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Japanese Journal of Applied Physics

Dynamic Properties of Polar Molecules Confined in Electrostatic Trap

Masatoshi Kajita, Takayuki Suzuki Takayuki Suzuki, Hitoshi Odashima, Yoshiki Moriwaki, Maki Tachikawa

Published Nov 1, 2001• 13 citations
Publisher

Abstract

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.

DOI
10.1143/jjap.40.l1260

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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.
We analyze the dynamics of a paramagnetic, dipolar molecule in a generic ``magneto-electrostatic'' trap where both magnetic and electric fields may be present. The potential energy that governs the dynamics of the molecules is found using a reduced molecular model that incorporates the main features of the system. We discuss the shape of the trapping potentials for different field geometries, as well as the possibility of nonadiabatic transitions to untrapped states, i.e., the analog of Majorana transitions in a quadrupole magnetic atomic trap. Maximizing the lifetime of molecules in a trap is of great concern in current experiments, and we assess the effect of nonadiabatic transitions on obtainable trap lifetimes.
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.
We propose a versatile electrostatic trap scheme using several charged spherical electrodes and a bias electric field. We first give the two-ball scheme and derive the analytical solution of the electric field. In order to make a comparison, we also give the numerical solution calculated by the finite element software (Ansoft Maxwell). Considering the loading of cold polar molecules into the trap, we give the three-ball scheme. We first give the analytical and numerical solutions of the distribution of the electric field. Then we simulate the dynamic process of the loading and trapping cold molecules using the classical Monte Carlo method. We analyze the influence of the velocity of the incident molecular beam and the loading time on the loading efficiency. After that, we give the temperature of the trapped cold molecules. Our study shows that the loading efficiency can reach 82%, and the corresponding temperature of the trapped molecules is about 24.6 mK. At last, we show that the single well divides into two ones by increasing the bias electric field or decreasing the voltages applied to the spherical electrodes.
Abstract We discuss the trapping of heteronuclear diatomic molecules prepared in their electronic and vibrational ground states. We tune and shape the trapping potential for bosonic polar molecules in superpositions of rotational states by dressing rotational excitations with a static sextupole electric field. The translational motion of a molecule is treated classically. We examine the Hamiltonian which governs the center of mass dynamics. The effective potential has a global minimum that provides the trapping ability of this trap. The first term of its Taylor series expansion, corresponding to the quadratic Stark shifts, results in the integrable potential. In terms of cylindrical coordinates the center of mass Hamiltonian splits into axial and radial parts. Corresponding trajectories are parameterized by elliptic functions. At low electric fields, the non-approximated Hamiltonian is treated as a small perturbation of the mentioned integrable system described by Kolmogorov–Arnold–Moser theory. The applicability of this approximation is discussed and illustrated using the Poincaré cross-section method. We present results of numerical simulations illustrating the trapping and confinement of a polar molecule in the trap.
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.
An electrostatic lattice is composed of many micro-scale traps. It is a powerful tool for manipulating cold polar molecules on a chip with the help of the interaction between the dipole moment and the inhomogeneous electric field. To the best of our knowledge, the existing electrostatic lattice still suffers the nonadiabatic transition that will lead to the escape of molecules from the electrostatic trap. In the paper, we skillfully design the electrode structure to avoid the zero-field zone at the center of every single microtrap, and the nonadiabatic transitions can be prevented. First, we numerically calculate the distribution of the spatial electrostatic field. Then, the influences of voltages on the electric field intensity and the height of the trap center are investigated. We simulate of the trajectory of molecules using the Monte Carlo method and figure out the factors impacting the loading efficiency of our electrostatic lattice. At last, we discuss how the voltages and the loading positions affect the positional distribution of trapped molecules.