Effective time-independent description of optical lattices with periodic driving

For a periodically driven quantum system an effective time-independent Hamiltonian is derived with an eigen-energy spectrum, which in the regime of large driving frequencies approximates the quasi-energies of the corresponding Floquet Hamiltonian. The effective Hamiltonian is evaluated for the case of optical lattice models in the tight-binding regime subjected to strong periodic driving. Three scenarios are considered: a periodically shifted one-dimensional (1D) lattice, a two-dimensional (2D) square lattice with inversely phased temporal modulation of the well depths of adjacent lattice sites, and a 2D lattice subjected to an array of microscopic rotors commensurate with its plaquette structure. In case of the 1D scenario the rescaling of the tunneling energy, previously considered by Eckardt et al. in Phys. Rev. Lett. 95, 260404 (2005), is reproduced. The 2D lattice with well depth modulation turns out as a generalization of the 1D case. In the 2D case with staggered rotation, the expression previously found in the case of weak driving by Lim et al. in Phys. Rev. Lett. 100, 130402 (2008) is generalized, such that its interpretation in terms of an artificial staggered magnetic field can be extended into the regime of strong driving.Comment: 10 pages, 5 figure

Large Amplitude Harmonic Driving of Highly Coherent Flux Qubits

The device for the Josephson flux qubit (DJFQ) can be considered as a solid state artificial atom with multiple energy levels. When a large amplitude harmonic excitation is applied to the system, transitions at the energy levels avoided crossings produce visible changes in the qubit population over many driven periods that are accompanied by a rich pattern of interference phenomena. We present a Floquet treatment of the periodically time-dependent Schr\"odinger equation of the strongly driven qubit beyond the standard two levels approach. For low amplitudes, the average probability of a given sign of the persistent current qubit exhibits, as a function of the static flux detuning and the driving amplitude, Landau-Zener-St\"uckelberg interference patterns that evolve into complex diamond-like patterns for large amplitudes. In the case of highly coherent flux qubits we find that the higher order diamonds can not be simply described relying on a two-level approximations. In addition we propose a new spectroscopic method based on starting the system in the first excited state instead of in the ground state, which can give further information on the energy level spectrum and dynamics in the case of highly coherent flux qubits. We compare our numerical results with recent experiments that perform amplitude spectroscopy to probe the energy spectrum of the artificial atom.Comment: 12 Pages and 12 Figures Phys. Rev. B (in press

Smooth optimal control with Floquet theory

This paper describes an approach to construct temporally shaped control pulses that drive a quantum system towards desired properties. A parametrization in terms of periodic functions with pre-defined frequencies permits to realize a smooth, typically simple shape of the pulses; their optimization can be performed based on a variational analysis with Floquet theory. As we show with selected specific examples, this approach permits to control the dynamics of interacting spins, such that gate operations and entanglement dynamics can be implemented with very high accuracy

Floquet theory and complex quasivibrational energy formalism for intense field molecular photodissociation

This is the published version, also available here: http://dx.doi.org/10.1063/1.442334.A practical and nonperturbative method is presented for studying molecular photodissociation processes in the presence of (weak or intense) electromagnetic fields, using only square‐integrable (L 2) functions. By means of the complex coordinate transformation and L 2 discretization of the vibrational continua, the complex quasivibrational energies (QVE) of the Floquet Hamiltonian can be determined by standard non‐Hermitian eigenvalueanalysis. The real parts of the QVE’s provide the ac Stark‐shifted vibronic energies, whereas the imaginary parts are related to the photodissociation transition rates. The theory is applied to the direct photodissociation of H+ 2(1sσ g –2pσ u ) in both weak and strong fields

Vibration Induced Non-adiabatic Geometric Phase and Energy Uncertainty of Fermions in Graphene

We investigate geometric phase of fermion states under relative vibrations of two sublattices in graphene by solving time-dependent Sch\"{o}dinger equation using Floquet scheme. In a period of vibration the fermions acquire different geometric phases depending on their momenta. There are two regions in the momentum space: the adiabatic region where the geometric phase can be approximated by the Berry phase and the chaotic region where the geometric phase drastically fluctuates in changing parameters. The energy of fermions due to vibrations shows spikes in the chaotic region. The results suggest a possible dephasing mechanism which may cause classical-like transport properties in graphene.Comment: 9 pages, 5 figure

