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Publisher's copyright statement:Reprinted with permission from the American Physical Society: Physical Review A 94, 043603 c (2016) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modi ed, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Multimode expansions in computational quantum dynamics promise convergence toward exact results upon increasing the number of modes. Convergence is difficult to ascertain in practice due to the unfavorable scaling of required resources for many-particle problems and therefore a simplified criterion based on a threshold value for the least occupied mode function is often used. Here we show how the separable quantum motion of the center of mass can be used to sensitively detect unconverged numerical multiparticle dynamics in harmonic potentials. Based on an experimentally relevant example of attractively interacting bosons in one dimension, we demonstrate that the simplified convergence criterion fails to assure qualitatively correct results. Furthermore, the numerical evidence for the creation of two-hump fragmented bright soliton-like states presented by A. I. Streltsov et al. [Phys. Rev. Lett. 100, 130401 (2008)] is shown to be inconsistent with exact results. Implications for understanding dynamical fragmentation in attractive boson systems are briefly discussed.

We propose an experimental realization of a time crystal using an atomic Bose-Einstein condensate in a high finesse optical cavity pumped with laser light detuned to the blue side of the relevant atomic resonance. By mapping out the dynamical phase diagram, we identify regions in parameter space showing stable limit cycle dynamics. Since the model describing the system is time-independent, the emergence of a limit cycle phase indicates the breaking of continuous time translation symmetry. Employing a semiclassical analysis to demonstrate the robustness of the limit cycles against perturbations and quantum fluctuations, we establish the emergence of a time crystal.