping in strong-field-seeking states can avoid the loss caused by the inelastic collision which is a stumbling block for evaporative and sympathetic cooling. Unfortunately, the formation of a magnetostatic maximum in free space is forbidden according to Maxwell’s equations and Earnshaw’s theory. In this paper, a dynamic magnetic trap consisting of three pairs of Helmholtz coils is proposed. The time-sequence control is given together with the distribution of the magnetic field in space. The influence of the switching frequency and electric current flowing through the wires on the number of trapped molecules is investigated. We obtain the changes in the locations and the phase-space distribution within a switching cycle by trajectory simulation. Finally, the influence of the time during which the field is off on the performance of our trap is studied.

DOI
10.1142/s0217979225500237

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Trapping molecules in strong-field-seeking states is particularly attractive to scientists in the field of molecular optics. If the external field is strong enough, all molecules are strong-field seekers. Contrary to the weak-field-seeking states, molecules trapping in strong-field-seeking states can avoid the loss caused by the inelastic collision which is a stumbling block for evaporative and sympathetic cooling. Unfortunately, the formation of a magnetostatic maximum in free space is forbidden according to Maxwell’s equations and Earnshaw’s theory. In this paper, a dynamic magnetic trap consisting of three pairs of Helmholtz coils is proposed. The time-sequence control is given together with the distribution of the magnetic field in space. The influence of the switching frequency and electric current flowing through the wires on the number of trapped molecules is investigated. We obtain the changes in the locations and the phase-space distribution within a switching cycle by trajectory simulation. Finally, the influence of the time during which the field is off on the performance of our trap is studied.
Abstract Strong-field-seeking states are the lowest-energy configurations for paramagnetic molecules in the magnetic field. Molecules in strong-field-seeking states cannot be trapped in a magnetostatic field because a magnetostatic maximum in free space is not allowed. In this paper, we propose an AC magnetic trap composed of two pairs of Helmholtz coils. The spatial magnetic field distribution is numerically calculated and the time-sequential control is depicted. We investigate the influence of the switching frequency and the electric current in the coils on the performance of our trap. Variations of the location and phase-space distribution during a whole switching cycle are simulated. Finally, we study the impact of time during which the field is switched off on the number of captured molecules in a switching cycle.
Polar molecules in high-field seeking states cannot be trapped in static traps as Maxwell's equations do not allow a maximum of the electric field in free space. It is possible to generate an electric field that has a saddle point by superposing an inhomogeneous electric field to an homogeneous electric field. In such a field, molecules are focused along one direction, while being defocused along the other. By reversing the direction of the inhomogeneous electric field the focusing and defocusing directions are reversed. When the fields are being switched back and forth at the appropriate rate, this leads to a net focusing force in all directions. We describe possible electrode geometries for creating the desired fields and discuss their merits. Trapping of 15ND3^{15}\mathrm{ND}_{3}15ND3​ ammonia molecules in a cylindrically symmetric ac trap is demonstrated. We present measurements of the spatial distribution of the trapped cloud as a function of the settings of the trap and compare these to both a simple model assuming a linear force and to full three-dimensional simulations of the experiment. With the optimal settings, molecules within a phase-space volume of 270mm3(m∕s)3270\phantom{\rule{0.3em}{0ex}}{\mathrm{mm}}^{3}\phantom{\rule{0.2em}{0ex}}(\mathrm{m}∕\mathrm{s}{)}^{3}270mm3(m∕s)3 remain trapped. This corresponds to a trap depth of about 5mK5\phantom{\rule{0.3em}{0ex}}\mathrm{mK}5mK and a trap volume of about 20mm320\phantom{\rule{0.3em}{0ex}}{\mathrm{mm}}^{3}20mm3.
The concept of a novel traveling wave Zeeman deccelerator based on a double-helix wire geometry capable of decelerating paramagnetic species with high efficiency is presented. A moving magnetic trap is created by running time-dependent currents through the decelerator coils. Paramagnetic species in low-field-seeking Zeeman states are confined in the moving traps and transported to the end of the decelerator with programmable velocities. Here, we present the theoretical foundations underlying the working principle of the traveling-trap decelerator. Using trajectory simulations, we characterise the performance of the new device and explore the conditions for phase-space stability of the transported molecules.
Synopsis We decelerate and trap molecular oxygen using time-dependent magnetic fields and superconducting magnets. The density-dependent, non-exponential decay in particle number provides a clear proof of molecule-molecule collisions within the trapped ensemble. The spatial distribution of molecules in the trap is found to change over time, allowing to set limits on the ratio between the elastic and inelastic collision cross sections. Our experimental scheme opens up new possibilities for studying quantum effects in chemistry as well as for evaporative cooling of molecules.
The collisional stability of ultracold polar molecules in electrostatic traps is considered. Rate constants for collisions that drive molecules from weak-electric-field-seeking to strong-field-seeking states are estimated using a simple model that emphasizes long-range dipolar forces. The rate constants for collisional losses are found to vary substantially as a function of molecular parameters used in the model, such as dipole moment, mass, and the splitting of the molecular $\ensuremath{\Lambda}$ doublet. Varying these parameters over physically reasonable ranges yields rate constants as low as ${10}^{\ensuremath{-}20} {\mathrm{cm}}^{3}/\mathrm{sec}$ and as high as ${10}^{\ensuremath{-}10} {\mathrm{cm}}^{3}/\mathrm{sec}.$ Nevertheless, the loss rates rise dramatically in the presence of the externally applied trapping electric field. For this reason it is argued that electrostatic traps are likely to be less stable against collisional losses than their magnetic counterparts.
A novel traveling-wave Zeeman decelerator based on a double-helix coil geometry capable of decelerating paramagnetic molecules with high efficiency is presented. Moving magnetic traps are generated by applying time-dependent currents through the decelerator coils. Paramagnetic molecules in low-field-seeking Zeeman states are confined inside the moving traps which are decelerated to lower forward velocities. As a prototypical example, we demonstrate the deceleration of OH radicals from an initial velocity of 445 m s −1 down to various final velocities. The experimental results are analyzed and numerically reproduced with the help of trajectory simulations confirming the phase-space stability and efficiency of the deceleration of the molecules in the new device.