The role of quasi-momentum in the resonant dynamics of the atom-optics kicked rotor

We examine the effect of the initial atomic momentum distribution on the dynamics of the atom-optical realisation of the quantum kicked rotor. The atoms are kicked by a pulsed optical lattice, the periodicity of which implies that quasi-momentum is conserved in the transport problem. We study and compare experimentally and theoretically two resonant limits of the kicked rotor: in the vicinity of the quantum resonances and in the semiclassical limit of vanishing kicking period. It is found that for the same experimental distribution of quasi-momenta, significant deviations from the kicked rotor model are induced close to quantum resonance, while close to the classical resonance (i.e. for small kicking period) the effect of the quasi-momentum vanishes.Comment: 10 pages, 4 figures, to be published in J. Phys. A, Special Issue on 'Trends in Quantum Chaotic Scattering

Brownian Motion Model of Quantization Ambiguity and Universality in Chaotic Systems

We examine spectral equilibration of quantum chaotic spectra to universal statistics, in the context of the Brownian motion model. Two competing time scales, proportional and inversely proportional to the classical relaxation time, jointly govern the equilibration process. Multiplicity of quantum systems having the same semiclassical limit is not sufficient to obtain equilibration of any spectral modes in two-dimensional systems, while in three-dimensional systems equilibration for some spectral modes is possible if the classical relaxation rate is slow. Connections are made with upper bounds on semiclassical accuracy and with fidelity decay in the presence of a weak perturbation.Comment: 13 pages, 6 figures, submitted to Phys Rev

On the Spectrum of the Resonant Quantum Kicked Rotor

It is proven that none of the bands in the quasi-energy spectrum of the Quantum Kicked Rotor is flat at any primitive resonance of any order. Perturbative estimates of bandwidths at small kick strength are established for the case of primitive resonances of prime order. Different bands scale with different powers of the kick strength, due to degeneracies in the spectrum of the free rotor.Comment: Description of related published work has been expanded in the Introductio

Theory of 2δ\delta-kicked Quantum Rotors

We examine the quantum dynamics of cold atoms subjected to {\em pairs} of closely spaced $\delta$-kicks from standing waves of light, and find behaviour quite unlike the well-studied quantum kicked rotor (QKR). Recent experiments [Jones et al, {\em Phys. Rev. Lett. {\bf 93}, 223002 (2004)}] identified a regime of chaotic, anomalous classical diffusion. We show that the corresponding quantum phase-space has a cellular structure, arising from a unitary matrix with oscillating band-width. The corresponding eigenstates are exponentially localized, but scale with a fractional power, $L \sim \hbar^{-0.75}$, in contrast to the QKR for which $L \sim \hbar^{-1}$. The effect of inter-cell (and intra-cell) transport is investigated by studying the spectral fluctuations with both periodic as well as `open' boundary conditions.Comment: 12 pages with 14 figure

Excitation of Small Quantum Systems by High-Frequency Fields

The excitation by a high frequency field of multi--level quantum systems with a slowly varying density of states is investigated. A general approach to study such systems is presented. The Floquet eigenstates are characterized on several energy scales. On a small scale, sharp universal quasi--resonances are found, whose shape is independent of the field parameters and the details of the system. On a larger scale an effective tight--binding equation is constructed for the amplitudes of these quasi--resonances. This equation is non--universal; two classes of examples are discussed in detail.Comment: 4 pages, revtex, no figure

Experimental observation of high-order quantum accelerator modes.

Using a freely falling cloud of cold cesium atoms periodically kicked by pulses from a vertical standing wave of laser light, we present the first experimental observation of high-order quantum accelerator modes. This confirms the recent prediction by Fishman, Guarneri, and Rebuzzini [Phys. Rev. Lett.10.1103/PhysRevLett.89.084101 89, 084101 (2002)]. We also show how these accelerator modes can be identified with the stable regions of phase space in a classical-like chaotic system, despite their intrinsically quantum origin

Quantum and classical chaos for a single trapped ion

In this paper we investigate the quantum and classical dynamics of a single trapped ion subject to nonlinear kicks derived from a periodic sequence of Guassian laser pulses. We show that the classical system exhibits diffusive growth in the energy, or 'heating', while quantum mechanics suppresses this heating. This system may be realized in current single trapped-ion experiments with the addition of near-field optics to introduce tightly focussed laser pulses into the trap.Comment: 8 pages, REVTEX, 8 figure

Quantum Poincare Recurrences for Hydrogen Atom in a Microwave Field

We study the time dependence of the ionization probability of Rydberg atoms driven by a microwave field, both in classical and in quantum mechanics. The quantum survival probability follows the classical one up to the Heisenberg time and then decays algebraically as P(t) ~ 1/t. This decay law derives from the exponentially long times required to escape from some region of the phase space, due to tunneling and localization effects. We also provide parameter values which should allow to observe such decay in laboratory experiments.Comment: revtex, 4 pages, 4 figure

Evolution of wave packets in quasi-1D and 1D random media: diffusion versus localization

We study numerically the evolution of wavepackets in quasi one-dimensional random systems described by a tight-binding Hamiltonian with long-range random interactions. Results are presented for the scaling properties of the width of packets in three time regimes: ballistic, diffusive and localized. Particular attention is given to the fluctuations of packet widths in both the diffusive and localized regime. Scaling properties of the steady-state distribution are also analyzed and compared with theoretical expression borrowed from one-dimensional Anderson theory. Analogies and differences with the kicked rotator model and the one-dimensional localization are discussed.Comment: 32 pages, LaTex, 11 PostScript figure

Antiresonance and Localization in Quantum Dynamics

The phenomenon of quantum antiresonance (QAR), i.e., exactly periodic recurrences in quantum dynamics, is studied in a large class of nonintegrable systems, the modulated kicked rotors (MKRs). It is shown that asymptotic exponential localization generally occurs for $\eta$ (a scaled $\hbar$) in the infinitesimal vicinity of QAR points $\eta_0$. The localization length $\xi_0$ is determined from the analytical properties of the kicking potential. This ``QAR-localization" is associated in some cases with an integrable limit of the corresponding classical systems. The MKR dynamical problem is mapped into pseudorandom tight-binding models, exhibiting dynamical localization (DL). By considering exactly-solvable cases, numerical evidence is given that QAR-localization is an excellent approximation to DL sufficiently close to QAR. The transition from QAR-localization to DL in a semiclassical regime, as $\eta$ is varied, is studied. It is shown that this transition takes place via a gradual reduction of the influence of the analyticity of the potential on the analyticity of the eigenstates, as the level of chaos is increased.Comment: To appear in Physical Review E. 51 pre-print pages + 9 postscript figure