Read the paper here:
Narrated presentation of the main concepts and results of this work. Note that this video contains an audio track. Problem formulation. Demonstration of solutions. Conditions of trajectoid existence are discussed. Heuristics of computing the shape of a trajectoid. Experimental validation of trajectoids. Performance of trajectoids with uphill excursions and self-intersections. Applications of TPT theorem in quantum mechanics.
Investigation of the existence of TPTs. This animation shows dependence of the plots described in Extended Data Fig. 5 on the anglein Extended Data Fig. 5k. Taper ratio is defined asScaling the driving field pulses in quantum-mechanical analogy to the existence of TPTs. In this analogy, modulating the radius\\to E/r,{B}_{xy}\to {B}_{xy}/r)\)for NMR and electric dipole transitions; planar magnetic fieldfor magnetic dipole in magnetic field).
Small-radius limit of trajectoids. The right side shows the spherical trace of the contact point of anradius sphere that has completed a roll from start to end along the path shown on the left side. Colour corresponds to arc length along the path, measured from the starting point. The value ofdecreases over the course of the video, as reflected by the ratio of path period length to the sphere’s circumference 2πindicated in the top left.
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