Localization of quantum wave packets

We study the semiclassical propagation of squeezed Gau{\ss}ian states. We do so by considering the propagation theorem introduced by Combescure and Robert \cite{CR97} approximating the evolution generated by the Weyl-quantization of symbols $H$. We examine the particular case when the Hessian $H^{\prime\prime}(X_{t})$ evaluated at the corresponding solution $X_{t}$ of Hamilton's equations of motion is periodic in time. Under this assumption, we show that the width of the wave packet can remain small up to the Ehrenfest time. We also determine conditions for ``classical revivals'' in that case. More generally, we may define recurrences of the initial width. Some of these results include the case of unbounded classical motion. In the classically unstable case we recover an exponential spreading of the wave packet as in \cite{CR97}

Rigorous derivation of coherent resonant tunneling time and velocity in finite periodic systems

The velocity $v_{res}$ of resonant tunneling electrons in finite periodic structures is analytically calculated in two ways. The first method is based on the fact that a transmission of unity leads to a coincidence of all still competing tunneling time definitions. Thus, having an indisputable resonant tunneling time $\tau_{res},$ we apply the natural definition $v_{res}=L/\tau_{res}$ to calculate the velocity. For the second method we combine Bloch's theorem with the transfer matrix approach to decompose the wave function into two Bloch waves. Then the expectation value of the velocity is calculated. Both different approaches lead to the same result, showing their physical equivalence. The obtained resonant tunneling velocity $v_{res}$ is smaller or equal to the group velocity times the magnitude of the complex transmission amplitude of the unit cell. Only at energies where the unit cell of the periodic structure has a transmission of unity $v_{res}$ equals the group velocity. Numerical calculations for a GaAs/AlGaAs superlattice are performed. For typical parameters the resonant velocity is below one third of the group velocity.Comment: 12 pages, 3 figures, LaTe

Covariant Lyapunov vectors of a quasi-geostrophic baroclinic model: analysis of instabilities and feedbacks

The classical approach for studying atmospheric variability is based on defining a background state and studying the linear stability of the small fluctuations around such a state. Weakly non-linear theories can be constructed using higher order expansions terms. While these methods have undoubtedly great value for elucidating the relevant physical processes, they are unable to follow the dynamics of a turbulent atmosphere. We provide a first example of extension of the classical stability analysis to a non-linearly evolving quasi-geostrophic flow. The so-called covariant Lyapunov vectors (CLVs) provide a covariant basis describing the directions of exponential expansion and decay of perturbations to the non-linear trajectory of the flow. We use such a formalism to re-examine the basic barotropic and baroclinic processes of the atmosphere with a quasi-geostrophic beta-plane two-layer model in a periodic channel driven by a forced meridional temperature gradient ΔT. We explore three settings of ΔT, representative of relatively weak turbulence, well-developed turbulence, and intermediate conditions. We construct the Lorenz energy cycle for each CLV describing the energy exchanges with the background state. A positive baroclinic conversion rate is a necessary but not sufficient condition of instability. Barotropic instability is present only for few very unstable CLVs for large values of ΔT. Slowly growing and decaying hydrodynamic Lyapunov modes closely mirror the properties of the background flow. Following classical necessary conditions for barotropic/baroclinic instability, we find a clear relationship between the properties of the eddy fluxes of a CLV and its instability. CLVs with positive baroclinic conversion seem to form a set of modes for constructing a reduced model of the atmosphere dynamics

Investigation of potential extreme load reduction for a two-bladed upwind turbine with partial pitch

This paper presents a wind turbine concept with an innovative design combining partial pitch with a two-bladed (PP-2B) turbine configuration. Special emphasis is on extreme load reduction during storm situations at standstill, but operational loads are also investigated. In order to compare the loads and dynamics of the PP-2B turbine, a partial pitch three-bladed (PP-3B) turbine and a normal pitch regulated three-bladed (3B) turbine are introduced on the basis of solidity similarity scaling. From the dynamic comparisons between two- and three-bladed turbines, it has been observed that the blade vibrations are transferred differently from the rotor to the tower. For a three-bladed turbine, blade vibrations seen in a fixed frame of reference are split with ±1P only. A two-bladed turbine has a similar split of ±1P but also includes contributions on higher harmonics (±2P, ±3P, ... etc.). Further on, frequency split is also seen for the tower vibrations, where an additional ±2P contribution has been observed for the two-bladed turbine. Regarding load comparisons, the PP-2B turbine produces larger tower load variations because of 2P excitation during the operational cases. However, extreme loads are reduced by approximately 20% for the PP-2B and 18% for the PP-3B compared with the 3B turbine for the parked condition in a storm situation. Moreover, a huge potential of 60% is observed for the reduction of the extreme tower bottom bending moment for the PP-2B turbine, when the wind direction is from ±90° to the turbine, but this also requires that the turbine is parked in a T-configuration