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.