We investigate the quantum chaos of ultracold atoms in a quadruple-well potential, emphasizing the influence of synthetic gauge fields and many-body atomic interactions on the transitions from regular behavior to quantum chaos. We compare the metrics that the eigenvalue statistics of nearest-neighbor spacings distribution and gap ratio analysis, and the eigenfunction statistics using the Kullback–Leibler divergence and the inverse participation ratio, to diagnose the transition from regular to chaotic behavior. Numerically, we obtain the phase diagram of the regular and chaotic behavior on the parameter plane of many-body atomic interactions and synthetic gauge fields. Our results provide insight into the chaotic behavior of ultracold atoms with synthetic gauge fields and have potential applications in the quantum engineering of wave chaos.
We investigate the quantum chaos of ultracold atoms in a quadruple-well potential, emphasizing the influence of synthetic gauge fields and many-body atomic interactions on the transitions from regular behavior to quantum chaos. We compare the metrics that the eigenvalue statistics of nearest-neighbor spacings distribution and gap ratio analysis, and the eigenfunction statistics using the Kullback–Leibler divergence and the inverse participation ratio, to diagnose the transition from regular to chaotic behavior. Numerically, we obtain the phase diagram of the regular and chaotic behavior on the parameter plane of many-body atomic interactions and synthetic gauge fields. Our results provide insight into the chaotic behavior of ultracold atoms with synthetic gauge fields and have potential applications in the quantum engineering of wave chaos.
The exploration of tunneling dynamics in many-body quantum systems plays a pivotal role in realizing groundbreaking atomtronic devices and achieving precise control over entanglement. Here, we delve into the intricate many-body tunneling dynamics of ultracold atoms confined within a quadruple-well potential, with a particular emphasis on the manipulative role played by interatomic interactions and synthetic gauge fields. The quantum dynamics displayed by the system closely mimic the operations of qudit hybrid gates, which are comprised of two relatively independent sets of qudits. In the Rabi regime, which is characterized by strong coupling, we observe an intriguing phenomenon: the cyclic collapse and revival of discrete tunneling dynamics within two distinct qudits. Notably, this intricate dynamical behavior exhibits remarkable synchronous and anti-synchronous revival features, offering a unique opportunity to engineer many-body synchronization pulse signals. In the resonant tunneling regime, distinguished by strong interatomic interactions, we made a remarkable observation: the hybrid qudits undergo a dimensionality reduction, effectively transforming into a qudit. This dimensionality reduction is accompanied by an intriguing phenomenon: the periodicity of its dynamics is intimately intertwined with the occurrence of the entanglement cycle. Remarkably, synthetic gauge fields emerge as potent regulators of this entanglement cycle. Our results uncover the profound implications of synthetic gauge fields on quantum tunneling processes within many-body systems, which hold promising potential applications for engineering atomtronic devices and controlling quantum entanglement.
We studied signatures of quantum chaos in dynamics of Rydberg-dressed bosonic atoms held in a one-dimensional triple-well potential. Long-range nearest-neighbor and next-nearest-neighbor interactions, induced by laser dressing atoms to strongly interacting Rydberg states, drastically affect mean-field and quantum many-body dynamics. By analyzing the mean-field dynamics, classical chaos regions with positive and large Lyapunov exponents were identified as a function of the potential well tilting and dressed interactions. In the quantum regime, it was found that level statistics of the eigen-energies gain a Wigner–Dyson distribution when the Lyapunov exponents are large, giving rise to signatures of strong quantum chaos. We found that both the time-averaged entanglement entropy and survival probability of the initial state have distinctively large values in the quantum chaos regime. We further showed that population variances could be used as an indicator of the emergence of quantum chaos. This might provide a way to directly probe quantum chaotic dynamics through analyzing population dynamics in individual potential wells.
