A planar Penning trap with tunable dimensionality of the trapping potential

• We present a planar Penning trap with tunable dimensionality of the potential.
• The presented planar trap has the magnetic field axis parallel to the surface of the chip.
• We show how to compensate the electrostatic potential.
• We calculate the frequency shifts caused by the magnetic field gradient and curvature in an elliptical Penning trap.
• We discuss one example with a single electron in our planar trap.

The coplanar-waveguide Penning trap developed at the University of Sussex is modified by enclosing it in a rectangular microwave cavity and adding two “side electrodes”. These permit to expand the range of useful trapping positions, where the linear fluctuations of the axial frequency with the axial energy – caused by electrostatic anharmonicities – are eliminated. That is the critical condition for the accurate measurement of the eigenfrequencies of a single trapped electron – or ion – as required for quantum computation or mass spectrometry applications. The side electrodes also allow for adjusting the dimensionality of the potential. The trap can be driven into the “ultra elliptical”, regime, where the magnetron motion vanishes and the particle is confined within a quasi two-dimensional potential. Furthermore, we calculate the deviations of the eigenfrequencies caused by the gradient and curvature of the magnetic field. The obtained frequency shifts matrices have universal validity for all Penning traps. They include those obtained for conventional traps, i.e. with cylindrical symmetry, as a particular case.

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