A quantum motor: directed wavepacket motion in an optical lattice

We propose a method for arbitrary manipulations of a quantum wavepacket in an optical lattice by a suitable modulation of the lattice amplitude. A theoretical model allows to determine the modulation corresponding to a given wavepacket motion, so that arbitrary atomic trajectories can be generated. The method is immediately usable in state of the art experiments

Stochastic Oscillations Induced by Intrinsic Fluctuations in a Self-Repressing Gene

AbstractBiochemical reaction networks are subjected to large fluctuations attributable to small molecule numbers, yet underlie reliable biological functions. Thus, it is important to understand how regularity can emerge from noise. Here, we study the stochastic dynamics of a self-repressing gene with arbitrarily long or short response time. We find that when the mRNA and protein half-lives are approximately equal to the gene response time, fluctuations can induce relatively regular oscillations in the protein concentration. To gain insight into this phenomenon at the crossroads of determinism and stochasticity, we use an intermediate theoretical approach, based on a moment-closure approximation of the master equation, which allows us to take into account the binary character of gene activity. We thereby obtain differential equations that describe how nonlinearity can feed-back fluctuations into the mean-field equations to trigger oscillations. Finally, our results suggest that the self-repressing Hes1 gene circuit exploits this phenomenon to generate robust oscillations, inasmuch as its time constants satisfy precisely the conditions we have identified

Oscillations in the expression of a self-repressed gene induced by a slow transcriptional dynamics

We revisit the dynamics of a gene repressed by its own protein in the case where the transcription rate does not adapt instantaneously to protein concentration but is a dynamical variable. We derive analytical criteria for the appearance of sustained oscillations and find that they require degradation mechanisms much less nonlinear than for infinitely fast regulation. Deterministic predictions are also compared with stochastic simulations of this minimal genetic oscillator

Oscillations in the expression of a self-repressed gene induced by a slow transcriptional dynamics

We revisit the dynamics of a gene repressed by its own protein in the case where the transcription rate does not adapt instantaneously to protein concentration but is a dynamical variable. We derive analytical criteria for the appearance of sustained oscillations and find that they require degradation mechanisms much less nonlinear than for infinitely fast regulation. Deterministic predictions are also compared with stochastic simulations of this minimal genetic oscillator

Classical chaos with Bose-Einstein condensates in tilted optical lattices

A widely accepted definition of ``quantum chaos'' is ``the behavior of a quantum system whose \emph{classical} \emph{limit is chaotic}''. The dynamics of quantum-chaotic systems is nevertheless very different from that of their classical counterparts. A fundamental reason for that is the linearity of Schr{\"o}dinger equation. In this paper, we study the quantum dynamics of an ultra-cold quantum degenerate gas in a tilted optical lattice and show that it displays features very close to \emph{classical} chaos. We show that its phase space is organized according to the Kolmogorov-Arnold-Moser theorem.Comment: 4 pages, 3 figure

Atomic motion in tilted optical lattices

This paper presents a formalism describing the dynamics of a quantum particle in a one-dimensional, time-dependent, tilted lattice. The formalism uses the Wannier-Stark states, which are localized in each site of the lattice, and provides a simple framework allowing fully-analytical developments. Analytic solutions describing the particle motion are explicit derived, and the resulting dynamics is studied.Comment: 6 pages, 2 figs, submitted to EPJD, Springer Verlag styl

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

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

Dynamique quantique dans les potentiels lumineux

Membres du jury C. Salomon, E. Arimondo, D. Delande, J.M. Robbe, J.C. Garreau et V. ZehnleNumerous studies on the quantum dynamics in periodic potential have been carried since the Bloch's work on the cristal electron dynamics. This dynamics can be experimentally observe with cold atoms. Such dynamics is here theoritically sutied in both case of a single atoms and a Bose-Einstein condensate. In a first part, the dynamics of a quantum particle in a one-dimensional, tilted ("washboard") and time-dependent lattice is studied. The description uses the Wannier-Stark states, which are localized in each site of the lattice, and provides a simple framework to describe the dynamics. Particular attention is devoted to the case of a time-dependent potential. The approach leads to analytical results that show a rich variety of dynamical behavior and illustrate the fundamental role of interference in quantum systems. In a second part we study the quantum dynamics of an ultracold quantum degenerate gas in a tilted optical lattice and show that it displays features very close to classical chaos. We show that its phase space is organized according to the Kolmogorov-Arnold-Moser theorem.La dynamique quantique dans un potentiel périodique a fait l'objet de nombreuses études depuis les travaux de Bloch, dans les années 30, portant sur la dynamique des électrons dans un solide cristalisé. Cette dynamique est expérimentalement observable à l'aide d'atomes refroidis. L'utilisation de potentiels optiques permet de synthétiser, de façon très souple, des formes variées de potentiels, périodique, stationnaire ou dépendant du temps. Outre la grande variété de potentiels accessibles, l'atout majeur présenté par ces systémes est l'absence de dissipation et de processus de décohérence. Le travail présenté s'inscrit dans cette perspective et propose une description théorique, simple et analytique, de la dynamique quantique dans un potentiel périodique dépendant du temps. Il est connu depuis les travaux de Zener (1934), que la dynamique quantique dans un potentiel périodique en escalier, contrairement à l'intuition classique, est un mouvement d'oscillations nommé Oscillations de Bloch. Nous montrons que lors d'une modulation harmonique du potentiel des phénomènes de résonance apparaissent entre la fréquence de modulation et la fréquence des oscillations de Bloch et engendrent un transport de la particule dans le réseau. Cette dynamique est alors interprétée comme une interférence quantique mettant ainsi en exergue le role fondamental des cohérences quantiques de l'état initial. La réalisation expérimentale récente (1995) de la condensation de Bose Einstein d'un gaz atomique permet d'obtenir un état quantique cohérent mésoscopique. Récemment, des oscillations de Bloch ont été observées à l'aide de tels Ètats. Nous montrons que, outre ces oscillations, le condensat dans un potentiel périodique en escalier présente des régimes dynamiques chaotiques. Notre description introduit une base d'états adaptée et nous pouvons alors décrire la dynamique comme une évolution hamiltonienne classique portant sur les amplitudes et phases des états introduits. Les couplages non-linÈaires entre les différents états engendrent, pour certains états initiaux, des dynamiques chaotiques au sens classique bien que le condensat de Bose Einstein soit un objet quantique