Since the realization of Bose-Einstein condensation in 1995, experimentalists in ultracold atomic gas community have developed a set of entirely new methods to study quantum gases. In ultracold atomic gases, implementation of synthetic gauge fields, the spin-orbit coupling, optical lattices and Feshbach resonances, provides a clean and highly controllable platform to tune the parameters of the system, which are typically fixed for real materials. Motivated by the rapid developments of experimental progresses, I investigate the ultracold atomic gases with synthetic gauge fields. \n \nIn this thesis, a bosonic gas in optical lattices in the presence of an effective staggered magnetic flux will be studied, using a generalized Bose-Hubbard model. Phase transition from the Mott insulating phase to the superfluid phase will be discussed. Novel superfluid phases including the stripe phase and the plane wave phase will be discussed. Furthermore, the existence of a tricritical point in the phase diagram is predicted. \n \nTo study Fermi systems with synthetic gauge fields, a spin-1=2 Fermi gas with Rashba spin-orbit coupling is investigated by studying the structure of vortex line through the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation (BCSBEC) crossover. Due to the spin-orbit coupling, the s-wave interacting Fermi gas behaves like an effective p-wave paired system. A discussion about the vortex line structure will be provided by calculating the spatial distribution of the gap function, the density, the particle current, and also the elementary excitations. It has been found that the most robust superfluid occurs around the unitary point, indicated by the smallest healing length and the largest critical current. \n \nFinally, motivated by the recent progress of p-wave resonantly Fermi gas in experiment, an extension of Nozières-Schmitt-Rink method to the p-wave case will be given. An investigation of the normal state properties will be given by calculating the equation of state and the p-wave contacts, which have been measured by the experiment. Furthermore, the superfluid transition temperature with realistic parameters appropriate for experiment is calculated and is found to be within experimental reach.
We systematically study the chaotic signatures in a quantum many-body system consisting of an ensemble of interacting two-level atoms coupled to a single-mode bosonic field, the so-called extended Dicke model. The presence of the atom-atom interaction also leads us to explore how the atomic interaction affects the chaotic characters of the model. By analyzing the energy spectral statistics and the structure of eigenstates, we reveal the quantum signatures of chaos in the model and discuss the effect of the atomic interaction. We also investigate the dependence of the boundary of chaos extracted from both eigenvalue-based and eigenstate-based indicators on the atomic interaction. We show that the impact of the atomic interaction on the spectral statistics is stronger than on the structure of eigenstates. Qualitatively, the integrablity-to-chaos transition found in the Dicke model is amplified when the interatomic interaction in the extended Dicke model is switched on.
We investigate signatures of quantum chaos within Ising spin chains subjected to transverse and longitudinal fields, incorporating both local (nearest-neighbor) and non-local (long-range) couplings. While local Ising models may exhibit integrable or chaotic dynamics contingent on interaction strengths and field parameters, systems with non-local interactions generally display a stronger propensity toward chaos, even when the non-local couplings are weak. By examining the distribution of energy level spacings through the level spacing ratio, we delineate the transition from integrable to chaotic regimes and characterize the emergence of quantum chaos in these systems. Our analysis demonstrates that non-local couplings facilitate faster operator spreading and more intricate dynamical behavior, enabling these systems to approach maximal chaos more readily than their local counterparts. Additionally, we analyze Krylov complexity as a dynamical probe of chaos, observing a characteristic peak followed by a plateau at late times in chaotic regimes. This behavior provides a quantitative means to distinguish between integrable and chaotic phases, with the growth rate and saturation level of the complexity serving as effective indicators. Our findings underscore the role of non-local interactions in accelerating the onset of chaos and modifying dynamical complexity in quantum spin chains.
While the concepts of quantum many-body integrability and chaos are of fundamental importance for the understanding of quantum matter, their precise definition has so far remained an open question. In this Letter, we introduce an alternative indicator for quantum many-body integrability and chaos, which is based on the statistics of eigenstates by means of nearest-neighbor subsystem trace distances. We show that this provides us with a faithful classification through extensive numerical simulations for a large variety of paradigmatic model systems including random matrix theories, free fermions, Bethe-ansatz solvable systems, and models of many-body localization. While existing indicators, such as those obtained from level-spacing statistics, have already been utilized with great success, they also face limitations. This concerns, for instance, the quantum many-body kicked top, which is exactly solvable but classified as chaotic in certain regimes based on the level-spacing statistics, while our introduced indicator signals the expected quantum many-body integrability. We discuss the universal behaviors we observe for the nearest-neighbor trace distances and point out that our indicator might be useful also in other contexts such as for the many-body localization transition.