Abstract
We present the quantum theory of the elliptical Penning trap, i.e. the general case where the cylindrical symmetry of the electrostatic trapping potential around the trapping magnetic field axis is broken. The theory applies to both slightly and highly elliptical traps, where it is shown that the difference between the quantum states of particles in these traps corresponds to a variation of the degree of squeezing of their motional modes in the xy-plane. In a trap with tunable ellipticity, such as the Geonium Ghip planar Penning trap, it follows that control of the ellipticity via the trapping voltages enables squeezing of the quantum states of the particle. We discuss the adiabatic preparation of such squeezed states, which follows naturally from the appearance of an avoided crossing between the diabatic levels of the coupled motional states of the particle.
Highlights
We present the quantum theory of the elliptical Penning trap, i.e. the general case where the cylindrical symmetry of the electrostatic trapping potential around the trapping magnetic field axis is broken
In a trap with tunable ellipticity, such as the Geonium Ghip planar Penning trap, it follows that control of the ellipticity via the trapping voltages enables squeezing of the quantum states of the particle
Since their initial development [1], Penning traps have become indispensable in high precision mass spectrometry [2, 3], in quantum electrodynamics (QED) measurements [4,5,6], and in anti-matter experiments [7,8,9,10]
Summary
Since their initial development [1], Penning traps have become indispensable in high precision mass spectrometry [2, 3], in quantum electrodynamics (QED) measurements [4,5,6], and in anti-matter experiments [7,8,9,10]. The Geonium Chip [22,23,24,25] belongs to the class of planar, elliptical Penning traps and is, designed to form a compact, mobile device [26]. It is being developed for applications in quantum technology with trapped electrons, such as the detection and generation of quantum microwave radiation [27].
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