Abstract
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.
Highlights
The interest in quantum chaos, especially when caused by the interactions between particles, has grown significantly in the last few years due to its relationship with several questions of current experimental and theoretical research that arise in atomic, molecular, optical, condensed matter, and high energy physics, as well as in quantum information science
Quantum chaos refers to properties of the spectrum and eigenstates that appear in the quantum domain when the classical counterpart of the system is chaotic in the sense of mixing and positive Lyapunov exponent
The features are similar to what we find in random matrix theory [76], namely the eigenvalues are strongly correlated [44] and the eigenstates in the meanfield basis are close to random vectors [114]
Summary
The interest in quantum chaos, especially when caused by the interactions between particles, has grown significantly in the last few years due to its relationship with several questions of current experimental and theoretical research that arise in atomic, molecular, optical, condensed matter, and high energy physics, as well as in quantum information science. The features are similar to what we find in random matrix theory [76], namely the eigenvalues are strongly correlated [44] and the eigenstates in the meanfield basis are close to random vectors [114] This quantum-classical correspondence is well established for systems with few degrees of freedom [103], such as billiards, the kicked rotor, and the Dicke model, where the source of chaos is respectively the shape of the billiard, the strength of the kicks, and the collective interaction between light and matter. We provide numerical evidence that when the interaction strength and the barrier strength are simultaneously finite, integrability is broken In this case, strong signatures of quantum chaos emerge for N = 4 particles in the presence of just one barrier (double-well system). Our analysis is done for bosons, but can be extended to systems with a small number of distinguishable fermions
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