Toward rotation-mediated bosonic Josephson junctions in position and momentum spaces

The ground state of a rotating Bose-Einstein condensate in a two-dimensional anharmonic--anisotropic trap potential is analyzed numerically at the infinite-particle-number limit. First, we show that the density in position space splits into two bosonic clouds along the $x$ direction and, side by side, the density in momentum space splits into two clouds along the $p_y$ direction. The resulting unusually-split bosonic cloud can thus be interpreted as living in effective double-well potentials both in position and momentum spaces, which opens up the idea to look for Josephson-junction dynamics both in position and momentum spaces. Furthermore, the bosons exhibit unique correlations. To this end, it is demonstrated that the anisotropies of the many-particle position and momentum variances become opposite when computed at the many-body and mean-field levels of theory with an increase in the rotation frequency, despite the system being $100\%$ condensed. Implications for and examples of out-of-equilibrium properties of rotating bosons undergoing Josephson-junction dynamics in barrierless traps are presented and discussed.