An accelerator mode based technique for studying quantum chaos

We experimentally demonstrate a method for selecting small regions of phase space for kicked rotor quantum chaos experiments with cold atoms. Our technique uses quantum accelerator modes to selectively accelerate atomic wavepackets with localized spatial and momentum distributions. The potential used to create the accelerator mode and subsequently realize the kicked rotor system is formed by a set of off-resonant standing wave light pulses. We also propose a method for testing whether a selected region of phase space exhibits chaotic or regular behavior using a Ramsey type separated field experiment.Comment: 5 pages, 3 figures, some modest revisions to previous version (esp. to the figures) to aid clarity; accepted for publication in Physical Review A (due out on January 1st 2003

Wavepacket reconstruction via local dynamics in a parabolic lattice

We study the dynamics of a wavepacket in a potential formed by the sum of a periodic lattice and of a parabolic potential. The dynamics of the wavepacket is essentially a superposition of ``local Bloch oscillations'', whose frequency is proportional to the local slope of the parabolic potential. We show that the amplitude and the phase of the Fourier transform of a signal characterizing this dynamics contains information about the amplitude and the phase of the wavepacket at a given lattice site. Hence, {\em complete} reconstruction of the the wavepacket in the real space can be performed from the study of the dynamics of the system.Comment: 4 pages, 3 figures, RevTex

Exponential Gain in Quantum Computing of Quantum Chaos and Localization

We present a quantum algorithm which simulates the quantum kicked rotator model exponentially faster than classical algorithms. This shows that important physical problems of quantum chaos, localization and Anderson transition can be modelled efficiently on a quantum computer. We also show that a similar algorithm simulates efficiently classical chaos in certain area-preserving maps.Comment: final published versio

Dynamical Localization in Quasi-Periodic Driven Systems

We investigate how the time dependence of the Hamiltonian determines the occurrence of Dynamical Localization (DL) in driven quantum systems with two incommensurate frequencies. If both frequencies are associated to impulsive terms, DL is permanently destroyed. In this case, we show that the evolution is similar to a decoherent case. On the other hand, if both frequencies are associated to smooth driving functions, DL persists although on a time scale longer than in the periodic case. When the driving function consists of a series of pulses of duration $\sigma$, we show that the localization time increases as $\sigma^{-2}$ as the impulsive limit, $\sigma\to 0$, is approached. In the intermediate case, in which only one of the frequencies is associated to an impulsive term in the Hamiltonian, a transition from a localized to a delocalized dynamics takes place at a certain critical value of the strength parameter. We provide an estimate for this critical value, based on analytical considerations. We show how, in all cases, the frequency spectrum of the dynamical response can be used to understand the global features of the motion. All results are numerically checked.Comment: 7 pages, 5 figures included. In this version is that Subsection III.B and Appendix A on the quasiperiodic Fermi Accelerator has been replaced by a reference to published wor

Phase Control of Nonadiabaticity-induced Quantum Chaos in An Optical Lattice

The qualitative nature (i.e. integrable vs. chaotic) of the translational dynamics of a three-level atom in an optical lattice is shown to be controllable by varying the relative laser phase of two standing wave lasers. Control is explained in terms of the nonadiabatic transition between optical potentials and the corresponding regular to chaotic transition in mixed classical-quantum dynamics. The results are of interest to both areas of coherent control and quantum chaos.Comment: 3 figures, 4 pages, to appear in Physical Review Letter

Quantum Chaos of a particle in a square well : Competing Length Scales and Dynamical Localization

The classical and quantum dynamics of a particle trapped in a one-dimensional infinite square well with a time periodic pulsed field is investigated. This is a two-parameter non-KAM generalization of the kicked rotor, which can be seen as the standard map of particles subjected to both smooth and hard potentials. The virtue of the generalization lies in the introduction of an extra parameter R which is the ratio of two length scales, namely the well width and the field wavelength. If R is a non-integer the dynamics is discontinuous and non-KAM. We have explored the role of R in controlling the localization properties of the eigenstates. In particular the connection between classical diffusion and localization is found to generalize reasonably well. In unbounded chaotic systems such as these, while the nearest neighbour spacing distribution of the eigenvalues is less sensitive to the nature of the classical dynamics, the distribution of participation ratios of the eigenstates proves to be a sensitive measure; in the chaotic regimes the latter being lognormal. We find that the tails of the well converged localized states are exponentially localized despite the discontinuous dynamics while the bulk part shows fluctuations that tend to be closer to Random Matrix Theory predictions. Time evolving states show considerable R dependence and tuning R to enhance classical diffusion can lead to significantly larger quantum diffusion for the same field strengths, an effect that is potentially observable in present day experiments.Comment: 29 pages (including 14 figures). Better quality of Figs. 1,3 & 9 can be obtained from author

Opto-mechanical measurement of micro-trap via nonlinear cavity enhanced Raman scattering spectrum

High-gain resonant nonlinear Raman scattering on trapped cold atoms within a high-fineness ring optical cavity is simply explained under a nonlinear opto-mechanical mechanism, and a proposal using it to detect frequency of micro-trap on atom chip is presented. The enhancement of scattering spectrum is due to a coherent Raman conversion between two different cavity modes mediated by collective vibrations of atoms through nonlinear opto-mechanical couplings. The physical conditions of this technique are roughly estimated on Rubidium atoms, and a simple quantum analysis as well as a multi-body semiclassical simulation on this nonlinear Raman process is conducted.Comment: 7 pages, 2 figure

Control of Dynamical Localization

Control over the quantum dynamics of chaotic kicked rotor systems is demonstrated. Specifically, control over a number of quantum coherent phenomena is achieved by a simple modification of the kicking field. These include the enhancement of the dynamical localization length, the introduction of classical anomalous diffusion assisted control for systems far from the semiclassical regime, and the observation of a variety of strongly nonexponential lineshapes for dynamical localization. The results provide excellent examples of controlled quantum dynamics in a system that is classically chaotic and offer new opportunities to explore quantum fluctuations and correlations in quantum chaos.Comment: 9 pages, 7 figures, to appear in Physical Review