This is a continuation of our preceding paper devoted to signatures of quantum chaos in the geometric collective model of atomic nuclei. We apply the method by Peres to study ordered and disordered patterns in quantum spectra drawn as lattices in the plane of energy vs. average of a chosen observable. A good qualitative agreement with standard measures of chaos is manifested. The method provides an efficient tool for studying structural changes of eigenstates across quantum spectra of general systems.
We consider two coupled quantum tops with angular momentum vectors $\mathbf{L}$ and $\mathbf{M}$. The coupling Hamiltonian defines the Feinberg-Peres model which is a known paradigm of quantum chaos. We show that this model has a nonstandard symmetry with respect to the Altland-Zirnbauer tenfold symmetry classification of quantum systems which extends the well-known threefold way of Wigner and Dyson (referred to as `standard' symmetry classes here). We identify that the nonstandard symmetry classes BD$I_0$ (chiral orthogonal class with no zero modes), BD$I_1$ (chiral orthogonal class with one …
Peres lattices are employed as a visual method to identify the presence of chaos in different regions of the energy spectra in the Dicke model. The coexistence of regular and chaotic regions can be clearly observed for certain energy regions, even if the coupling constant is smaller than the critical value to reach superradiance. It also exhibits the presence of two Excited-State Quantum Phase Transitions, a static and a dynamic one. The diagonalization is performed in a extended bosonic coherent basis which enable us to reach a large number of excited states with good numerical convergence.
Spectra of the geometric collective model of atomic nuclei are analyzed to identify chaotic correlations among nonrotational states. The model has been previously shown to exhibit a high degree of variability of regular and chaotic classical features with energy and control parameters. Corresponding signatures are now verified also on the quantum level for different schemes of quantization and with a variable classicality constant.
We study a method to simulate quantum many-body dynamics of spin ensembles using measurement-based feedback. By performing a weak collective measurement on a large ensemble of two-level quantum systems and applying global rotations conditioned on the measurement outcome, one can simulate the dynamics of a mean-field quantum kicked top, a standard paradigm of quantum chaos. We analytically show that there exists a regime in which individual quantum trajectories adequately recover the classical limit, and show the transition between noisy quantum dynamics to full deterministic chaos described by…
We analyze the interplay of chaos, entanglement and decoherence in a system of qubits whose collective behaviour is that of a quantum kicked top. The dynamical entanglement between a single qubit and the rest can be calculated from the mean of the collective spin operators. This allows the possibility of efficiently measuring entanglement dynamics in an experimental setting. We consider a deeply quantum regime and show that signatures of chaos are present in the dynamical entanglement for parameters accessible in an experiment that we propose using cold atoms. The evolution of the entanglement…
The non-integrable Dicke model and its integrable approximation, the Tavis-Cummings (TC) model, are studied as functions of both the coupling constant and the excitation energy. The present contribution extends the analysis presented in the previous paper by focusing on the statistical properties of the quantum fluctuations in the energy spectrum and their relation with the excited state quantum phase transitions (ESQPT). These properties are compared with the dynamics observed in the semi-classical versions of the models. The presence of chaos for different energies and coupling constants is …
The critical behavior in an important class of excited state quantum phase transitions is signaled by the presence of a new constant of motion only at one side of the critical energy. We study the impact of this phenomenon in the development of chaos in a modified version of the paradigmatic Dicke model of quantum optics, in which a perturbation is added that breaks the parity symmetry. Two asymmetric energy wells appear in the semiclassical limit of the model, whose consequences are studied both in the classical and in the quantum cases. Classically, Poincaré sections reveal that the degree o…
We theoretically investigate the generation of microscopic atomic NOON states, corresponding to the coherent |N,0> + |0,N> superposition with N ~ 5 particles, via collective tunneling of interacting ultracold bosonic atoms within a symmetric double-well potential in the self-trapping regime. We show that a periodic driving of the double well with suitably tuned amplitude and frequency parameters allows one to substantially boost this tunneling process without altering its collective character. The time scale to generate the NOON superposition, which corresponds to half the tunneling time and w…
The chaotic dynamics in nuclear collective motion is studied in the framework of a schematic shell model which has only monopole and quadrupole degrees of freedom. The model is shown to reproduce the experimentally observed global trend toward less chaotic motion in heavier nuclei. The relation between current approach and the earlier studies with bosonic models is discussed.
