Table 1 Physical conditions (in cgs) to achieve the squeezing transformations \(\lambda _x=-0.43\) and \(\lambda _y=-1.125\) on a proton moving inside a cylindrical solenoid. The reported quantities have been calculated regarding the example in Fig. 4. The physical magnitudes of q, p and v, with \(q=x=y\) and \(p=p_x=p_y\) correspond to the dimensionless values \(x'=y'=p'_x=p'_y=1\) according to Eq. (6). Note how the incredibly modest strength of the magnetic field grows as the operation time T becomes shorter, to form an idea, a control operation of \(T=10^{-2}\)s. would require half the strength of Earth’s magnetic field on the equator. In the last row it is reported the average ratio of the Abraham-Lorentz radiative force to the time-dependent oscillator forces, at different operation intervals T.

From: Quantum control operations with fuzzy evolution trajectories based on polyharmonic magnetic fields