Trial Wave Functions for Ring-Trapped Ions and Neutral Atoms: Microscopic Description of the Quantum Space-Time Crystal

A theory for quantum space-time crystals (QSTCs) of N interacting and ring-confined rotating particles is presented. The QSTC many-body trial wave functions are obtained via symmetry breaking at the mean-field level followed by symmetry restoration using projection techniques. These wave functions are stationary states and preserve the rotational symmetries, and at the same time they reflect the point-group
symmetries of the mean-field crystals. This yields a sequences of magic angular momenta L_m. For angular momenta away from the magic values, the trial functions vanish. Symmetry breaking beyond mean field is induced by superpositions of good-L_m stationary states.
Superposing a pair of adjacent L_m states leads to formation of special broken-symmetry states with QSTC behavior. The particle densities rotate around the ring, showing undamped and nondispersed periodic crystalline evolution in both space and time. The experimental synthesis of such QSTC wave packets is favored in the vicinity of ground-state energy crossings of the Aharonov-Bohm spectra accessed via an applied magnetic field. These results are illustrated for Coulomb-repelling fermionic ions and for a lump of contact-interaction attracting bosons; see PRA 96, 043610 (2017)