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

Coulomb-enhanced dynamic localization and Bell state generation in coupled quantum dots

We investigate the dynamics of two interacting electrons in coupled quantum dots driven by an AC field. We find that the two electrons can be trapped in one of the dots by the AC field, in spite of the strong Coulomb repulsion. In particular, we find that the interaction may enhance the localization effect. We also demonstrate the field excitation procedure to generate the maximally entangled Bell states. The generation time is determined by both analytic and numerical solutions of the time dependent Schrodinger equation.Comment: 12 pages, 5 figure

Chaos and flights in the atom-photon interaction in cavity QED

We study dynamics of the atom-photon interaction in cavity quantum electrodynamics (QED), considering a cold two-level atom in a single-mode high-finesse standing-wave cavity as a nonlinear Hamiltonian system with three coupled degrees of freedom: translational, internal atomic, and the field. The system proves to have different types of motion including L\'{e}vy flights and chaotic walkings of an atom in a cavity. It is shown that the translational motion, related to the atom recoils, is governed by an equation of a parametric nonlinear pendulum with a frequency modulated by the Rabi oscillations. This type of dynamics is chaotic with some width of the stochastic layer that is estimated analytically. The width is fairly small for realistic values of the control parameters, the normalized detuning $\delta$ and atomic recoil frequency $\alpha$. It is demonstrated how the atom-photon dynamics with a given value of $\alpha$ depends on the values of $\delta$ and initial conditions. Two types of L\'{e}vy flights, one corresponding to the ballistic motion of the atom and another one corresponding to small oscillations in a potential well, are found. These flights influence statistical properties of the atom-photon interaction such as distribution of Poincar\'{e} recurrences and moments of the atom position $x$. The simulation shows different regimes of motion, from slightly abnormal diffusion with $\sim\tau^{1.13}$ at $\delta =1.2$ to a superdiffusion with $\sim \tau^{2.2}$ at $\delta=1.92$ that corresponds to a superballistic motion of the atom with an acceleration. The obtained results can be used to find new ways to manipulate atoms, to cool and trap them by adjusting the detuning $\delta$.Comment: 16 pages, 7 figures. To be published in Phys. Rev.

Theoretical analysis of quantum dynamics in 1D lattices: Wannier-Stark description

This papers presents a formalism describing the dynamics of a quantum particle in a one-dimensional tilted time-dependent lattice. The description uses the Wannier-Stark states, which are localized in each site of the lattice and provides a simple framework leading to fully-analytical developments. Particular attention is devoted to the case of a time-dependent potential, which results in a rich variety of quantum coherent dynamics is found.Comment: 8 pages, 6 figures, submitted to PR

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.Comment: 6 pages, 5 figures, send to EPJ

On initial conditions for the Hot Big Bang

We analyse the process of reheating the Universe in the electroweak theory where the Higgs field plays a role of the inflaton. We estimate the maximal temperature of the Universe and fix the initial conditions for radiation-dominated phase of the Universe expansion in the framework of the Standard Model (SM) and of the nuMSM -- the minimal extension of the SM by three right-handed singlet fermions. We show that the inflationary epoch is followed by a matter dominated stage related to the Higgs field oscillations. We investigate the energy transfer from Higgs-inflaton to the SM particles and show that the radiation dominated phase of the Universe expansion starts at temperature T_r~(3-15)*10^{13} GeV, where the upper bound depends on the Higgs boson mass. We estimate the production rate of singlet fermions at preheating and find that their concentrations at T_r are negligibly small. This suggests that the sterile neutrino Dark Matter (DM) production and baryogenesis in the nuMSM with Higgs-driven inflation are low energy phenomena, having nothing to do with inflation. We study then a modification of the nuMSM, adding to its Lagrangian higher dimensional operators suppressed by the Planck scale. The role of these operators in Higgs-driven inflation is clarified. We find that these operators do not contribute to the production of Warm Dark Matter (WDM) and to baryogenesis. We also demonstrate that the sterile neutrino with mass exceeding 100 keV (a Cold Dark Matter (CDM) candidate) can be created during the reheating stage of the Universe in necessary amounts. We argue that the mass of DM sterile neutrino should not exceed few MeV in order not to overclose the Universe.Comment: 41 pages, 5 figures. Journal version accepted in JCA

The possibility of a metal insulator transition in antidot arrays induced by an external driving

It is shown that a family of models associated with the kicked Harper model is relevant for cyclotron resonance experiments in an antidot array. For this purpose a simplified model for electronic motion in a related model system in presence of a magnetic field and an AC electric field is developed. In the limit of strong magnetic field it reduces to a model similar to the kicked Harper model. This model is studied numerically and is found to be extremely sensitive to the strength of the electric field. In particular, as the strength of the electric field is varied a metal -- insulator transition may be found. The experimental conditions required for this transition are discussed.Comment: 6 files: kharp.tex, fig1.ps fig2.ps fi3.ps fig4.ps fig5.p

Coherent Manipulation of Quantum Delta-kicked Dynamics: Faster-than-classical Anomalous Diffusion

Large transporting regular islands are found in the classical phase space of a modified kicked rotor system in which the kicking potential is reversed after every two kicks. The corresponding quantum system, for a variety of system parameters and over long time scales, is shown to display energy absorption that is significantly faster than that associated with the underlying classical anomalous diffusion. The results are of interest to both areas of quantum chaos and quantum control.Comment: 6 pages, 4 figures, to appear in Physical Review

Chaos in a double driven dissipative nonlinear oscillator

We propose an anharmonic oscillator driven by two periodic forces of different frequencies as a new time-dependent model for investigating quantum dissipative chaos. Our analysis is done in the frame of statistical ensemble of quantum trajectories in quantum state diffusion approach. Quantum dynamical manifestation of chaotic behavior, including the emergence of chaos, properties of strange attractors, and quantum entanglement are studied by numerical simulation of ensemble averaged Wigner function and von Neumann entropy.Comment: 9 pages, 18 figure

A Numerical Investigation of the Effects of Classical Phase Space Structure on a Quantum System

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; classical diffusion is observed but quantum diffusion is only significant when the classical phase space area escaping through the cantorus per kicking period greatly exceeds Planck's constant. 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 behaviour 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.Comment: 15 pages, 22 figure