On the Formation of Lines in Quantum Phase Space

We theoretically study the formation of lines in phase space using Wigner’s distribution W. In trapped quantum systems such lines form generically, crisscrossing phase space and they can have astonishing extent, reaching across the entire state. In classical systems this does not happen. We show that the formation of such straight line patterns is due to the formation of ‘randomized comb-states’. We establish their stability to perturbations, and that they are tied to coherences in configuration space. We additionally identify generic higher-order ‘eye’ patterns in phase space which occur less often since they arise from more specific symmetric comb-states; we show that the perturbation of eye patterns through their randomization tends to deform them into lines. Lines in phase space should give rise to large probability peaks in measurements.