Acoustic resonances in microfluidic chips: full-image micro-PIV experiments and numerical simulations

We show that full-image micro-PIV analysis in combination with images of transient particle motion is a powerful tool for experimental studies of acoustic radiation forces and acoustic streaming in microfluidic chambers under piezo-actuation in the MHz range. The measured steady-state motion of both large 5 um and small 1 um particles can be understood in terms of the acoustic eigenmodes or standing ultra-sound waves in the given experimental microsystems. This interpretation is supported by numerical solutions of the corresponding acoustic wave equation.Comment: RevTex, 10 pages, 9 eps figures; NOTE first authors changed his name to S. Melker Hagsater in the published versio

Theory of dressed states in quantum optics

The dual Dyson series [M.Frasca, Phys. Rev. A {\bf 58}, 3439 (1998)], is used to develop a general perturbative method for the study of atom-field interaction in quantum optics. In fact, both Dyson series and its dual, through renormalization group methods to remove secular terms from the perturbation series, give the opportunity of a full study of the solution of the Schr\"{o}dinger equation in different ranges of the parameters of the given hamiltonian. In view of recent experiments with strong laser fields, this approach seems well-suited to give a clarification and an improvement of the applications of the dressed states as currently done through the eigenstates of the atom-field interaction, showing that these are just the leading order of the dual Dyson series when the Hamiltonian is expressed in the interaction picture. In order to exploit the method at the best, a study is accomplished of the well-known Jaynes-Cummings model in the rotating wave approximation, whose exact solution is known, comparing the perturbative solutions obtained by the Dyson series and its dual with the same approximations obtained by Taylor expanding the exact solution. Finally, a full perturbative study of high-order harmonic generation is given obtaining, through analytical expressions, a clear account of the power spectrum using a two-level model, even if the method can be successfully applied to a more general model that can account for ionization too. The analysis shows that to account for the power spectrum it is needed to go to first order in the perturbative analysis. The spectrum obtained gives a way to measure experimentally the shift of the energy levels of the atom interacting with the laser field by looking at the shifting of hyper-Raman lines.Comment: Revtex, 17 page

Nonlinear level crossing models

We examine the effect of nonlinearity at a level crossing on the probability for nonadiabatic transitions $P$. By using the Dykhne-Davis-Pechukas formula, we derive simple analytic estimates for $P$ for two types of nonlinear crossings. In the first type, the nonlinearity in the detuning appears as a {\it perturbative} correction to the dominant linear time dependence. Then appreciable deviations from the Landau-Zener probability $P_{LZ}$ are found to appear for large couplings only, when $P$ is very small; this explains why the Landau-Zener model is often seen to provide more accurate results than expected. In the second type of nonlinearity, called {\it essential} nonlinearity, the detuning is proportional to an odd power of time. Then the nonadiabatic probability $P$ is qualitatively and quantitatively different from $P_{LZ}$ because on the one hand, it vanishes in an oscillatory manner as the coupling increases, and on the other, it is much larger than $P_{LZ}$. We suggest an experimental situation when this deviation can be observed.Comment: 9 pages final postscript file, two-column revtex style, 5 figure

Bose-Einstein Condensates in Optical Lattices: Band-Gap Structure and Solitons

We analyze the existence and stability of spatially extended (Bloch-type) and localized states of a Bose-Einstein condensate loaded into an optical lattice. In the framework of the Gross-Pitaevskii equation with a periodic potential, we study the band-gap structure of the matter-wave spectrum in both the linear and nonlinear regimes. We demonstrate the existence of families of spatially localized matter-wave gap solitons, and analyze their stability in different band gaps, for both repulsive and attractive atomic interactions

Statistical properties of power-law random banded unitary matrices in the delocalization-localization transition regime

Power-law random banded unitary matrices (PRBUM), whose matrix elements decay in a power-law fashion, were recently proposed to model the critical statistics of the Floquet eigenstates of periodically driven quantum systems. In this work, we numerically study in detail the statistical properties of PRBUM ensembles in the delocalization-localization transition regime. In particular, implications of the delocalization-localization transition for the fractal dimension of the eigenvectors, for the distribution function of the eigenvector components, and for the nearest neighbor spacing statistics of the eigenphases are examined. On the one hand, our results further indicate that a PRBUM ensemble can serve as a unitary analog of the power-law random Hermitian matrix model for Anderson transition. On the other hand, some statistical features unseen before are found from PRBUM. For example, the dependence of the fractal dimension of the eigenvectors of PRBUM upon one ensemble parameter displays features that are quite different from that for the power-law random Hermitian matrix model. Furthermore, in the time-reversal symmetric case the nearest neighbor spacing distribution of PRBUM eigenphases is found to obey a semi-Poisson distribution for a broad range, but display an anomalous level repulsion in the absence of time-reversal symmetry.Comment: 10 pages + 13 fig

