Probing the edge between integrability and quantum chaos in interacting few-atom systems

Thomás Fogarty1, Miguel Ángel García-March2, Lea F. Santos3, and Nathan L. Harshman4

1Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan
2Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, E-46022 València, Spain
3Department of Physics, Yeshiva University, New York, New York 10016, USA
4Department of Physics, American University, 4400 Massachusetts Ave. NW, Washington, DC 20016, USA

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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.

Ultracold atoms trapped in light allow for exquisite experimental control and may form the working units of future quantum information processing devices. However, we show that even systems with a few interacting atoms in a simple trap could manifest signatures of chaotic behavior. Our research on this simple model probes the boundary where the constraints of symmetry become too weak, and the system descends into chaos.

The model we study confines the atoms into a one-dimensional infinite square well broken into sub-wells by thin barriers. This model is solvable in the extreme limiting cases of no interactions and barriers, and infinite interaction and barriers. In the intermediate parameter range of finite barriers and interactions we use numerical methods to find the energy spectrum and to calculate some well-known indicators of quantum chaos. What we find is that for two particles, the system shows no signs of chaos and for four particles the system is chaotic for a wide range of parameters. The intermediate case of three particles can exhibit a wide range of behaviors depending on the number of subwells and the strengths of the interactions and barriers.

Our results indicate that is experimentally feasible to explore the transition to quantum chaos in these small, simple systems. The implications of quantum chaos for control have relevance for applications to quantum information processing. Knowing where this boundary lies means that one could avoid chaotic regimes, or alternatively exploit the randomness of chaos for novel protocols.

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[2] E. R. Castro, Jorge Chávez-Carlos, I. Roditi, Lea F. Santos, and Jorge G. Hirsch, "Quantum-classical correspondence of a system of interacting bosons in a triple-well potential", arXiv:2105.10515.

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