Triple-NOON states are superpositions of the form $e^{i φ_1} |{N,0,0}\rangle + e^{i φ_2} |{0,N,0}\rangle + e^{i φ_3} |{0,0,N}\rangle$ involving $N$ bosonic quanta distributed over three modes. We theoretically show how such highly entangled states can be generated with interacting ultracold bosonic atoms in a symmetric three-site lattice. The basic protocol consists in preparing all atoms on one site of the lattice and then letting the system evolve during a specific time such that collective tunneling of the atoms to the other two sites takes place. The key point put forward here is that this…
We identify signatures of chaos in the dynamics of discord in a multiqubit system collectively modelled as a quantum kicked top. The evolution of discord between any two qubits is quasiperiodic in regular regions, while in chaotic regions, the quasiperiodicity is lost. As the initial wave function is varied from the regular regions to the chaotic sea, a contour plot of the time averaged discord remarkably reproduces the structures of the classical stroboscopic map. We also find surprisingly opposite behaviour of two-qubit discord versus two-qubit entanglement. Our calculations provide the firs…
We study the nature of the dynamics in a first-order quantum phase transition between spherical and prolate-deformed nuclear shapes. Classical and quantum analyses reveal a change in the system from a chaotic Hénon-Heiles behavior on the spherical side into a pronounced regular dynamics on the deformed side. Both order and chaos persist in the coexistence region and their interplay reflects the Landau potential landscape and the impact of collective rotations.
We discuss the onset of quantum chaos and thermalization in the two-mode Dicke model, which describes the dipolar interaction between an ensemble of spins and two bosonic modes. The two-mode Dicke model exhibits normal to superradiant quantum phase transition with spontaneous breaking either of a discrete or continuous symmetry. We study the behaviour of the fidelity out-of-time-order correlator derived from the Loschmidt echo signal in the quantum phases of the model and show that its exponential growth cannot be related to a classical unstable point in the general case. Moreover, we find tha…
Excited-state quantum phase transitions and chaos in a three-level Lipkin model
Escuela Politécnica Superior, Universidad CEU Fernando III, CEU Universities（CEU费尔南多三世大学高等理工学院）；Departamento de Física Aplicada III, Escuela Técnica Superior de Ingeniería, Universidad de Sevilla（塞维利亚大学高等工程学院应用物理系）；Multidisciplinary Unit for Energy Science, Universidad de Sevilla（塞维利亚大学能源科学多学科单元）；Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla（塞维利亚大学物理学院原子、分子和核物理系）
We find quantum signatures of classical chaos in various metrics of information gain in quantum tomography. We employ a quantum state estimator based on weak collective measurements of an ensemble of identically prepared systems. The tomographic measurement record consists of a sequence of expectation values of a Hermitian operator that evolves under repeated application of the Floquet map of the quantum kicked top. We find an increase in information gain and hence higher fidelities in the reconstruction algorithm when the chaoticity parameter map increases. The results are well predicted by r…
We study the evolution of the dynamics across a generic first order quantum phase transition in an interacting boson model of nuclei. The dynamics inside the phase coexistence region exhibits a very simple pattern. A classical analysis reveals a robustly regular dynamics confined to the deformed region and well separated from a chaotic dynamics ascribed to the spherical region. A quantum analysis discloses regular bands of states in the deformed region, which persist to energies well above the phase-separating barrier, in the face of a complicated environment. The impact of kinetic collective …
We explore the dynamics of entanglement in classically chaotic systems by considering a multiqubit system that behaves collectively as a spin system obeying the dynamics of the quantum kicked top. In the classical limit, the kicked top exhibits both regular and chaotic dynamics depending on the strength of the chaoticity parameter $κ$ in the Hamiltonian. We show that the entanglement of the multiqubit system, considered for both bipartite and pairwise entanglement, yields a signature of quantum chaos. Whereas bipartite entanglement is enhanced in the chaotic region, pairwise entanglement is su…
We theoretically investigate thermalization and spin diffusion driven by a quantum spin bath for a realistic solid-state NMR experiment. We consider polycrystalline L-alanine, and investigate how the spin polarization spreads among several $^{13}$C nuclear spins, which interact via dipole-dipole coupling with the bath of strongly dipolar-coupled $^1$H nuclear (proton) spins. We do this by using direct numerical simulation of the many-spin time-dependent Schrödinger equation. We find that, although the proton spins located near the carbon sites interact most strongly with the $^{13}$C spins, th…
Long-time average behavior of quantum correlations in a multi-qubit system, collectively modeled as a kicked top, is addressed here. The behavior of dynamical generation of quantum correlations such as entanglement, discord, concurrence, as previously studied, and Bell correlation function and tangle, as identified in this study, is a function of initially localized coherent states. Their long-time average reproduces coarse-grained classical phase space structures of the kicked top which contrast, often starkly, chaotic and regular regions. Apart from providing numerical evidence of such corre…
Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University（查理大学数学物理学院粒子与核物理研究所）；Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Complutense de Madrid（马德里康普顿斯大学复杂系统跨学科小组(GISC)）；Departamento de Estructura de la Materia, Física Térmica y Electrónica, Universidad Complutense de Madrid（马德里康普顿斯大学物质结构、热学和电子学系）
This work aims at giving Trotter errors in digital quantum simulation (DQS) of collective spin systems an interpretation in terms of quantum chaos of the kicked top. In particular, for DQS of such systems, regular dynamics of the kicked top ensures convergence of the Trotterized time evolution, while chaos in the top, which sets in above a sharp threshold value of the Trotter step size, corresponds to the proliferation of Trotter errors. We show the possibility to analyze this phenomenology in a wide variety of experimental realizations of the kicked top, ranging from single atomic spins to tr…
