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.

Automated summary

We theoretically investigate the emergence of lines in phase space using Wigner's distribution W. These lines frequently appear in confined quantum systems, crisscrossing the entire phase space with astonishing extent. In contrast, such patterns do not occur in classical systems. We reveal that the formation of straight lines is attributed to the existence of randomized comb-states, which possess stability against perturbations and are connected to coherence in configuration space. Moreover, we reveal the occurrence of higher-order eye patterns in phase space, albeit less frequently, as they arise from specific symmetric comb-states. Randomization of eye patterns tends to transform them into lines. The presence of lines in phase space leads to significant probability peaks in measurement outcomes.