Superballistic wavepacket spreading in double kicked rotor

We investigate possible ways in which a quantum wavepacket spreads. We show that in a general class of double kicked rotor system, a wavepacket may undergo superballistic spreading; i.e., its variance increases as the cubic of time. The conditions for the observed superballistic spreading and two related characteristic time scales are studied. Our results suggest that the symmetry of the studied model and whether it is a Kolmogorov-Arnold-Moser system are crucial to its wavepacket spreading behavior. Our study also sheds new light on the exponential wavepacket spreading phenomenon previously observed in the double kicked rotor system.     

Hierarchical structures in the phase space and fractional kinetics: II. Immense delocalization in quantized systems

Anomalous transport due to Levy-type flights in quantum kicked systems is studied. These systems are kicked rotor and kicked Harper model. It is confirmed for a kicked rotor that there exist special "magic" values of a control parameter of chaos K=K(*)=6.908 745 em leader for which an essential increasing of a localization length is obtained. Functional dependence of the localization length on both parameter of chaos and quasiclassical parameter h is studied. We also observe immense delocalization of the order of 10(9) for a kicked Harper model when a control parameter K is taken to be K(*)=6.349 972. This "magic" value corresponds to special phase space topology in the classical limit, when a hierarchical self-similar set of sticky islands emerges. The origin of the effect is of the general nature and similar immense delocalization as well as increasing of localization length can be found in other systems. (c) 2000 American Institute of Physics.     

Classical dynamics and particle transport in kicked billiards

We study nonlinear dynamics of the kicked particle whose motion is confined by square billiard. The kick source is considered as localized at the center of a square with central symmetric spatial distribution. It is found that ensemble averaged energy of the particle diffusively grows as a function of time. This growth is much more extensive than that of kicked rotor energy. It is shown that momentum transfer distribution in a kicked billiard is considerably different than that for kicked free particle. Time-dependence of the ensemble averaged energy for different localizations of the kick source is also explored. It is found that changing of localization does not lead to crucial changes in the time-dependence of the energy. Also, escape and transport of particles are studied by considering a kicked open billiard with one and three holes, respectively. It is found that for the open billiard with one hole the number of (non-interacting) billiard particles decreases according to exponential law.     

Resonant nonlinear quantum transport for a periodically kicked bose condensate

Our realistic numerical results show that the fundamental and higher-order quantum resonances of the delta-kicked rotor are observable in state-of-the-art experiments with a Bose condensate in a shallow harmonic trap, kicked by a spatially periodic optical lattice. For stronger confinement, interaction-induced destruction of the resonant motion of the kicked harmonic oscillator is predicted.     

Chaotic systems in complex phase space

This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in complex phase space. Additionally, it is shown that the short-time and long-time behaviours of these two PT-symmetric dynamical models in complex phase space exhibit strong qualitative similarities.     

Experimental demonstration of localization in the frequency domain of mode-locked lasers with dispersion

Mode-locked lasers with intracavity dispersion are experimentally shown to exhibit localization behavior in their frequency domain. The localization, with its typical exponential spectrum structure, is analogous to that which occurs for the quantum kicked rotor. The experimental demonstration of our optical kicked rotor is done with a long mode-locked dispersive fiber laser. The localization effect sets a basic limit on the spectrum bandwidth and the minimum pulse width in such lasers. It also provides a special experimental test bed for the study of optical kicked rotors and localization effects.     

A spectroscopical measure for the exploration of phase space

Many nonintegrable systems have eigenstates that typically require numerous basis states to represent them. We develop a criterion to judge the extent to which phase space is explored by the spectrum of such a Hamiltonian. Our criterion uses the eigenvalues rather than the eigenfunctions and is based on identifying a direct relation between the intensity of Shnirelman's peak and the localization length. We illustrate our procedure by applying it to the spectrum of two prototypical nonintegrable systems, the kicked rotor and the kicked top. (c) 1998 American Institute of Physics.     

A super-Ohmic energy absorption in driven quantum chaotic systems

We consider energy absorption by driven chaotic systems of the symplectic symmetry class. According to our analytical perturbative calculation, at the initial stage of evolution the energy growth with time can be faster than linear. This appears to be an analog of weak anti-localization in disordered systems with spin-orbit interaction. Our analytical result is also confirmed by numerical calculations for the symplectic quantum kicked rotor.     

Numerical investigation of the effects of classical phase space structure on a quantum system with decoherence

We present a detailed numerical study of a chaotic classical system and its quantum counterpart. The system is a special case of a kicked rotor and for certain parameter values possesses cantori dividing chaotic regions of the classical phase space. We investigate the diffusion of particles through a cantorus. A quantum analysis confirms that the cantori act as barriers. We numerically estimate the classical phase space flux through the cantorus per kick and relate this quantity to the behavior of the quantum system. We introduce decoherence via environmental interactions with the quantum system and observe the subsequent increase in the transport of quantum particles through the boundary.     

