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arXiv:2605.02332

Field configurations for field-free RF trap networks

Janus H. Wesenberg

quant-phSubmitted May 4, 2026• Announced May 5, 2026• 0 citations
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Abstract

We develop a constructive framework for designing radio-frequency (RF) trap networks from planar data and show that non-smooth field-free guide lines are possible in such networks. Given analytic Cauchy data on a symmetry plane, namely the potential and its normal derivative, Laplace's equation determines a local three-dimensional continuation. The odd subclass of this harmonic extension maps an arbitrary analytic generating function $P(x,y)$ to a harmonic potential whose in-plane radio-frequency null set is exactly $P(x,y)=0$. This yields explicit field-free guide networks beyond smooth straight-line intersections, including cusp guides, cotangential contacts, and periodic lattices. We further derive Fourier-space formulas for periodic extensions and present square-lattice network families with tunable local crossing angle and rounded connectivity. These results provide a compact parametrization for the design space for quantum charge-coupled device (QCCD) architectures.

Comments
Preliminary version with draft figures and very limited references

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We develop a constructive framework for designing radio-frequency (RF) trap networks from planar data and show that non-smooth field-free guide lines are possible in such networks. Given analytic Cauchy data on a symmetry plane, namely the potential and its normal derivative, Laplace's equation determines a local three-dimensional continuation. The odd subclass of this harmonic extension maps an arbitrary analytic generating function P(x,y)P(x,y)P(x,y) to a harmonic potential whose in-plane radio-frequency null set is exactly P(x,y)=0P(x,y)=0P(x,y)=0. This yields explicit field-free guide networks beyond smooth straight-line intersections, including cusp guides, cotangential contacts, and periodic lattices. We further derive Fourier-space formulas for periodic extensions and present square-lattice network families with tunable local crossing angle and rounded connectivity. These results provide a compact parametrization for the design space for quantum charge-coupled device (QCCD) architectures.
Trapped ions offer long internal state (spin) coherence times and strong interparticle interactions mediated by the Coulomb force. This makes them interesting candidates for quantum simulation of coupled lattices. To this end, it is desirable to be able to trap ions in arbitrary conformations with precisely controlled local potentials. We provide a general method for optimizing periodic planar radio-frequency electrodes for generating ion trapping potentials with specified trap locations and curvatures above the electrode plane. A linear-programming algorithm guarantees globally optimal electrode shapes that require only a single radio-frequency voltage source for operation. The optimization method produces final electrode shapes that are smooth and exhibit low fragmentation. Such characteristics are desirable for practical fabrication of surface-electrode trap lattices.
We investigate the possible form of ideal intersections for two-dimensional rf trap networks suitable for quantum information processing with trapped ions. We show that the lowest order multipole component of the rf field that can contribute to an ideal intersection is a hexapole term uniquely determined by the tangents of the intersecting paths. The corresponding ponderomotive potential does not provide any confinement perpendicular to the paths if these intersect at right angles, indicating that ideal right-angle X\mathsf{X}X intersections are impossible to achieve with hexapole fields. Based on this result, we propose an implementation of an ideal oblique-X\mathsf{X}X intersection using a three-dimensional electrode structure.
We present a method for the creation of closed-loop lattices for ultra-cold atoms using dressed potentials. We analytically describe the generation of trap lattices that are state-dependent with dynamically controlled lattice depths and positioning. In a design akin to a synchronous motor, the potentials arise from the combination of a static, ring-shaped quadrupole field and multipole radio-frequency fields. Our technique relies solely on static and radio-frequency (rf) magnetic fields, enabling the creation of robust atom traps with simple control via rf amplitudes and phases. Potential applications of our scheme span the range from quantum many-body simulations to guided Sagnac interferometers.
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.
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We report a linear surface-electrode trap that can be used to form parallel ion strings. By adjusting the balance of the radio-frequency (RF) voltages applied to central and RF electrodes, the RF pseudopotential can be varied from single-well to double-well in the radial direction. Ions located on two parallel lines of the RF potential null are in principle free from excess micromotion if appropriate static voltages are applied. Calcium ions were trapped for the evaluation of the designed electrode. An ion string in the single-well potential and two ion strings in the double-well potential were observed by changing the RF voltages. Such traps could be used for quantum simulation of coupled spin systems.