Long-lasting exponential spreading in periodically driven quantum systems

Pseudoclassical Dynamics of the Kicked Top

The kicked rotor and the kicked top are two paradigms of quantum chaos. The notions of quantum resonance and the pseudoclassical limit, developed in the study of the kicked rotor, have revealed an intriguing and unconventional aspect of classical-quantum correspondence. Here, we show that, by extending these notions to the kicked top, its rich dynamical behavior can be appreciated more thoroughly; of special interest is the entanglement entropy. In particular, the periodic synchronization between systems subject to different kicking strength can be conveniently understood and elaborated from the pseudoclassical perspective. The applicability of the suggested general pseudoclassical theory to the kicked rotor is also discussed.

Shannon entropy at avoided crossings in the quantum transition from order to chaos

Shannon entropy is studied for the series of avoided crossings that characterize the transition from order to chaos in quantum mechanics. In order to be able to study jointly this entropy for discrete and continuous probability, calculations have been performed on a quantized map, the kicked Harper map, resulting in a different behavior, as order-chaos transition takes place, for the discrete (position representation) and continuous (coherent state representation) cases. This different behavior is analyzed in terms of the distribution of zeros of the Husimi function.

Directed momentum current induced by the PT-symmetric driving

We investigate the directed momentum current in the quantum kicked rotor model with PT-symmetric deriving potential. For the quantum nonresonance case, the values of quasienergy become complex when the strength of the imaginary part of the kicking potential exceeds a threshold value, which demonstrates the appearance of the spontaneous PT symmetry breaking. In the vicinity of the transition point, the momentum current exhibits a staircase growth with time. Each platform of the momentum current corresponds to the mean momentum of some eigenstates of the Floquet operator whose imaginary parts of the quasienergy are significantly large. Above the transition point, the momentum current increases linearly with time. Interestingly, its acceleration rate exhibits a kind of "quantized" increment with the kicking strength. We propose a modified classical acceleration mode of the kicked rotor model to explain such an intriguing phenomenon. Our theoretical prediction is in good agreement with numerical results.

Nonexponential Decoherence and Subdiffusion in Atom-Optics Kicked Rotor

Quantum systems lose coherence upon interaction with the environment and tend towards classical states. Quantum coherence is known to exponentially decay in time so that macroscopic quantum superpositions are generally unsustainable. In this work, slower than exponential decay of coherences is experimentally realized in an atom-optics kicked rotor system subjected to nonstationary Lévy noise in the applied kick sequence. The slower coherence decay manifests in the form of quantum subdiffusion that can be controlled through the Lévy exponent. The experimental results are in good agreement with the analytical estimates and numerical simulations for the mean energy growth and momentum profiles of an atom-optics kicked rotor.

Quantum properties of double kicked systems with classical translational invariance in momentum

Double kicked rotors (DKRs) appear to be the simplest nonintegrable Hamiltonian systems featuring classical translational symmetry in phase space (i.e., in angular momentum) for an infinite set of values (the rational ones) of a parameter η. The experimental realization of quantum DKRs by atom-optics methods motivates the study of the double kicked particle (DKP). The latter reduces, at any fixed value of the conserved quasimomentum βℏ, to a generalized DKR, the "β-DKR." We determine general quantum properties of β-DKRs and DKPs for arbitrary rational η. The quasienergy problem of β-DKRs is shown to be equivalent to the energy eigenvalue problem of a finite strip of coupled lattice chains. Exact connections are then obtained between quasienergy spectra of β-DKRs for all β in a generically infinite set. The general conditions of quantum resonance for β-DKRs are shown to be the simultaneous rationality of η,β, and a scaled Planck constant ℏ(S). For rational ℏ(S) and generic values of β, the quasienergy spectrum is found to have a staggered-ladder structure. Other spectral structures, resembling Hofstadter butterflies, are also found. Finally, we show the existence of particular DKP wave-packets whose quantum dynamics is free, i.e., the evolution frequencies of expectation values in these wave-packets are independent of the nonintegrability. All the results for rational ℏ(S) exhibit unique number-theoretical features involving η,ℏ(S), and β.

Planck's quantum-driven integer quantum Hall effect in chaos

We find in a canonical chaotic system, the kicked spin-1/2 rotor, a Planck's quantum(he)-driven phenomenon bearing a close analogy to the integer quantum Hall effect but of chaos origin. Specifically, the rotor's energy growth is unbounded ("metallic" phase) for a discrete set of critical values of he, but otherwise bounded ("insulating" phase). The latter phase is topological and characterized by a quantum number ("quantized Hall conductance"). The number jumps by unity whenever he passes through each critical value as it decreases. Our findings indicate that rich topological quantum phenomena can emerge from chaos.

