We show that left-handed properties can be electromagnetically induced in a general four-level atomic medium for a finite spectral range. We use an electric (magnetic) atomic transition as an electric (magnetic) resonator to modify the permittivity (permeability), both at the same frequency. The implementation of the four-level model is carried out in atomic hydrogen and neon. In each case the existence of left-handed properties is predicted inside an experimentally reachable domain of parameters. DOI: 10.1103/PhysRevLett.96.053601 PACS numbers: 42.50.Gy, 42.25.Bs, 78.20.Ci The propagation of electromagnetic waves in matter is characterized by the frequency-dependent relative dielectric permittivity " r and magnetic permeability r . Their product defines the index of refraction: " r r n 2 . Lefthanded media are characterized by negative real parts of " r , r [1]. It has been shown that in this case the negative root must be used for the index of refraction n ÿ " r r p[1]. Left-handed media have recently attracted significant attention since it has been discovered that a slab of lefthanded materials is able, for instance, to focus light into a spot much smaller than the wavelength, realizing a ''perfect'' lens [2]. Experimentally, left-handed properties in the microwave domain were obtained with a composite medium made of a periodic array alternation of split ring resonators and continuous wires [3]. Left handedness has been recently analyzed in a three-level medium [4]. However, the proposed scheme requires the conflicting demand that the middle state is involved in both a magnetic transition and an electric transition at the same frequency. An independent study of the same scheme has reached a similar conclusion [5].In this Letter we demonstrate that a four-level medium may be left handed in a restricted domain of parameters. In our model an electric transition and a magnetic transition play the role of an electric resonator and a magnetic resonator, respectively. They involve two different pairs of states, leading to a realistic energy configuration. Explicit calculation predict the occurrence of a left-handed domain in hydrogen and neon gases with Ref" r g < 0 andNumerous works have been carried out over the past 15 years to control the index of refraction by quantum interference. They led, in particular, to electromagnetically induced transparency (EIT) [6], refractive index enhancement [7], and slow light [8]. As the magnetic transition strengths are typically 2 orders of magnitude smaller than the electric transition strengths, the permeability does not change significantly from unity as the frequency of the probe magnetic field reaches a magnetic resonance. Therefore, the modification of the index of refraction is in general due mainly to a modification of the electrical susceptibility. However, a significant change of the permeability can be obtained from a magnetic moment induced by coupled electric transitions [4]. In this Letter we combine the modification of the permeability by an induced magneti...

The development of systemic approaches in biology has put emphasis on identifying genetic modules whose behavior can be modeled accurately so as to gain insight into their structure and function. However, most gene circuits in a cell are under control of external signals and thus, quantitative agreement between experimental data and a mathematical model is difficult. Circadian biology has been one notable exception: quantitative models of the internal clock that orchestrates biological processes over the 24-hour diurnal cycle have been constructed for a few organisms, from cyanobacteria to plants and mammals. In most cases, a complex architecture with interlocked feedback loops has been evidenced. Here we present the first modeling results for the circadian clock of the green unicellular alga Ostreococcus tauri. Two plant-like clock genes have been shown to play a central role in the Ostreococcus clock. We find that their expression time profiles can be accurately reproduced by a minimal model of a two-gene transcriptional feedback loop. Remarkably, best adjustment of data recorded under light/dark alternation is obtained when assuming that the oscillator is not coupled to the diurnal cycle. This suggests that coupling to light is confined to specific time intervals and has no dynamical effect when the oscillator is entrained by the diurnal cycle. This intringuing property may reflect a strategy to minimize the impact of fluctuations in daylight intensity on the core circadian oscillator, a type of perturbation that has been rarely considered when assessing the robustness of circadian clocks.

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The circadian clocks keeping time in many living organisms rely on self-sustained biochemical oscillations entrained by external cues, such as light, to the 24-h cycle induced by Earth's rotation. However, environmental cues are unreliable due to the variability of habitats, weather conditions, or cue-sensing mechanisms among individuals. A tempting hypothesis is that circadian clocks have evolved so as to be robust to fluctuations in the signal that entrains them. To support this hypothesis, we analyze the synchronization behavior of weakly and periodically forced oscillators in terms of their phase response curve (PRC), which measures phase changes induced by a perturbation applied at different times of the cycle. We establish a general relationship between the robustness of key entrainment properties, such as stability and oscillator phase, on the one hand, and the shape of the PRC as characterized by a specific curvature or the existence of a dead zone, on the other hand. The criteria obtained are applied to computational models of circadian clocks and account for the disparate robustness properties of various forcing schemes. Finally, the analysis of PRCs measured experimentally in several organisms strongly suggests a case of convergent evolution toward an optimal strategy for maintaining a clock that is accurate and robust to environmental fluctuations.

