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arXiv:1008.3058 · Physical Review A

From a single- to a double-well Penning trap

Giacomo Ciaramicoli, Irene Marzoli, P. Tombesi

Published Oct 18, 2010• 5 citations
arXivHTMLPDF

Abstract

The new generation of planar Penning traps promises to be a flexible and versatile tool for quantum-information studies. Here, we propose a fully controllable and reversible way to change the typical trapping harmonic potential into a double-well potential, in the axial direction. In this configuration a trapped particle can perform coherent oscillations between the two wells. The tunneling rate, which depends on the barrier height and width, can be adjusted at will by varying the potential difference applied to the trap electrodes. Most notably, tunneling rates in the range of kHz are achievable even with a trap size of the order of $100$ $\ensuremath{\mu}$m.

DOI
10.1103/physreva.82.044302

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The new generation of planar Penning traps promises to be a flexible and versatile tool for quantum-information studies. Here, we propose a fully controllable and reversible way to change the typical trapping harmonic potential into a double-well potential, in the axial direction. In this configuration a trapped particle can perform coherent oscillations between the two wells. The tunneling rate, which depends on the barrier height and width, can be adjusted at will by varying the potential difference applied to the trap electrodes. Most notably, tunneling rates in the range of kHz are achievable even with a trap size of the order of 100100100 \ensuremathμ\ensuremath{\mu}\ensuremathμm.
We present a detailed account of the design choices required for planar Penning traps that feature a highly harmonic confining potential. High harmonicity is indispensable for a number of applications, particularly for confinement of single electrons as qubits in quantum-information processing. The present work extends previous studies [D. Goldmann and G. Gabrielse, Phys. Rev. A 81, 052335 (2010)] by a fully analytic treatment of finite electrode gaps and their relevance for small traps on the millimetre size scale and below, when relative gap sizes are non-negligible. We derive the overall trap potential with a particular focus on different models of finite-gap potentials and show how to find the optimum trap geometry and electrode voltages to minimize anharmonicities. The analytic calculations are compared with detailed finite-element simulations.
A one-electron qubit would offer a new option for quantum information science, including the possibility of extremely long coherence times. One-quantum cyclotron transitions and spin flips have been observed for a single electron in a cylindrical Penning trap. However, an electron suspended in a planar Penning trap is a more promising building block for the array of coupled qubits needed for quantum information studies. The optimized design configurations identified here promise to make it possible to realize the elusive goal of one trapped electron in a planar Penning trap---a substantial step toward a one-electron qubit.
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Double-well potentials are important potential models that underlie the study of macroscopic quantum tunneling in Bose–Einstein Condensates (BECs), which are most commonly constructed in the form of a combination of a finite square-well potential and a square potential barrier. We propose another possibility of constructing a double-well potential, which consists of the combination of a square-well potential and a movable Gaussian-type potential barrier, and by adjusting the width, height, symmetry, and position of the movable potential barrier, symmetric and asymmetric double-well potentials with rich structures can be constructed. By numerically solving the Gross–Pitaevskii equation, we give the ground state structures of the BEC in this double-well potential, and then study the tunneling dynamics in this double-well potential. Different from trivial symmetric barrier displacement, the independently tunable two half-Gaussian widths bring an extra control degree of freedom; it is shown that the ground–state properties and tunneling dynamics are far more sensitive to asymmetric segmented barriers than to symmetrically shifted barriers. This feature offers a flexible strategy for atomic manipulation and is not merely a trivial qualitative observation.
We discuss the potential of the Penning ion trap for quantum information processing. An ion plasma in a Penning trap rotates about the trap (or magnetic field) axis. We have demonstrated phase-locked control of this rotation by a rotating electric field perturbation (a “rotating wall”). This precise control enables the formation of planar arrays of ions that could potentially be used for quantum computation with the Cirac-Zoller scheme, mimicking a “hard disk” geometry. Current experiments with miniature rf traps observe significant heating and decoherence which is believed to be due to fluctuating patch fields on the trap electrodes. This heating should be several orders of magnitude less in the larger Penning trap.