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

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.

Interacting bosons in a triple well: Preface of many-body quantum chaos

“…Systems with few-degrees of freedom, such as the Dicke model [74], spin-1/2 models with less than four excitations [75], and multiwell Kronig-Penney-like systems with few particles [76], often present shapes other than Gaussian. We see in Appendix A that the bare triple-well Bose-Hubbard model and the extended triple-well Bose-Hubbard model show distributions that, similar to our model in Fig.…”

Statistics of phase space localization measures and quantum chaos in the kicked top model

“…In contrast to the case of classical chaos, which is well defined as the exponential divergence of the closest orbits for initial perturbations [12,13], the definition of quantum chaos in the narrow sense remains an open question [14]. One, therefore, turns to focus on how to probe and measure the signatures of chaos in various quantum systems [1,2,[15][16][17][18][19][20][21][22]. To date, the presence of chaos in a quantum system is commonly ascertained from its spectral properties.…”

Quantum Chaos in the Extended Dicke Model

“…In recent years, the study of quantum chaos in many-body systems has attracted much attention, both theoretically and experimentally in different fields of physics, such as statistical physics [ 1 , 2 , 3 , 4 , 5 ], condensed matter physics [ 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 ], and high-energy physics [ 14 , 15 , 16 , 17 , 18 , 19 ], as well as quantum information science [ 20 , 21 , 22 , 23 , 24 , 25 , 26 ]. To some extent, this great interest in quantum many-body chaos is due to the close connections of chaos to several fundamental questions that arise in current theoretical and experimental studies.…”