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.

我们提出了椭圆彭宁陷阱的量子理论，即围绕俘获磁场轴的静电俘获势的圆柱对称性被破坏的一般情况。该理论适用于轻微和高度椭圆形的陷阱，其中表明这些陷阱中粒子的量子态之间的差异对应于它们在xy平面中的运动模式的压缩程度的变化。在椭圆度可调的陷阱中，例如Geonium Ghip平面 Penning 陷阱，它遵循通过俘获电压控制椭圆率能够压缩粒子的量子态。我们讨论了这种压缩状态的绝热准备，这自然是由于粒子耦合运动状态的非绝热能级之间避免交叉的出现。