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arXiv:2110.11218 · Physical Review A

Signatures of quantum chaos in low-energy mixtures of few fermions

Patrycja Łydżba, Tomasz Sowiński

Published Jul 1, 2022• 15 citations
arXivHTMLPDF

Abstract

The low-energy dynamics of mesoscopic systems strongly depends on the presence of internal equilibration. For this reason, a better interpretation of ultracold atom experiments requires a more accurate understanding of how quantum chaos manifests itself in these systems. In this paper, we consider a simple but experimentally relevant one-dimensional system of a few ultracold fermions moving in a double-well potential. We analyze its many-body spectral properties, which are commonly used to trace quantum chaos. We observe some sig- natures of quantum chaos already in the system with three particles. Generally, these signatures become more pronounced when fermions are evenly added to both components. In contrast, they become suppressed when the particle imbalance is increased.

DOI
10.1103/physreva.106.013301

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The low-energy dynamics of mesoscopic systems strongly depends on the presence of internal equilibration. For this reason, a better interpretation of ultracold atom experiments requires a more accurate understanding of how quantum chaos manifests itself in these systems. In this paper, we consider a simple but experimentally relevant one-dimensional system of a few ultracold fermions moving in a double-well potential. We analyze its many-body spectral properties, which are commonly used to trace quantum chaos. We observe some sig- natures of quantum chaos already in the system with three particles. Generally, these signatures become more pronounced when fermions are evenly added to both components. In contrast, they become suppressed when the particle imbalance is increased.
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 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 demonstrate that an ultracold many-body bosonic ensemble confined in a one-dimensional double-well potential can exhibit chaotic dynamics due to the presence of a single impurity. The nonequilibrium dynamics is triggered by a quench of the impurity-Bose interaction and is illustrated via the evolution of the population imbalance for the bosons between the two wells. While the increase of the postquench interaction strength always facilitates the irregular motion for the bosonic population imbalance, it becomes regular again when the impurity is initially populated in the highly excited states. Such an integrability to chaos (ITC) transition is fully captured by the transient dynamics of the corresponding linear entanglement entropy, whose infinite-time-averaged value additionally characterizes the edge of the chaos and implies the existence of an effective Bose-Bose attraction induced by the impurity. To elucidate the physical origin for the observed ITC transition, we perform a detailed spectral analysis for the mixture with respect to both the energy spectrum as well as the eigenstates. Specifically, two distinguished spectral behaviors upon a variation of the interspecies interaction strength are observed. While the avoided level crossings take place in the low-energy spectrum, the energy levels in the high-energy spectrum possess a bandlike structure and are equidistant within each band. This leads to a significant delocalization of the low-lying eigenvectors, which, in turn, accounts for the chaotic nature of the bosonic dynamics. By contrast, those highly excited states bear a high resemblance to the noninteracting integrable basis, which explains the recovery of the integrability for the bosonic species. Finally, we discuss the induced Bose-Bose attraction as well as its impact on the bosonic dynamics.
The appearance of chaotic quantum dynamics significantly depends on the symmetry properties of a system, and in cold atomic systems many of these can be experimentally controlled. In this work, we systematically study the emergence of quantum chaos in a minimal system describing one-dimensional harmonically trapped Bose-Bose mixtures by tuning the particle-particle interactions. Using an improved exact diagonalization scheme, we examine the transition from integrability to chaos when the inter-component interaction changes from weak to strong. Our study is based on the analysis of the level spacing distribution and the distribution of the matrix elements of observables in terms of the eigenstate thermalization hypothesis and their dynamics. We show that one can obtain strong signatures of chaos by increasing the inter-component interaction strength and breaking the symmetry of intra-component interactions.
We study dynamical signatures of quantum chaos in one of the most relevant models in many-body quantum mechanics, the Bose-Hubbard model, whose high degree of symmetries yields a large number of invariant subspaces and degenerate energy levels. The standard procedure to reveal signatures of quantum chaos requires classifying the energy levels according to their symmetries, which may be experimentally and theoretically challenging. We show that this classification is not necessary to observe manifestations of spectral correlations in the temporal evolution of the survival probability, which makes this quantity a powerful tool in the identification of chaotic many-body quantum systems.
We numerically investigate the minimum number of interacting particles, which is required for the onset of strong chaos in quantum systems on a one-dimensional lattice with short-range and long-range interactions. We consider multiple system sizes which are at least three times larger than the number of particles and find that robust signatures of quantum chaos emerge for as few as 4 particles in the case of short-range interactions and as few as 3 particles for long-range interactions, and without any apparent dependence on the size of the system.