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Physical Review A

Electrodynamic trap for neutral polar particles

R. Blümel

Published Apr 18, 2011• 4 citations
Publisher

Abstract

A superposition of inhomogeneous static and rapidly oscillating electric fields is capable of trapping neutral particles with a permanent electric dipole moment. Detailed numerical simulations prove the validity and stability of our trapping scheme. Thin rods of barium titanate (BaTiO${}_{3}$) are presented as an example for trapping on the macroscale. HC${}_{17}$N, a polar molecule of astrophysical significance, is presented as an example for trapping on the microscale. For HC${}_{17}$N and the parameters chosen, the depth of the trap is $40 $mK.

DOI
10.1103/physreva.83.045402

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A superposition of inhomogeneous static and rapidly oscillating electric fields is capable of trapping neutral particles with a permanent electric dipole moment. Detailed numerical simulations prove the validity and stability of our trapping scheme. Thin rods of barium titanate (BaTiO3{}_{3}3​) are presented as an example for trapping on the macroscale. HC17{}_{17}17​N, a polar molecule of astrophysical significance, is presented as an example for trapping on the microscale. For HC17{}_{17}17​N and the parameters chosen, the depth of the trap is 4040 40mK.
Abstract A novel design for an electromagnetic trap is proposed for confinement of neutral particles having a permanent electric dipole moment. The device uses a combination of a sextupole electric and quadrupole magnetic fields superimposed with a strong constant electric field perfectly aligned along the z-axis. We use the extended dipole model to study the dynamics of particle in this position dependent electromagnetic field. The motion of the centre of mass of the dipole is nonlinearly coupled with its rotation. We find three families of particular solutions for which the orbits are periodic or quasiperiodic. They correspond to the particular cases when the whole energy is accumulated in either translational or rotational degrees of freedom. Stability analysis of chosen particular solutions provides trapping conditions. We present several numerical simulations which illustrate trapping and confinement of an electric dipole in the proposed trap. These simulations were performed for three kinds of polar particles and various fields selections. We hope that the proposed model allows experimental physicists to apply a wide variety of non-destructive methods for manipulation, detection and analysis of trapped particles.
A detailed treatment of an electro-optical trap for polar molecules, realized by embedding an optical trap within a uniform electrostatic field, is presented and the trap's properties analyzed and discussed. The electro-optical trap offers significant advantages over an optical trap that include an increased trap depth and conversion of alignment of the trapped molecules to marked orientation. Tilting the polarization plane of the optical field with respect to the electrostatic field diminishes both the trap depth and orientation and lifts the degeneracy of the $\ifmmode\pm\else\textpm\fi{}M$ states of the trapped molecules. These and other features of the electro-optical trap are examined in terms of the eigenproperties of the polar and polarizable molecules subject to the combined permanent and induced electric dipole interactions at play.
A polar molecule experiences a force in an inhomogeneous electric field. Using this force, neutral molecules can be decelerated and trapped. It is shown here that this can in principle be done without loss in phase-space density. Using a series of 64 pulsed inhomogeneous electric fields a supersonic beam of ammonia molecules (14NH3,{(}^{14}{\mathrm{NH}}_{3},(14NH3​, 14ND3,{}^{14}{\mathrm{ND}}_{3},14ND3​, 15ND3){}^{15}{\mathrm{ND}}_{3})15ND3​) is decelerated. Subsequently, the decelerated molecules are loaded into an electrostatic quadrupole trap. Densities on the order of 107molecules/cm3{10}^{7} {\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}/\mathrm{c}\mathrm{m}}^{3}107molecules/cm3 at a temperature of 25 mK are obtained for 14ND3{}^{14}{\mathrm{ND}}_{3}14ND3​ and 15ND3{}^{15}{\mathrm{ND}}_{3}15ND3​ separately and simultaneously. This corresponds to a phase-space density in the trap of $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13},$ 50 times less than the initial phase-space density in the beam.
We theoretically investigate the dynamics of linear polar molecules in static quadrupole electric fields. Numerical calculation shows that molecules rotating in a specific direction experience a restoring force, being three-dimensionally trapped in the center of the field distribution. We formulate the probability of Majorana transition and the trapping lifetime with a simple model of a rotating dipole. Potential depth of the electrostatic trap is quantum-mechanically estimated to be in the order of 100 mK.
Heavy polar molecules can be used to measure the electric dipole moment of the electron, which is a sensitive probe of physics beyond the Standard Model. The value is determined by measuring the precession of the molecule’s spin in a plane perpendicular to an applied electric field. The longer this precession evolves coherently, the higher the precision of the measurement. For molecules in a trap, this coherence time could be very long indeed. We evaluate the sensitivity of an experiment where neutral molecules are trapped electrically, and compare this to an equivalent measurement in a molecular beam. We consider the use of a Stark decelerator to load the trap from a supersonic source, and calculate the deceleration efficiency for YbF molecules in both strong-field seeking and weak-field seeking states. With a 1 s holding time in the trap, the statistical sensitivity could be ten times higher than it is in the beam experiment, and this could improve by a further factor of five if the trap can be loaded from a source of larger emittance. We study some effects due to field inhomogeneity in the trap and find that rotation of the electric field direction, leading to an inhomogeneous geometric phase shift, is the primary obstacle to a sensitive trap-based measurement. 1
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.