We realize experimentally an atom-optics quantum chaotic system, the quasiperiodic kicked rotor, which is equivalent to a 3D disordered that allow us demonstrate Anderson metal-insulator transition. Sensitive measurements of atomic wavefunction dynamics and use finite-size scaling techniques make it possible extract both critical parameters exponent transition, in good agreement with value obtained numerical simulations model.

Spectral statistics of disordered systems encode Thouless and Heisenberg timescales, whose ratio determines whether the system is chaotic or localized. We show that scaling time with size disorder strength very similar in one-body Anderson models quantum many-body systems. argue two parameter breaks down vicinity transition to localized phase, signaling a slowing-down dynamics.

The transition to chaos in "the hydrogen atom a magnetic field" is numerically studied and shown lead well-defined signature on the energy-level fluctuations. Upon an increase energy, calculated statistics evolve from Poisson Gaussian orthogonal ensemble according regular or chaotic character of classical motion. Several methods are employed test generic nature these distributions.

The possibility of observing many-body localization ultracold atoms in a one-dimensional optical lattice is discussed for random interactions. In the noninteracting limit, such system reduces to single-particle physics absence disorder, i.e., extended states. effect, observed inherently due interactions and thus genuine effect. studied, manifests itself lack thermalization visible temporal propagation specially prepared initial state, transport properties, logarithmic growth entanglement...

Dimension 2 is expected to be the lower critical dimension for Anderson localization in a time-reversal-invariant disordered quantum system. Using an atomic quasiperiodic kicked rotor---equivalent two-dimensional Anderson-like model---we experimentally study and we observe localized wave function dynamics. We also show that length depends exponentially on disorder strength anisotropy quantitative agreement with predictions of self-consistent theory 2D localization.

The positive-energy spectrum of the hydrogen atom in a magnetic field is deduced by making use complex-rotation method combined with Sturmian-type expansions. This yields energies and widths resonances especially for fields atomic interest. Accidental destructive interference generates ultranarrow above ionization threshold as experimentally observed.

We propose a new theoretical scheme for exciting atoms in circular Rydberg states with high efficiency whatever the atomic species. It only requires use of weak magnetic field crossed to time-varying electric field. The is based on symmetry properties Coulomb interaction.

Classical periodic orbits are stationary-phase points in path integral representations of quantum propagators. We show that complex solutions the equation, not corresponding to real classical orbits, give additional contributions propagator which can be important, especially near bifurcations. reveal existence and relevance such ghost for a kicked top.

This article studies multiple scattering of matter waves by a disordered optical potential in two and three dimensions. We calculate fundamental transport quantities such as the mean free path $\ell_s$, Boltzmann $\elltrb$, diffusion constant $D_B$, using diagrammatic Green functions approach. Coherent induces interference corrections known weak localization which entail reduced constant. derive corresponding expressions for wave an correlated speckle provide relevant parameter values...

Using a three-frequency one-dimensional kicked rotor experimentally realized with cold atomic gas, we study the transport properties at critical point of metal-insulator Anderson transition. We accurately measure time evolution an initially localized wave packet and show that it displays scaling invariance characteristic this second-order phase The shape momentum distribution is found to be in excellent agreement analytical form deduced from self-consistent theory localization.

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

Using a cold atomic gas exposed to laser pulses---a realization of the chaotic quasiperiodic kicked rotor with three incommensurate frequencies---we study experimentally and theoretically Anderson metal-insulator transition in dimensions. Sensitive measurements wave function use finite-size scaling techniques make it possible unambiguously demonstrate existence quantum phase measure its critical exponents. By taking proper account systematic corrections one-parameter scaling, we show...

We study Anderson localization of ultracold atoms in weak one-dimensional speckle potentials using perturbation theory beyond Born approximation. show the existence a series sharp crossovers (effective mobility edges) between energy regions where lengths differ by orders magnitude. also point out that correction to term explicitly depends on sign potential. Our results are agreement with numerical calculations regime relevant for experiments. Finally, we analyze our findings light...

Using the transfer-matrix method, we numerically compute precise position of mobility edge atoms exposed to a laser speckle potential and study its dependence versus disorder strength correlation function. Our results deviate significantly from previous theoretical estimates using an approximate, self-consistent approach localization. In particular, find that in blue-detuned speckles is much lower than red-detuned counterpart, pointing out crucial role played by asymmetric on-site...

We study the diffusive propagation of multiply scattered light in an optically thick cloud cold rubidium atoms illuminated by a quasiresonant laser beam. In vicinity sharp atomic resonance, energy transport velocity is almost 5 orders magnitude smaller than vacuum speed light, reducing strongly diffusion constant. verify theoretical prediction frequency-independent time around resonance. also observe effect residual at long times.

This paper presents the first experimental evidence of transition from dynamical localization to delocalization under influence a quasiperiodic driving on quantum system. A kicked rotator is realized by placing cold atoms in pulsed, far-detuned, standing wave. If wave periodically one observes suppression classical chaotic diffusion, i.e., localization. pulsed quasiperiodically, observed or not, depending frequencies being commensurable incommensurable. One can thus study localized...

The motion of energy levels in quantum systems that show a chaotic classical limit is statistically analyzed. A quantitative comparison made between the tails curvature distribution and numerical results obtained for various physical models. Approximate analytic expressions full are derived from statistical mechanics fictitious gas refined formulation recovers random-matrix theory an arbitrary number levels. They provide better description data than just tail-limiting available previously....

We present a detailed comparison of the observed and computed negative- positive-energy spectrum Rydberg atom in strong magnetic field. The study extends from -30 to +30 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ at field 6 T. experimental resolution is sufficiently high provide well-resolved spectra over entire range. calculated for hydrogen remarkable agreement with lithium.

We show how to build atomic states that mimic the classical Bohr-Sommerfeld elliptic orbits with minimum quantum fluctuations. These are uniquely defined from symmetry considerations. They coherent of SO(4) group Coulomb interaction in three dimensions and superpositions usual spherical well-defined weights phases. can be experimentally produced laser excitation Rydberg atoms crossed electric magnetic fields. finally indicate wave packets localized both space time.

Using the complex coordinate method, it is possible to compute physical properties of atomic resonances above ionization threshold. We show how define and electronic densities associated with these resonances. The method general illustrated for Rydberg states in static time-dependent external fields.

We consider ultracold atoms in 2D disordered optical potentials and calculate microscopic quantities characterizing matter wave quantum transport the noninteracting regime. derive diffusion constant as a function of all relevant parameters show that coherent multiple scattering induces significant weak localization effects. In particular, we find even strong regime is accessible with current experimental techniques corresponding length.

The authors present a formalism based on the non-invariance algebra for Coulomb problems that allows one to deduce an effective Hamiltonian wide variety of perturbing potentials. Applications problem hydrogen atom in magnetic field are performed. They especially derive exact first- and second-order expressions diamagnetic under general operator form. Some consequences further developments briefly indicated.

We investigate the transient coherent transmission of light through an optically thick cold stron-tium gas. observe a superflash just after abrupt probe extinction, with peak intensity more than three times incident one. show that this is direct signature cooperative forward emission atoms. By engineering fast phenomena on field, we give clear and simple picture physical mechanisms at play.