We show how a nonlinear chaotic system, the parametrically kicked nonlinear oscillator, may be realised in the dynamics of a trapped, laser-cooled ion, interacting with a sequence of standing wave pulses. Unlike the original optical scheme [G.J.Milburn and C.A.Holmes, Phys. Rev A, 44, p4704, (1991)], the trapped ion enables strongly quantum dynamics with minimal dissipation. This should permit an experimental test of one of the quantum signatures of chaos; irregular collapse and revival dynamics of the average vibrational energy.
A scheme to generate long-range spin-spin interactions between three-level ions in a chain is presented, providing a feasible experimental route to the rich physics of well-known $SU_3$ models. In particular, we demonstrate different signatures of quantum chaos which can be controlled and observed in experiments with trapped ions.
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 quantum signatures of chaos by using the concept of bipartite fluctuations in the kicked two-site Bose-Hubbard model, which can be mapped to the well-studied kicked top model. We find that the evolution of bipartite fluctuations is quasiperiodic when the initial state centered in the regular regions, while it becomes irregular as the initial state centered in the chaotic regions. As a result, the quantum signatures of chaos can be identified in both the dynamical bipartite fluctuations and the long time averaged bipartite fluctuations. We further demonstrate that the regular versu…
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 analyze the fidelity of a quantum simulation and we show that it displays fractal fluctuations iff the simulated dynamics is chaotic. This analysis allows us to investigate a given simulated dynamics without any prior knowledge. In the case of integrable dynamics, the appearance of fidelity fractal fluctuations is a signal of a highly corrupted simulation. We conjecture that fidelity fractal fluctuations are a signature of the appearance of quantum chaos. Our analysis can be realized already by a few qubit quantum processor.
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 have studied entanglement entropy and Husimi $Q$ distribution as a tool to explore chaos in the quantum two-photon Dicke model. With the increase of the energy of system, the linear entanglement entropy of coherent state prepared in the classical chaotic and regular regions become more distinguishable, and the correspondence relationship between the distribution of time-averaged entanglement entropy and the classical Poincaré section has been improved obviously. Moreover, Husimi $Q$ distribution for the initial states corresponded to the points in the chaotic region in the higher energy sys…
The realization of a paradigm chaotic system, namely the harmonically driven oscillator, in the quantum domain using cold trapped ions driven by lasers is theoretically investigated. The simplest characteristics of regular and chaotic dynamics are calculated. The possibilities of experimental realization are discussed.
Exactly solvable models that exhibit quantum signatures of classical chaos are both rare as well as important - more so in view of the fact that the mechanisms for ergodic behavior and thermalization in isolated quantum systems and its connections to non-integrability are under active investigation. In this work, we study quantum systems of few qubits collectively modeled as a kicked top, a textbook example of quantum chaos. In particular, we show that the 3 and 4 qubit cases are exactly solvable and yet, interestingly, can display signatures of ergodicity and thermalization. Deriving analytic…
We propose a method which can effectively stabilize fixed points in the classical and quantum dynamics of a phase-sensitive chaotic system with feedback. It is based on feeding back a selected quantum sub-ensemble whose phase and amplitude stabilize the otherwise chaotic dynamics. Although the method is rather general, we apply it to realizations of the inherently chaotic Ikeda map. One suggested realization involves the Mach-Zender interferometer with Kerr nonlinearity. Another realization involves a trapped ion interacting with laser fields.
Homoclinic motion plays a key role in the organization of classical chaos in Hamiltonian systems. In this Letter, we show that it also imprints a clear signature in the corresponding quantum spectra. By numerically studying the fluctuations of the widths of wavefunctions localized along periodic orbits we reveal the existence of an oscillatory behavior, that is explained solely in terms of the primary homoclinic motion. Furthermore, our results indicate that it survives the semiclassical limit.