Adiabatic population transfer via multiple intermediate states

This paper discusses a generalization of stimulated Raman adiabatic passage (STIRAP) in which the single intermediate state is replaced by $N$ intermediate states. Each of these states is connected to the initial state \state{i} with a coupling proportional to the pump pulse and to the final state \state{f} with a coupling proportional to the Stokes pulse, thus forming a parallel multi-$\Lambda$ system. It is shown that the dark (trapped) state exists only when the ratio between each pump coupling and the respective Stokes coupling is the same for all intermediate states. We derive the conditions for existence of a more general adiabatic-transfer state which includes transient contributions from the intermediate states but still transfers the population from state \state{i} to state \state{f} in the adiabatic limit. We present various numerical examples for success and failure of multi-$\Lambda$ STIRAP which illustrate the analytic predictions. Our results suggest that in the general case of arbitrary couplings, it is most appropriate to tune the pump and Stokes lasers either just below or just above all intermediate states.Comment: 14 pages, two-column revtex style, 10 figure

Multistate modeling of habitat dynamics: factors affecting Florida scrub transition probabilities

Many ecosystems are influenced by disturbances that create specific successional states and habitat structures that species need to persist. Estimating transition probabilities between habitat states and modeling the factors that influence such transitions have many applications for investigating and managing disturbance-prone ecosystems. We identify the correspondence between multistate capture-recapture models and Markov models of habitat dynamics. We exploit this correspondence by fitting and comparing competing models of different ecological covariates affecting habitat transition probabilities in Florida scrub and flatwoods, a habitat important to many unique plants and animals. We subdivided a large scrub and flatwoods ecosystem along central Florida\u27s Atlantic coast into 10-ha grid cells, which approximated average territory size of the threatened Florida Scrub-Jay (Aphelocoma coerulescens), a management indicator species. We used 1.0-m resolution aerial imagery for 1994, 1999, and 2004 to classify grid cells into four habitat quality states that were directly related to Florida Scrub-Jay source-sink dynamics and management decision making. Results showed that static site features related to fire propagation (vegetation type, edges) and temporally varying disturbances (fires, mechanical cutting) best explained transition probabilities. Results indicated that much of the scrub and flatwoods ecosystem was resistant to moving from a degraded state to a desired state without mechanical cutting, an expensive restoration tool. We used habitat models parameterized with the estimated transition probabilities to investigate the consequences of alternative management scenarios on future habitat dynamics. We recommend this multistate modeling approach as being broadly applicable for studying ecosystem, land cover, or habitat dynamics. The approach provides maximum-likelihood estimates of transition parameters, including precision measures, and can be used to assess evidence among competing ecological models that describe system dynamics

Chaos assisted tunnelling with cold atoms

In the context of quantum chaos, both theory and numerical analysis predict large fluctuations of the tunnelling transition probabilities when irregular dynamics is present at the classical level. We consider here the non-dissipative quantum evolution of cold atoms trapped in a time-dependent modulated periodic potential generated by two laser beams. We give some precise guidelines for the observation of chaos assisted tunnelling between invariant phase space structures paired by time-reversal symmetry.Comment: submitted to Phys. Rev. E ; 16 pages, 13 figures; figures of better quality can be found at http://www.phys.univ-tours.fr/~mouchet

Scattering Theory of Photon-Assisted Electron Transport

The scattering matrix approach to phase-coherent transport is generalized to nonlinear ac-transport. In photon-assisted electron transport it is often only the dc-component of the current that is of experimental interest. But ac-currents at all frequencies exist independently of whether they are measured or not. We present a theory of photon-assisted electron transport which is charge and current conserving for all Fourier components of the current. We find that the photo-current can be considered as an up- and down-conversion of the harmonic potentials associated with the displacement currents. As an example explicit calculations are presented for a resonant double barrier coupled to two reservoirs and capacitively coupled to a gate. Two experimental situations are considered: in the first case the ac-field is applied via a gate, and in the second case one of the contact potentials is modulated. For the first case we show that the relative weight of the conduction sidebands varies with the screening properties of the system. In contrast to the non-interacting case the relative weights are not determined by Bessel functions. Moreover, interactions can give rise to an asymmetry between absorption and emission peaks. In the contact driven case, the theory predicts a zero-bias current proportional to the asymmetry of the double barrier. This is in contrast to the discussion of Tien and Gordon which, in violation of basic symmetry principles, predicts a zero-bias current also for a symmetric double barrier.Comment: 15 pages, 6 figures, REVTE

Location of crossings in the Floquet spectrum of a driven two-level system

Calculation of the Floquet quasi-energies of a system driven by a time-periodic field is an efficient way to understand its dynamics. In particular, the phenomenon of dynamical localization can be related to the presence of close approaches between quasi-energies (either crossings or avoided crossings). We consider here a driven two-level system, and study how the locations of crossings in the quasi-energy spectrum alter as the field parameters are changed. A perturbational scheme provides a direct connection between the form of the driving field and the quasi-energies which is exact in the limit of high frequencies. We firstly obtain relations for the quasi-energies for some common types of applied field in the high-frequency limit. We then show how the locations of the crossings drift as the frequency is reduced, and find a simple empirical formula which describes this drift extremely well in general, and appears to be exact for the specific case of square-wave driving.Comment: 6 pages, 6 figures. Minor changes to text, this version to be published in Physical Review