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