We investigate both the quantum and classical dynamics of a non-Hermitian system via a kicked rotor model with $\mathcal{PT}$ symmetry. For the quantum dynamics, both the mean momentum and mean square of momentum exhibits the staircase growth with time when the system parameter is in the neighborhood of the $\mathcal{PT}$ symmetry breaking point. If the system parameter is very larger than the $\mathcal{PT}$ symmetry breaking point, the accelerator mode results in the directed spreading of the wavepackets as well as the ballistic diffusion in momentum space. For the classical dynamics, the non…
The driven-dissipative Dicke model features normal, superradiant, and lasing steady-states that may be regular or chaotic. We report quantum signatures of chaos in a quench protocol from the lasing states. Within the framework of a classical mean-field perspective, once quenched, the system relaxes either to the normal or to the superradiant state. Quench-from-chaos, unlike quench from a regular lasing state, exhibits erratic dependence on control parameters. In the quantum domain this sensitivity implies an effect that is similar to universal conductance fluctuations.
We study the particle-entanglement dynamics witnessed by the quantum Fisher information (QFI) of a trapped Bose-Einstein condensate governed by the kicked rotor Hamiltonian. The dynamics is investigated with a beyond mean-field approach. We link the time scales of the validity of this approximation in, both, classical regular and chaotic regions, with the maximum Lyapunov exponents of the classical system. This establishes an effective connection between the classical chaos and the QFI. We finally study the critical point of a quantum phase transition using the beyond mean-field approximation …
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 extracte…
We study the coherence dynamics of a kicked two-mode Bose-Hubbard model starting with an arbitrary coherent spin preparation. For preparations in the chaotic regions of phase-space we find a generic behavior with Flouquet participation numbers that scale as the entire $N$-particle Hilbert space, leading to a rapid loss of single particle coherence. However, the chaotic behavior is not uniform throughout the chaotic sea, and unique statistics is found for preparations at the vicinity of hyperbolic points that are embedded in it. This is contrasted with the low log(N) participation that is respo…
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…
Recent experiments with cold atoms provide a significant step toward a better understanding of tunnelling when irregular dynamics is present at the classical level. In this paper, we lay out numerical studies which shed light on the previous experiments, help to clarify the underlying physics and have the ambition to be guidelines for future experiments.
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 signatures of quantum chaos already in the system with three particl…
Universidad de Buenos Aires（布宜诺斯艾利斯大学）；CONICET - Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA)（阿根廷国家科学研究委员会-布宜诺斯艾利斯大学，布宜诺斯艾利斯物理研究所）
Two properties are needed for a classical system to be chaotic: exponential stretching and mixing. Recently, out-of-time order correlators were proposed as a measure of chaos in a wide range of physical systems. While most of the attention has previously been devoted to the short time stretching aspect of chaos, characterized by the Lyapunov exponent, we show for quantum maps that the out-of-time correlator approaches its stationary value exponentially with a rate determined by the Ruelle-Pollicot resonances. This property constitutes clear evidence of the dual role of the underlying classical…
We show that a multi-step quantum walk can be realized for a single trapped ion with interpolation between quantum and random walk achieved by randomizing the generalized Hadamard coin flip phase. The signature of the quantum walk is manifested not only in the ion's position but also its phonon number, which makes an ion trap implementation of the quantum walk feasible.
Time-delay signature (TDS) suppression of semiconductor lasers with external optical feedback is necessary to ensure the security of chaos-based secure communications. Here we numerically and experimentally demonstrate a technique to effectively suppress the TDS of chaotic lasers using quantum noise. The TDS and dynamical complexity are quantified using the autocorrelation function and normalized permutation entropy at the feedback delay time, respectively. Quantum noise from quadrature fluctuations of vacuum state is prepared through balanced homodyne measurement. The effects of strength and …
A nonlinear stimulated Raman adiabatic passage (STIRAP) is a fascinating physical process that dynamically explores chaotic and non-chaotic phases. In a recent paper Phys. Rev. Res. 2, 042004 (R) (2020), such a phenomenon is realized in a cavity-QED platform. There, the emergence of chaos and its impact on STIRAP efficiency are mainly demonstrated in the semiclassical limit. In the present paper I treat the problem in a fully quantum many-body framework. With the aim of extracting quantum signatures of a classically chaotic system, it is shown that an out-of-time-ordered correlator (OTOC) meas…
We consider the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic system's set of cupolets, which are essentially highly-accurate stabilizations of its unstable periodic orbits. The discussion is motivated by the bound or entangled states that we have recently detected between interacting chaotic systems, wherein pairs of cupolets are induced into a state of mutually-sustaining stabilization that can be maintained without ex…
We study entanglement entropy (EE) as a signature of quantum chaos in ergodic and non-ergodic systems. In particular we look at the quantum kicked top and kicked rotor as multi-qubit systems, and investigate the single qubit EE which characterizes bipartite entanglement of this qubit 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 non-ergodic systems. In particular, we show that EE can be maximi…
We numerically investigated the entanglement product in the simplest coupled kicked top model with the spin $j=1$. Different from the dynamical pattern of entanglement in the semiclassical regime, two similar initial states may have discordant entanglement oscillations. A candidate of the quantum signature of this classical chaotic system was proposed. The potential antimonotonic relation between the rank correlation coefficient qualifying the concordant of two entanglement evolutions and the stationary entanglement was preliminarily revealed.