8 pages, 6 figuresThis 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

We show that lanthanide-doped crystals can be made left handed for a finite spectral range. The electronic transitions in the dopant ions are both dipolar electric and dipolar magnetic allowed. This enables tuning the permittivity and the permeability at the same frequency. The analysis focuses on erbium-doped crystals where left-handed properties are predicted inside an experimentally reachable domain of parameters. © 2006 Optical Society of America OCIS codes: 160.5690, 230.1150, 020.1670 Media having negative values of the real parts of their permittivity and permeability (called lefthanded media) are promising materials for optical devices. They have recently attracted significant attention since it has been discovered that a slab of lefthanded material is able, for instance, to focus light into a spot much smaller than the wavelength, realizing a "perfect" lens. 1,2 Experimentally, the first lefthanded properties were obtained in the microwave domain with a composite medium made of a periodic alternation of split ring resonators and continuous wires 3 and more recently in the near-infrared domain with a doubly periodic array of pairs of parallel nanorods. 4 In this Letter left handedness in lanthanide-doped crystals is analyzed. In our model an electric transition and a magnetic transition play the role of an electric resonator and a magnetic resonator, respectively. Explicit calculations for an erbium-doped crystal predict the occurrence of a left-handed domain for a probe field oscillating at approximately 1.54 m. Contrary to previous studies on atomic gases, 5,6 no strong electromagnetic fields are required.Let a medium interact with a weak probe electromagnetic beam oscillating at frequency and described by the electric field E, the magnetic field B, and the wave vector k. During the interaction, the medium develops a macroscopic polarization P and a macroscopic magnetization M. These are the mean values of the atomic electric dipoles and the atomic magnetic dipoles. We assume a linear response P = 0 ␣ e E and 0 M = ␣ m B, where ␣ e and ␣ m are the polarizability and the magnetizability, respectively.7 A magnetizability and a polarizability of order unity and at the same frequency are required to obtain a domain of parameter with negative real parts of the relative permeability r = ͑1−␣ m ͒ −1 and of the relative permittivity r =1+␣ e . An electronic transition involving an electric (magnetic) dipole tunes the permittivity (permeability) in the same way as an electric (magnetic) resonator having the transition frequency among its eigenfrequencies. Therefore a medium having a nearly degenerate electric dipolar transition and magnetic dipolar transition is a good candidate to realize a left-handed material around the transition frequencies. This can be found in lanthanidedoped crystals.The lanthanides correspond to the 14 elements with an unfilled 4f subshell. According to the Klechkowski rules, the 5s and 5p subshells are populated before the 4f subshell. Thus the inner unfilled 4f subshell is compresse...

Environmental stress, such as oxidative or heat stress, induces the activation of the heat shock response (HSR) and leads to an increase in the heat shock proteins (HSPs) level. These HSPs act as molecular chaperones to maintain cellular proteostasis. Controlled by highly intricate regulatory mechanisms, having stress-induced activation and feedback regulations with multiple partners, the HSR is still incompletely understood. In this context, we propose a minimal molecular model for the gene regulatory network of the HSR that reproduces quantitatively different heat shock experiments both on heat shock factor 1 (HSF1) and HSPs activities. This model, which is based on chemical kinetics laws, is kept with a low dimensionality without altering the biological interpretation of the model dynamics. This simplistic model highlights the titration of HSF1 by chaperones as the guiding line of the network. Moreover, by a steady states analysis of the network, three different temperature stress regimes appear: normal, acute, and chronic, where normal stress corresponds to pseudo thermal adaption. The protein triage that governs the fate of damaged proteins or the different stress regimes are consequences of the titration mechanism. The simplicity of the present model is of interest in order to study detailed modelling of cross regulation between the HSR and other major genetic networks like the cell cycle or the circadian clock.

The microscopic green alga Ostreococcus tauri is rapidly emerging as a promising model organism in the green lineage. In particular, recent results by Corellou et al. [Plant Cell 21, 3436 (2009)] and Thommen et al. [PLOS Comput. Biol. 6, e1000990 (2010)] strongly suggest that its circadian clock is a simplified version of Arabidopsis thaliana clock, and that it is architectured so as to be robust to natural daylight fluctuations. In this work, we analyze the time series data from luminescent reporters for the two central clock genes TOC1 and CCA1 and correlate them with microarray data previously analyzed. Our mathematical analysis strongly supports both the existence of a simple two-gene oscillator at the core of Ostreococcus tauri clock and the fact that its dynamics is not affected by light in normal entrainment conditions, a signature of its robustness.