Quantum and classical superballistic transport in a relativistic kicked-rotor system

As an unusual type of anomalous diffusion behavior, (transient) superballistic transport is not well known but has been experimentally simulated recently. Quantum superballistic transport models to date are mainly based on connected sublattices which are constructed to have different properties. In this work, we show that both quantum and classical superballistic transport in the momentum space can occur in a simple periodically driven Hamiltonian system, namely, a relativistic kicked-rotor system with a nonzero mass term. The nonzero mass term essentially realizes a situation, now in the momentum space, in which two (momentum) sublattices with different dispersion relations (and hence different nature of on-site potential) are connected as a junction. It is further shown that the quantum and classical superballistic transport should occur under much different choices of the system parameters. The results are of interest to studies of anomalous transport, quantum and classical chaos, and the issue of quantum-classical correspondence.

Quantifying local density of optical states of nanorods by fluorescence lifetime imaging

In this letter, we demonstrate a facile far-field approach to quantify the near-field local density of optical states (LDOS) of a nanorod using CdTe quantum dots (QDs) emitters tethered to the surface of nanorods as beacons for optical read-outs. Radiative decay rate was extracted to quantify the LDOS; our analysis indicates that the LDOS of the nanorod enhance both the radiative and nonradiative decay of QD, particularly radiative decay of QDs at the end of nanorod is enhanced by 1.17 times greater than that at the waist, while the nonradiative decay was uniformly enhanced over the nanorod. To the best of our knowledge, our effort constitutes the first to map the LDOS of a nanostructure via far-field method, to provide clarity on the interaction mechanism between emitters and the nanostructure, and to be potentially employed in the LDOS mapping of high-throughput nanostructures.

Classical and quantum transport in one-dimensional periodically kicked systems

This paper is a brief review of classical and quantum transport phenomena, as well as related spectral properties, exhibited by one-dimensional periodically kicked systems. Two representative and fundamentally different classes of systems will be considered: those satisfying the classical Kolmogorov−Arnol’d−Moser scenario and those that do not. The experimental realization of some of these systems using atom-optics methods will be mentioned.

Exponential quantum spreading in a class of kicked rotor systems near high-order resonances

Long-lasting exponential quantum spreading was recently found in a simple but very rich dynamical model, namely, an on-resonance double-kicked rotor model [J. Wang, I. Guarneri, G. Casati, and J. B. Gong, Phys. Rev. Lett. 107, 234104 (2011)]. The underlying mechanism, unrelated to the chaotic motion in the classical limit but resting on quasi-integrable motion in a pseudoclassical limit, is identified for one special case. By presenting a detailed study of the same model, this work offers a framework to explain long-lasting exponential quantum spreading under much more general conditions. In particular, we adopt the so-called "spinor" representation to treat the kicked-rotor dynamics under high-order resonance conditions and then exploit the Born-Oppenheimer approximation to understand the dynamical evolution. It is found that the existence of a flat band (or an effectively flat band) is one important feature behind why and how the exponential dynamics emerges. It is also found that a quantitative prediction of the exponential spreading rate based on an interesting and simple pseudoclassical map may be inaccurate. In addition to general interests regarding the question of how exponential behavior in quantum systems may persist for a long time scale, our results should motivate further studies toward a better understanding of high-order resonance behavior in δ-kicked quantum systems.

Kicked-Harper model versus on-resonance double-kicked rotor model: from spectral difference to topological equivalence

Recent studies have established that, in addition to the well-known kicked-Harper model (KHM), an on-resonance double-kicked rotor (ORDKR) model also has Hofstadter's butterfly Floquet spectrum, with strong resemblance to the standard Hofstadter spectrum that is a paradigm in studies of the integer quantum Hall effect. Earlier it was shown that the quasienergy spectra of these two dynamical models (i) can exactly overlap with each other if an effective Planck constant takes irrational multiples of 2π and (ii) will be different if the same parameter takes rational multiples of 2π. This work makes detailed comparisons between these two models, with an effective Planck constant given by 2πM/N, where M and N are coprime and odd integers. It is found that the ORDKR spectrum (with two periodic kicking sequences having the same kick strength) has one flat band and N-1 nonflat bands with the largest bandwidth decaying in a power law as ~K(N+2), where K is a kick strength parameter. The existence of a flat band is strictly proven and the power-law scaling, numerically checked for a number of cases, is also analytically proven for a three-band case. By contrast, the KHM does not have any flat band and its bandwidths scale linearly with K. This is shown to result in dramatic differences in dynamical behavior, such as transient (but extremely long) dynamical localization in ORDKR, which is absent in the KHM. Finally, we show that despite these differences, there exist simple extensions of the KHM and ORDKR model (upon introducing an additional periodic phase parameter) such that the resulting extended KHM and ORDKR model are actually topologically equivalent, i.e., they yield exactly the same Floquet-band Chern numbers and display topological phase transitions at the same kick strengths. A theoretical derivation of this topological equivalence is provided. These results are also of interest to our current understanding of quantum-classical correspondence considering that the KHM and ORDKR model have exactly the same classical limit after a simple canonical transformation.

Exponential spreading and singular behavior of quantum dynamics near hyperbolic points

Quantum dynamics of a particle in the vicinity of a hyperbolic point is considered. Expectation values of dynamical variables are calculated, and the singular behavior is analyzed. Exponentially fast extension of quantum dynamics is obtained, and conditions for this realization are analyzed.