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 meanfield 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 global measure 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 β with β R = 0.51 ± 0.004 and β 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.

Superradiant optomechanical phases of cold atomic gases in optical resonators

“…The chaotic phase, in particular, characterizes the asymptotic phase of an incoherent dynamics, it emerges from the interplay between quantum fluctuations, noise, and all-to-all, global interactions mediated by the cavity field, and is thus qualitatively different from chaos reported in the quantum dynamics of Hamiltonian all-to-all, global-range interacting systems [43,44]. It is intriguing whether it presents features which can be understood in terms of many-body quantum chaos [45]. where we used the decomposition Ĵ2 = Ĵ(1) 1 + Ĵ(2)…”

Unpredictable condensate–depletion dynamics in one-dimensional power-law traps

“…The phenomenon of condensate depletion (CD) has always drawn significant interest in the ultracold physics community [1][2][3][4][5][6][7] and although its dynamics has been explored intensively for a very long time now [8][9][10][11][12][13][14][15][16][17][18][19], further investigations are required for a deeper understanding of its response to factors such as trapping geometry and interactions in the presence of external driving. The depleted part of the condensate is identified by an occupancy of the higher natural orbitals (NOs) [20,21], when particles are excited from the lowest energy and maximally occupied NO [the Bose-Einstein condensate (BEC)] to higher NOs.…”

“…Short time condensate depletion dynamics (CDD) has also been demonstrated in driven and tilted bichromatic optical lattices [19]. Other work included the role of a chaotic potential in the CD [35], the CDD following the quench of a BEC [36] to the strongly interacting regime [17], the derivation of equations for the densities and velocities of the condensate and the associated depletion via the hydrodynamic approach [1], and the CD in a many-body quantum rachet system [7].…”