The studied model describes a particle that obeys a one-dimensional nonlinear Schrödinger equation in the potential of a double-well. Transitions between the two lowest self-trapped states of this system under the influence of the external time-dependent perturbation are studied in the two-mode approximation. If the perturbation dependence on time is harmonic with the frequency $ω$, then transitions between the states become possible if the amplitude of the perturbation $F$ exceeds some threshold value $F_c(ω)$; above the threshold motion of the system becomes chaotic. If the perturbation is a…
The driven non-linear duffing osillator is a very good, and standard, example of a quantum mechanical system from which classical-like orbits can be recovered from unravellings of the master equation. In order to generated such trajectories in the phase space of this oscillator in this paper we use a the quantum jumps unravelling together with a suitable application of the correspondence principle. We analyse the measured readout by considering the power spectra of photon counts produced by the quantum jumps. Here we show that localisation of the wave packet from the measurement of the oscilla…
We present the multifractal analysis of coherent states in kicked top model by expanding them in the basis of Floquet operator eigenstates. We demonstrate the manifestation of phase space structures in the multifractal properties of coherent states. In the classical limit, the classical dynamical map can be constructed, allowing us to explore the corresponding phase space portraits and to calculate Lyapunov exponent. By tuning the kicking strength, the system undergoes a transition from regularity to chaos. We show that the variation of multifractal dimensions of coherent states with kicking s…
Classical chaotic systems are distinguished by their sensitive dependence on initial conditions. The absence of this property in quantum systems has lead to a number of proposals for perturbation-based characterizations of quantum chaos, including linear growth of entropy, exponential decay of fidelity, and hypersensitivity to perturbation. All of these accurately predict chaos in the classical limit, but it is not clear that they behave the same far from the classical realm. We investigate the dynamics of a family of quantizations of the baker's map, which range from a highly entangling unita…
We establish the emergence of chaotic motion in optomechanical systems. Chaos appears at negative detuning for experimentally accessible values of the pump power and other system parameters. We describe the sequence of period doubling bifurcations that leads to chaos, and state the experimentally observable signatures in the optical spectrum. In addition to the semi-classical dynamics we analyze the possibility of chaotic motion in the quantum regime. We find that quantum mechanics protects the optomechanical system against irregular dynamics, such that simple periodic orbits reappear and repl…
We establish a rigorous connection between quantum coherence and quantum chaos by employing coherence measures originating from the resource theory framework as a diagnostic tool for quantum chaos. We quantify this connection at two different levels: quantum states and quantum channels. At the level of states, we show how several well-studied quantifiers of chaos are, in fact, quantum coherence measures in disguise (or closely related to them). We further this connection for all quantum coherence measures by using tools from majorization theory. Then, we numerically study the coherence of chao…
We study how perturbations affect dynamics of integrable many-body quantum systems, causing transition from integrability to chaos. Looking at spin transport in the Heisenberg chain with impurities we find that in the thermodynamic limit transport gets diffusive already at an infinitesimal perturbation. Small extensive perturbations therefore cause an immediate transition from integrability to chaos. Nevertheless, there is a remnant of integrability encoded in the dependence of the diffusion constant on the impurity density, namely, at small densities it is proportional to the square root of t…
Ergodicity and chaos play an integral role in the dynamical behavior of many-particle systems and are crucial to the formulation of statistical mechanics. Still, a general understanding of how randomness and chaos emerge in the dynamical evolution of closed quantum systems remains elusive. Here, we develop an experimental platform for the realization of canonical quantum chaotic Hamiltonians based on quantum simulation with synthetic lattices. We map the angular momentum projection states of an effective quantum spin onto the linear momentum states of a $^{87}$Rb Bose-Einstein condensate, whic…
