Quantum-classical correspondence in the vicinity of periodic orbits

Avoided crossings and dynamical tunneling close to excited-state quantum phase transitions

Using the Wehrl entropy, we study the delocalization in phase space of energy eigenstates in the vicinity of avoided crossings in the Lipkin-Meshkov-Glick model. These avoided crossings, appearing at intermediate energies in a certain parameter region of the model, originate classically from pairs of trajectories lying in different phase-space regions which, contrary to the low-energy regime, are not connected by the discrete parity symmetry of the model. As coupling parameters are varied, a sudden increase of the Wehrl entropy is observed for eigenstates participating in avoided crossings that are close to the critical energy of the excited-state quantum phase transition. This allows us to detect when an avoided crossing is accompanied by a superposition of the pair of classical trajectories in the Husimi function of eigenstates. This superposition yields an enhancement of dynamical tunneling, which is observed by considering initial Bloch states that evolve partially into the partner region of the paired classical trajectories, thus breaking the quantum-classical correspondence in the evolution of observables.

Nonlinear dynamics and quantum chaos of a family of kicked p-spin models

We introduce kicked p-spin models describing a family of transverse Ising-like models for an ensemble of spin-1/2 particles with all-to-all p-body interaction terms occurring periodically in time as delta-kicks. This is the natural generalization of the well-studied quantum kicked top (p=2) [Haake, Kuś, and Scharf, Z. Phys. B 65, 381 (1987)10.1007/BF01303727]. We fully characterize the classical nonlinear dynamics of these models, including the transition to global Hamiltonian chaos. The classical analysis allows us to build a classification for this family of models, distinguishing between p=2 and p>2, and between models with odd and even p's. Quantum chaos in these models is characterized in both kinematic and dynamic signatures. For the latter, we show numerically that the growth rate of the out-of-time-order correlator is dictated by the classical Lyapunov exponent. Finally, we argue that the classification of these models constructed in the classical system applies to the quantum system as well.

Simulating Nonlinear Dynamics of Collective Spins via Quantum Measurement and Feedback

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 classical Lyapunov exponents. We also analyze the effects of decoherence, and show that the proposed scheme represents a robust method to explore the emergence of chaos from complex quantum dynamics in a realistic experimental platform based on an atom-light interface.

NMR studies of quantum chaos in a two-qubit kicked top

Quantum chaotic kicked top model is implemented experimentally in a two-qubit system comprising of a pair of spin-1/2 nuclei using nuclear magnetic resonance techniques. The essential nonlinear interaction was realized using indirect spin-spin coupling, while the linear kicks were realized using radio-frequency pulses. After a variable number of kicks, quantum state tomography was employed to reconstruct the single-qubit reduced density matrices, using which we could extract von Neumann entropies and Husimi distributions. These measures enabled the study of correspondence with classical phase space as well as probing distinct features of quantum chaos, such as symmetries and temporal periodicity in the two-qubit kicked top.

Quantum chaos and entanglement in ergodic and nonergodic systems

We study entanglement entropy (EE) as a signature of quantum chaos in ergodic and nonergodic systems. In particular we look at the quantum kicked top and kicked rotor as multispin systems and investigate the single-spin EE which characterizes bipartite entanglement of this spin with the rest of the system. We study the correspondence of the Kolmogorov-Sinai entropy of the classical kicked systems with the EE of their quantum counterparts. We find that EE is a signature of global chaos in ergodic systems and local chaos in nonergodic systems. In particular, we show that EE can be maximized even when systems are highly nonergodic, when the corresponding classical system is locally chaotic. In contrast, we find evidence that the quantum analog of Kolmogorov-Arnol'd-Moser (KAM) tori are tori of low entanglement entropy. We conjecture that entanglement should play an important role in any quantum KAM theory.

Three-dimensional classical and quantum stable structures of dissipative systems

We study the properties of classical and quantum stable structures in a three-dimensional (3D) parameter space corresponding to the dissipative kicked top. This is a model system in quantum and classical chaos that gives a starting point for many body examples. We are able to identify the influence of these structures in the spectra and eigenstates of the corresponding (super)operators. This provides a complementary view with respect to the typical two-dimensional parameter space systems found in the literature. Many properties of the eigenstates, like its localization behavior, can be generalized to this higher-dimensional parameter space and spherical phase space topology. Moreover, we find a 3D phenomenon-generalizable to more dimensions-that we call the coalescence-separation of (q)ISSs, whose main consequence is a marked enhancement of quantum localization. This could be of relevance for systems that have attracted a lot of attention very recently.