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Journal of Applied Physics

Analysis of Paul–Straubel trap and its variations

Nan Yu, Warren Nagourney

Published Apr 15, 1995• 13 citations
Publisher

Abstract

Unconventional rf traps of the Paul–Straubel type and its variations have found increasing use in ion trapping experiments. Calculations of the properties of these traps are presented. Simple realistic trap geometries are studied for their voltage loss factor, anharmonicity, and radial symmetry breaking. Optimum geometries for these traps are indicated.

DOI
10.1063/1.358598

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In some recently proposed experiments using ion traps, a Paul trap of conventional size and design is insufficient. We have constructed a miniature Paul-Straubel trap. It has a small elliptic ring ( approximately 0.2 mm) and three pairs of planar electrodes ( approximately 2 cm part) arranged so that they form a cube. The two conventional end-cap electrodes are replaced by the six planar electrodes. The ring is heatable to a high temperature for improving the uniformity of the dc potential on the ring surface. With this trap, we hope to do such fundamental studies as the true zero-point confinement of a single ion.

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Trapping ions in Paul traps require high radio frequency voltages, which are generated using resonators. When operating traps in a cryogenic environment, an in-vacuum resonator showing low loss is crucial to limit the thermal load to the cryostat. In this study, we present a guide for the design and production of compact, shielded cryogenic resonators. We produced and characterized three different types of resonators and furthermore demonstrate efficient impedance matching of these resonators at cryogenic temperatures.

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Bulletin of the American Physical Society•May 1, 1993•0 citations
Unconventional rf traps of the Paul–Straubel type and its variations have found increasing use in ion trapping experiments. Calculations of the properties of these traps are presented. Simple realistic trap geometries are studied for their voltage loss factor, anharmonicity, and radial symmetry breaking. Optimum geometries for these traps are indicated.
New Paul–Straubel traps [H. Straubel, Naturwissenschaften 18, 506 (1955)] have been recently constructed and used to trap single Ba+ ions. Unlike a conventional rf trap, these traps use only a ring electrode surrounded by an uncritical ground electrode structure. The overall simplicity makes it easy to miniaturize the trap and to control the trapping potential spatial orientation. The new design also allows intense heating of the ring electrode with an ion in the trap simply by passing a large current through it. This removes surface layers responsible for large contact potentials varying over the ring surface and greatly reduces the forced micromotion of the ion, which is supposedly ‘‘at rest.’’
In some recently proposed experiments using ion traps, a Paul trap of conventional size and design is insufficient. We have constructed a miniature Paul-Straubel trap. It has a small elliptic ring ( approximately 0.2 mm) and three pairs of planar electrodes ( approximately 2 cm part) arranged so that they form a cube. The two conventional end-cap electrodes are replaced by the six planar electrodes. The ring is heatable to a high temperature for improving the uniformity of the dc potential on the ring surface. With this trap, we hope to do such fundamental studies as the true zero-point confinement of a single ion.
Planar quadrupole ion traps have been analyzed through numerical and analytic solutions of Laplace's equation. These involve either one or more conducting rings or their analogs, a hole in one or more conducting sheets. The leading terms in the potential are harmonic, corresponding to the Paul trap, but with coefficients that reduce their efficiency and for some traps, the anharmonic terms can be suppressed to eighth-order. Stable ion trapping is predicted for all electrode configurations possessing radial and axial symmetry. A three-hole microtrap with an inner hole radius of 80 \ensuremath{\mu}m trapped from one to many (dense clouds) laser-cooled Ba+{\mathrm{Ba}}^{+}Ba+ ions where the two-ion distance is compressed to 1 \ensuremath{\mu}m, allowing new experiments in quantum optics. Also, arrays of traps for optical clocks are contemplated using photolithographic fabrication.
Abstract Radio-frequency (RF) linear multipole traps have been shown to be very sensitive to mis-positioning of their electrodes, which results in a symmetry breaking and leads to extra local minima in the trapping potential as shown in Pedregosa-Gutierrez et al (2018 J. Mod. Opt. 65 529) disturbing the operation of the trap. In this work, we analytically describe the RF-potential of a realistic octupole trap by including lower order terms to the well-established equation for a perfectly symmetric octupole trap. We describe the geometry by a combination of identified defects, characterized by simple analytical expressions. A complete equation is proposed for a trap with any electrode deviation relying on a combination of the simple cases where the defects are taken individually. Our approach is validated by comparison between analytical and numerical results for defect sizes up to 4% of the trap radius. As described in Pedregosa-Gutierrez et al (2018 Rev. Sci. Instrum. 89 123101), an independent fine-tuning of the amplitude of the RF voltage applied on each electrode can be used to mitigate the geometrical defects of a realistic trap. In a different way than in Pedregosa-Gutierrez et al (2018 Rev. Sci. Instrum. 89 123101), the knowledge of an analytical equation for the potential allows to design the set of RF-voltages required for this compensation, based on the experimental measurement of the ion positions in the trap, without information concerning the exact position of each electrode, and with a small number of iterations. The requirements, performances and limitations of this protocol are discussed via comparison of numerical simulations and analytical results.
Trapping ions in Paul traps require high radio frequency voltages, which are generated using resonators. When operating traps in a cryogenic environment, an in-vacuum resonator showing low loss is crucial to limit the thermal load to the cryostat. In this study, we present a guide for the design and production of compact, shielded cryogenic resonators. We produced and characterized three different types of resonators and furthermore demonstrate efficient impedance matching of these resonators at cryogenic temperatures.
We report on development of a miniature linear rf ion trap and preliminary efforts to trap and laser-cool {sup 24}Mg{sup +} ions. This trap has a radial dimension of 50 {mu}m, one tenth the size of our previous trap. The rms confinement of a trapped ion scales as R{sup -2}, where R is the trap radius, so tight confinement of ions is possible at a modest rf voltage. Although the three-dimensional trapping potential for our trap cannot be calculated analytically, it can be described in terms of dimensionless parameters, measured by studying macroscopic charged particles in a much larger model of the trap. We expect that with this trap it will be possible to achieve secular frequencies high enough for resolved-sideband cooling of light ions using allowed dipole transitions. This will make it much easier to perform experiments on the quantum motion of trapped ions. This trap uses a two-wire design rather than the more common four-wire one, so the trap electrodes occlude a much smaller solid angle than either a four-wire linear trap or the more common quadrupole trap. Thus, it will be possible to couple optical devices, such as high-finesse cavities, much more efficiently to trapped ions.