Dynamics of Ultracold Bosons in Artificial Gauge Fields: Angular Momentum, Fragmentation, and the Variance of Entropy

We consider the dynamics of two-dimensional interacting ultracold bosons triggered by suddenly switching on an artificial gauge field. The system is initialized in the ground state of a harmonic trapping potential. As a function of the strength of the applied artificial gauge, we analyze the emergent dynamics by monitoring the angular momentum, the fragmentation as well the entropy and variance of the entropy of absorption or single-shot images. We solve the underlying time-dependent many-boson Schr\"odinger equation using the multiconfigurational time-dependent Hartree method for indistinguishable particles (MCTDH-X). We find that the artificial gauge field implants angular momentum in the system. Fragmentation -- multiple macroscopic eigenvalues of the reduced one-body density matrix -- emerges in sync with the dynamics of angular momentum: the bosons in the many-body state develop non-trivial correlations. Fragmentation and angular momentum are experimentally difficult to assess; here, we demonstrate that they can be probed by statistically analyzing the variance of the image entropy of single-shot images that are the standard projective measurement of the state of ultracold atomic systems.