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arXiv:1509.01809

Observing the emergence of chaos in a many-particle quantum system

Jiří Tomkovič, Wolfgang Muessel, Helmut Strobel, Steffen Löck, Peter Schlagheck, Roland Ketzmerick, Markus K. Oberthaler

Published Sep 6, 2015• 4 citations
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Abstract

Accessing the connection between classical chaos and quantum many-body systems has been a long-standing experimental challenge. Here, we investigate the onset of chaos in periodically driven two-component Bose-Einstein condensates, whose small quantum uncertainties allow for exploring the phase space with high resolution. By analyzing the uncertainties of time-evolved many-body states, we find signatures of elliptic and hyperbolic periodic orbits generated according to the Poincaré-Birkhoff theorem, and the formation of a chaotic region at increasing driving strengths. The employed fluctuation analysis allows for probing the phase-space structure by use of only short-time quantum dynamics.

DOI
10.48550/arxiv.1509.01809

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Accessing the connection between classical chaos and quantum many-body systems has been a long-standing experimental challenge. Here, we investigate the onset of chaos in periodically driven two-component Bose-Einstein condensates, whose small quantum uncertainties allow for exploring the phase space with high resolution. By analyzing the uncertainties of time-evolved many-body states, we find signatures of elliptic and hyperbolic periodic orbits generated according to the Poincaré-Birkhoff theorem, and the formation of a chaotic region at increasing driving strengths. The employed fluctuation analysis allows for probing the phase-space structure by use of only short-time quantum dynamics.
We investigate both the classical and quantum dynamics of a spin-1 Bose–Einstein condensate (BEC) system subject to periodic driving of quadratic Zeeman splitting. Without driving, the system is integrable. Here, we found that increasing the driving strength will drive the system to chaos. Classically, we demonstrate chaotic dynamics by examining the Poincaré section and Lyapunov exponent. While in the quantum regime, the level statistic and Husimi distribution are studied, and they also clearly indicate the onset of quantum chaos. The dynamics of atom number and out-of-time-ordered correlator (OTOC) are also studied. In the integrable region, the variance of atom number and OTOC both remain very small during the time evolution; while in the chaos region, a quick increase is observed in the early time. This work presents a quantum many-body system showing chaotic behavior and can be readily realized in experiment.
This work discusses the experimental realization of a mixed regular-chaotic phase space in a macroscopic quantum system. The effective Planck's constant of the system can be varied in a large range. Therefore, the semi-classical limit of the system can be studied, where the initial size of the many particle wave packet is much smaller than typical structures of the phase space. Thus, different structures of the phase space can be resolved. In a weakly driven system, the Poincaré-Birkhoff scenario is investigated by the dispersion of the wave packet at a stable or unstable fixed point. In a strongly driven system, different dynamics of a wave packet is found, dependent on preparation in a regular island or the chaotic sea. The time evolution can be described by a classical model, which is in good agreement with experiment as well as the mean field model for the considered observables. \n \nIn an independent experiment using an atomic beam setup the generation of motional coherence of a single atom by spontaneous emission of a single photon has been demonstrated.
Interacting quantum systems in the chaotic domain are at the core of various ongoing studies of many-body physics, ranging from the scrambling of quantum information to the onset of thermalization. We propose a minimum model for chaos that can be experimentally realized with cold atoms trapped in one-dimensional multi-well potentials. We explore the emergence of chaos as the number of particles is increased, starting with as few as two, and as the number of wells is increased, ranging from a double well to a multi-well Kronig-Penney-like system. In this way, we illuminate the narrow boundary between integrability and chaos in a highly tunable few-body system. We show that the competition between the particle interactions and the periodic structure of the confining potential reveals subtle indications of quantum chaos for 3 particles, while for 4 particles stronger signatures are seen. The analysis is performed for bosonic particles and could also be extended to distinguishable fermions.
We study a periodically driven macrospin system with anisotropic long-range interactions and collective dissipation, described by a Lindblad master equation. In the thermodynamic limit (N→∞N\to\inftyN→∞), a mean-field treatment yields classical equations of motion, whose dynamics are characterized via the maximal Lyapunov exponent (MLE). Focusing on the thermodynamic limit, we map out chaotic, quasiperiodic, and periodic phases via bifurcation diagrams, MLEs, and Fourier spectra of evolved observables, identifying classic period-doubling bifurcations and fractal boundaries in the regions of attractors. Finite-size quantum simulations in the Dicke basis reveal that while both quantum and classical systems exhibit diverse dynamical phases, finite-size effects suppress some behaviors present in the thermodynamic limit. The sign of λmaxλ_{\mathrm{max}}λmax​ serves as a key indicator of convergence between quantum and classical dynamics, which agree over timescales up to the Lyapunov time. Analysis of the density matrix shows that convergence occurs only when its nonzero elements are sharply localized. However, the nonconvergence does not imply a fundamental difference between quantum and classical dynamics: in chaotic regimes, although the evolution orbits of quantum and classical systems show significant differences, quantum evolution becomes mixed and diffusively explores the Hilbert space, signaling quantum chaos, which can be confirmed by the delocalized nature of the density matrix.
Interacting quantum systems in the chaotic domain are at the core of various ongoing studies of many-body physics, ranging from the scrambling of quantum information to the onset of thermalization. We propose a minimum model for chaos that can be experimentally realized with cold atoms trapped in one-dimensional multi-well potentials. We explore the emergence of chaos as the number of particles is increased, starting with as few as two, and as the number of wells is increased, ranging from a double well to a multi-well Kronig-Penney-like system. In this way, we illuminate the narrow boundary between integrability and chaos in a highly tunable few-body system. We show that the competition between the particle interactions and the periodic structure of the confining potential reveals subtle indications of quantum chaos for 3 particles, while for 4 particles stronger signatures are seen. The analysis is performed for bosonic particles and could also be extended to distinguishable fermions.