A quantum model is considered for $N$ bosons condensed in two orthogonal single-particle modes with tunable energy separation in the presence of flavor-changing contact interaction, which can be readily solved by direct diagonalization. Despite its elementary character, this model possesses chiral quantum phases with finite orbital angular momentum arising as the result of spontaneous breaking of time-reversal symmetry. The phase diagram is explored on a mean-field and full quantum level. Thermal and quantum fluctuations are characterized with respect to regions of universal scaling behavior. The nonequilibrium dynamics shows a sharp transition between a self-trapping and a pair-tunneling regime. A recently realized experimental implementation is discussed with bosonic atoms condensed in the two inequivalent energy minima $X_{\pm }$ of the second band of a bipartite two-dimensional optical lattice.

• Received 15 November 2018
• Corrected 3 September 2019

DOI:https://doi.org/10.1103/PhysRevA.99.013623