Abstract
Dynamical fermionization refers to the phenomenon when the momentum distribution of impenetrable bosons asymptotically reaches that of non interacting fermions on sudden release from the trap. Whereas on sudden change in trap frequency results to Bose-Fermi oscillation which has been experimentally confirmed in the case of the Lieb-Liniger model in the Tonks-Girardeau (TG) regime. Crystallization happens for sufficiently strongly interacting repulsive bosons with dipolar interactions in one spatial dimension. Crystallization resembles fermionization but distinctly different due to long-range interaction. The present work aims to distinguish dynamical crystallization from dynamical fermionization in the expansion and breathing dynamics of N=4 strongly interacting bosons in TG limit. Our results suggest that the N-fold complete splitting in one-body density for dipolar bosons makes a clear signature of crystallization in the Bose-Fermi oscillation. We investigate the many-body dynamics by employing multiconfigurational time-dependent Hartree method for bosons which solve the N-body time-dependent Schrödinger equation numerically exactly.
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