Quantum systems whose classical counterparts are chaotic typically have highly correlated eigenvalues and level statistics that coincide with those from ensembles of full random matrices. A dynamical manifestation of these correlations comes in the form of the so-called correlation hole, which is a dip below the saturation point of the survival probability's time evolution. In this work, we study the correlation hole in the spin-boson (Dicke) model, which presents a chaotic regime and can be realized in experiments with ultracold atoms and ion traps. We derive an analytical expression that des…
We study the quantum dynamics of the kicked Dicke model(KDM) in terms of the Floquet operator and analyze the connection between the chaos and thermalization in this context. The Hamiltonian map is constructed by taking the classical limit of the Heisenberg equation of motion suitably to study the corresponding phase space dynamics which shows a crossover from regular to chaotic motion by tuning the kicking strength. The fixed point analysis and calculation of the Lyapunov exponent(LE) provides us a complete picture of the onset of chaos in phase space dynamics. We carry out the spectral analy…
We study out-of-time-order correlation (OTOC) for one-dimensional periodically driven hardcore bosons in the presence of Aubry-André (AA) potential and show that both the spectral properties and the saturation values of OTOC in the steady state of these driven systems provide a clear distinction between the localized and delocalized phases of these models. Our results, obtained via exact numerical diagonalization of these boson chains, thus indicate that OTOC can provide a signature of drive induced delocalization even for systems which do not have a well defined semiclassical (and/or large N)…
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. While the standard procedure to reveal signatures of quantum chaos requires classifying the energy levels according to their symmetries, we show that this classification is not necessary to obtain manifestation of spectral correlations in the temporal evolution of the survival probability. Our findings exhibit the survival probability as a powerful tool…
We study the dynamics of a quantum spin ensemble controlled by trains of ultrashort pulses. To model disturbances of the kicks, we consider that the spins are submitted to different kick trains which follow regular, random, stochastic or chaotic dynamical processes. These are described by dynamical systems on a torus. We study the quantum decoherence and the population relaxation of the spin ensemble induced by these classical dynamical processes disturbing the kick trains. For chaotic kick trains we show that the decoherence and the relaxation processes exhibit a signature of chaos directly r…
We study signatures of quantum chaos in (1+1)D Quantum Field Theory (QFT) models. Our analysis is based on the method of Hamiltonian truncation, a numerical approach for the construction of low-energy spectra and eigenstates of QFTs that can be considered as perturbations of exactly solvable models. We focus on the double sine-Gordon, also studying the massive sine-Gordon and ${ϕ^4}$ model, all of which are non-integrable and can be studied by this method with sufficiently high precision from small to intermediate perturbation strength. We analyze the statistics of level spacings and of eigenv…
The non-integrability of quantum systems, often associated with chaotic behavior, is a concept typically applied to cases with a high-dimensional Hilbert space Among different indicators signaling this behavior, the study of the long-time oscillations of the out-of-time-ordered correlator (OTOC) appears as a versatile tool, that can be adapted to the case of systems with a small number of degrees of freedom. Using such an approach, we consider the oscillations observed after the scrambling time in the measurement of OTOCs of local operators for an Ising spin chain on a nuclear magnetic resonan…
In the context of quantum chaos, both theory and numerical analysis predict large fluctuations of the tunnelling transition probabilities when irregular dynamics is present at the classical level. We consider here the non-dissipative quantum evolution of cold atoms trapped in a time-dependent modulated periodic potential generated by two laser beams. We give some precise guidelines for the observation of chaos assisted tunnelling between invariant phase space structures paired by time-reversal symmetry.