Quantum scaling laws in the onset of dynamical delocalization

We study the destruction of dynamical localization experimentally observed in an atomic realization of the kicked rotor by a deterministic Hamiltonian perturbation, with a temporal periodicity incommensurate with the principal driving. We show that the destruction is gradual, with well-defined scaling laws for the various classical and quantum parameters, in sharp contrast to predictions based on the analogy with Anderson localization.     

Experimental test of universality of the Anderson transition

We experimentally test the universality of the Anderson three dimensional metal-insulator transition, using a quasiperiodic atomic kicked rotor. Nine sets of parameters controlling the microscopic details have been tested. Our observation indicates that the transition is of second order, with a critical exponent independent of the microscopic details; the average value 1.63±0.05 agrees very well with the numerically predicted value ν=1.58.     

Ballistic and localized transport for the atom optics kicked rotor in the limit of a vanishing kicking period

We present mean energy measurements for the atom optics kicked rotor as the kicking period tends to zero. A narrow resonance is observed marked by quadratic energy growth, in parallel with a complete freezing of the energy absorption away from the resonance peak. Both phenomena are explained by classical means, taking proper account of the atoms' initial momentum distribution.     

Driving the resonant quantum kicked rotor via extended initial?conditions

We study the resonances of the quantum kicked rotor subjected to an extended initial distribution. For the primary resonances we obtain the dispersion relation for the map of this system. We find an analytical dependence of the statistical moments on the shape of the initial distribution. For the secondary resonances we obtain numerically a similar dependence. This allows us to devise an extended initial condition which produces an average angular momentum pointing in a preset direction which increases with time with a preset ratio.     

Entanglement and dynamics of spin chains in periodically pulsed magnetic fields: accelerator modes

We study the dynamics of a single excitation in a Heisenberg spin-chain subjected to a sequence of periodic pulses from an external, parabolic, magnetic field. We show that, for experimentally reasonable parameters, a pair of counterpropagating coherent states is ejected from the center of the chain. We find an illuminating correspondence with the quantum time evolution of the well-known paradigm of quantum chaos, the quantum kicked rotor. From this we can analyze the entanglement production and interpret the ejected coherent states as a manifestation of the so-called "accelerator modes" of a classically chaotic system.     

Resonance- and chaos-assisted tunneling in mixed regular-chaotic systems

We present evidence that nonlinear resonances govern the tunneling process between symmetry-related islands of regular motion in mixed regular-chaotic systems. In a similar way as for near-integrable tunneling, such resonances induce couplings between regular states within the islands and states that are supported by the chaotic sea. On the basis of this mechanism, we derive a semiclassical expression for the average tunneling rate, which yields good agreement in comparison with the exact quantum tunneling rates calculated for the kicked rotor and the kicked Harper.     

Directed motion for delta-kicked atoms with broken symmetries: comparison between theory and experiment

We report an experimental investigation of momentum diffusion in the delta-function kicked rotor where time symmetry is broken by a two-period kicking cycle and spatial symmetry by an alternating linear potential. We exploit this, and a technique involving a moving optical potential, to create an asymmetry in the momentum diffusion that is due to the classical chaotic diffusion. This represents a realization of a type of Hamiltonian quantum ratchet.     

Virtual photon effects on classical chaos in a periodically kicked Rydberg atom system

We study classical chaos in the system of a two-level Rydberg atom interacting with a pulsed standing microwave. This model approaches the form of an atom optics realization of a usual delta-kicked rotor under the rotating-wave approximation (RWA). We find that the non-energy-conserving processes or virtual photon processes neglected in the RWA have a strong effect on the classical chaos, which can enhance, reduce and even completely suppress the chaos under certain kicked conditions. The system displays non-KAM dynamical behavior for rational and irrational kicks.     

Dynamical localization and repeated measurements in a quantum computation process

We study numerically the effects of measurements on dynamical localization in the kicked rotator model simulated on a quantum computer. Contrary to the previous studies, which showed that measurements induce a diffusive probability spreading, our results demonstrate that localization can be preserved for repeated single-qubit measurements. We detect a transition from a localized to a delocalized phase, depending on the system parameters and on the choice of the measured qubit.     

State reconstruction of the kicked rotor

We propose two experimentally feasible methods based on atom interferometry to measure the quantum state of the kicked rotor.     

Shape of the quantum diffusion front

We show that quantum diffusion has well-defined front shape. After an initial transient, the wave packet front (tails) is described by a stretched exponential P(x,t) = A(t)exp(-absolute value of [x/w](gamma)), with 1 < gamma < infinity, where w(t) is the spreading width which scales as w(t) approximately t(beta), with 0 < beta < or = 1. The two exponents satisfy the universal relation gamma = 1/(1-beta). We demonstrate these results through numerical work on one-dimensional quasiperiodic systems and the three-dimensional Anderson model of disorder. We provide an analytical derivation of these relations by using the memory function formalism of quantum dynamics. Furthermore, we present an application to experimental results for the quantum kicked rotor.