Layered Chaos in Mean-field and Quantum Many-body Dynamics

Abstract

We investigate the dimension of the phase space attractor of a quantum chaotic many-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 regime, and for each of them we calculate the correlation dimension. For the ground state of the ratchet formed by a system of field-free non-interacting particles, we find four distinct pockets of chaotic dynamics throughout these regimes. We show that a measurement of a local density in each of the dynamical regimes, has an attractor characterized with a higher fractal dimension, $D_R=2.59\pm 0.01$, $D_C=3.93\pm 0.04$, and $D_S=3.05\pm 0.05$, as compared to the global measure of current, $D_R=2.07\pm 0.02$, $D_C=2.96\pm 0.05$, and $D_S=2.30\pm 0.02$. We find that the many-body case converges to mean-field limit with strong sub-unity power laws in particle number $N$, namely $N^{\alpha }$ with ${\alpha }_R=0.28\pm 0.01$, ${\alpha }_C=0.34\pm 0.067$ and ${\alpha }_S=0.90\pm 0.24$ for each of the dynamical regimes mentioned above. The deviation between local and global measurement of the attractor's dimension corresponds to an increase towards high 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 as $N^{\beta }$ with ${\beta }_R=0.51\pm 0.004$ and ${\beta }_C=0.18\pm 0.004$ 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-trapped regimes but not in the chaotic regime. Based on the obtained results we outline pathways for the identification and characterization of the emergent phenomena in driven many-body systems.

References in corpus (45)

• Many-Body Physics with Ultracold Gases
• Photonic Floquet Topological Insulators
• Brownian motors: noisy transport far from equilibrium
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• Topological characterization of periodically-driven quantum systems
• Dynamical control of matter-wave tunneling in periodic potentials
• Spontaneous vortices in the formation of Bose-Einstein condensates
• Many-body localization in periodically driven systems
• Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link
• On the Implementation of the 0-1 Test for Chaos
• Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates
• Experimental observation of the Anderson transition with atomic matter waves
• Exponentially slow heating in periodically driven many-body systems
• Discrete breathers in nonlinear lattices: Experimental detection in a Josephson array
• Observation of breathers in Josephson ladders
• Directed current due to broken time-space symmetry
• Coherent control of dressed matter waves
• Experimental realization of Josephson junctions for an Atom SQUID
• Finite temperature excitations of a trapped Bose gas
• Quantised supercurrent decay in an annular Bose-Einstein condensate
• Simulations of Bose fields at finite temperature
• Directed Transport of Atoms in a Hamiltonian Quantum Ratchet
• Exploring dynamic localization with a Bose-Einstein condensate
• Quantum transport in ultracold atoms
• Damping in dilute Bose gases: a mean-field approach
• On the Validity of the 0-1 Test for Chaos
• Tunable transport with broken space-time symmetries
• Collective excitations of Bose-Einstein condensed gases at finite temperatures
• Thermal activation of vortex-antivortex pairs in quasi-2D Bose-Einstein condensates
• Exploring the phase space of the quantum delta kicked accelerator
• A number-conserving approach to a minimal self-consistent treatment of condensate and non-condensate dynamics in a degenerate Bose gas
• Controlling the Ratchet Effect for Cold Atoms
• Experimental control of transport resonances in a coherent quantum rocking ratchet
• Quantitative test of thermal field theory for Bose-Einstein condensates
• Second-order, number-conserving description of non-equilibrium dynamics in finite-temperature Bose-Einstein condensates
• Effective Josephson dynamics in resonantly driven Bose-Einstein condensates
• Coherence and Instability in a Driven Bose-Einstein Condensate: A Fully Dynamical Number-Conserving Approach
• Orbital Josephson effect and interactions in driven atom condensates on a ring
• Quantum tunneling of a vortex between two pinning potentials
• Entangled Dynamics in Macroscopic Quantum Tunneling of Bose-Einstein Condensates
• Many-body Quantum Chaos and Entanglement in a Quantum Ratchet
• Quantum ratchet transport with minimal dispersion rate
• Dynamics of trapped Bose gases at finite temperatures
• Complex Solitary Wave Dynamics, Pattern Formation, and Chaos in the Gain-Loss Nonlinear Schrödinger Equation

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