Publication: Layered chaos in mean-field and quantum many-body dynamics
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2019-06-17
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American Physical Society
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Abstract
We investigate the dimension of the phase-space attractor of a quantum chaoticmany-body ratchet in the mean-field limit. Specifically, we explore a driven Bose-Einstein condensate in three distinct dynamical regimes-Rabi oscillations, chaos, and self-trapping regimes-and for each of them we calculate the correlation dimension. For the ground state of the ratchet formed by a system of field-free noninteracting particles, we find four distinct pockets of chaotic dynamics throughout these regimes. We show that a measurement of local density in each of the dynamical regimes has an attractor characterized by a higher fractal dimension, D_R = 2.59 +/- 0.01, D_C = 3.93 +/- 0.04, and D-S = 3.05 +/- 0.05, compared to the globalmeasure of current, D_R = 2.07 +/- 0.02, D_C = 2.96 +/- 0.05, and D_S = 2.30 +/- 0.02. The deviation between local and global measurements of the attractor's dimension corresponds to an increase towards higher condensate depletion, which remains constant for long time scales in both Rabi and chaotic regimes. The depletion is found to scale polynomially with particle number N, namely, as N¬_beta with beta^R = 0.51 +/- 0.004 and beta_C = 0.18 +/- 0.004 for the two regimes. Thus, we find a strong deviation from the mean-field results, especially in the chaotic regime of the quantum ratchet. The ratchet also reveals quantum revivals in the Rabi and self-trapping regimes but not in the chaotic regime, with revival times scaling linearly in particle number for Rabi dynamics. Based on the obtained results, we outline pathways for the identification and characterization of emergent phenomena in driven many-body systems. This includes the identification of many-body localization from the many-body measures of the system, the influence of entanglement on the rate of the convergence to the mean-field limit, and the establishment of a polynomial scaling of the Ehrenfest time at which the mean-field description fails to describe the dynamics of the system.
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© American Physical Society
This material is based upon work supported by the National Science Foundation under Grants No. OAC-1740130, No. CCF-1839232, and No. PHY-1806372; by the U.S. Air Force Office of Scientific Research Grant No. FA9550-14-1-0287; and by the U. K. Engineering and Physical Sciences Research Council through the "Quantum Science with Ultracold Molecules" Programme (Grant No. EP/P01058X/1). This work has been supported by the Spanish Ministry of Science and Innovation through Grants No. FIS2013-41716-P and No. FIS2017-84368-P. This research was supported in part by the National Science Foundation under Grant No. PHY-1748958. F.S. would like to acknowledge the support of the Real Colegio Complutense at Harvard University and the HarvardMassachusetts Institute of Technology Center for Ultracold Atoms, where part of this work was done. The calculations were executed on the high-performance computing cluster maintained by the Golden Energy Computing Organization at the Colorado School of Mines.