On the topology of adiabatic passage

We examine the topology of eigenenergy surfaces characterizing the population transfer processes based on adiabatic passage. We show that this topology is the essential feature for the analysis of the population transfers and the prediction of its final result. We reinterpret diverse known processes, such as stimulated Raman adiabatic passage (STIRAP), frequency-chirped adiabatic passage and Stark-chirped rapid adiabatic passage (SCRAP). Moreover, using this picture, we display new related possibilities of transfer. In particular, we show that we can selectively control the level which will be populated in STIRAP process in Lambda or V systems by the choice of the peak amplitudes or the pulse sequence

Time Minimal Trajectories for a Spin 1/2 Particle in a Magnetic Field

In this paper we consider the minimum time population transfer problem for the $z$-component of the spin of a (spin 1/2) particle driven by a magnetic field, controlled along the x axis, with bounded amplitude. On the Bloch sphere (i.e. after a suitable Hopf projection), this problem can be attacked with techniques of optimal syntheses on 2-D manifolds. Let $(-E,E)$ be the two energy levels, and $|\Omega(t)|\leq M$ the bound on the field amplitude. For each couple of values $E$ and $M$, we determine the time optimal synthesis starting from the level $-E$ and we provide the explicit expression of the time optimal trajectories steering the state one to the state two, in terms of a parameter that can be computed solving numerically a suitable equation. For $M/E<<1$, every time optimal trajectory is bang-bang and in particular the corresponding control is periodic with frequency of the order of the resonance frequency $\omega_R=2E$. On the other side, for $M/E>1$, the time optimal trajectory steering the state one to the state two is bang-bang with exactly one switching. Fixed $E$ we also prove that for $M\to\infty$ the time needed to reach the state two tends to zero. In the case $M/E>1$ there are time optimal trajectories containing a singular arc. Finally we compare these results with some known results of Khaneja, Brockett and Glaser and with those obtained by controlling the magnetic field both on the $x$ and $y$ directions (or with one external field, but in the rotating wave approximation). As byproduct we prove that the qualitative shape of the time optimal synthesis presents different patterns, that cyclically alternate as $M/E\to0$, giving a partial proof of a conjecture formulated in a previous paper.Comment: 31 pages, 10 figures, typos correcte

Tribological properties of room temperature fluorinated graphite heat-treated under fluorine atmosphere

This work is concerned with the study of the tribologic properties of room temperature fluorinated graphite heat-treated under fluorine atmosphere. The fluorinated compounds all present good intrinsic friction properties (friction coefficient in the range 0.05–0.09). The tribologic performances are optimized if the materials present remaining graphitic domains (influenced by the presence of intercalated fluorinated species) whereas the perfluorinated compounds, where the fluorocarbon layers are corrugated (armchair configuration of the saturated carbon rings) present higher friction coefficients. Raman analyses reveal that the friction process induces severe changes in the materials structure especially the partial re-building of graphitic domains in the case of perfluorinated compounds which explains the improvement of μ during the friction tests for these last materials

Cold atoms at unitarity and inverse square interaction

Consider two identical atoms in a spherical harmonic oscillator interacting with a zero-range interaction which is tuned to produce an s-wave zero-energy bound state. The quantum spectrum of the system is known to be exactly solvable. We note that the same partial wave quantum spectrum is obtained by the one-dimensional scale-invariant inverse square potential. Long known as the Calogero-Sutherland-Moser (CSM) model, it leads to Fractional Exclusion Statistics (FES) of Haldane and Wu. The statistical parameter is deduced from the analytically calculated second virial coefficient. When FES is applied to a Fermi gas at unitarity, it gives good agreement with experimental data without the use of any free parameter.Comment: 11 pages, 3 figures, To appear in J. Phys. B. Atomic, Molecular and Optical Physic

Pulse-driven quantum dynamics beyond the impulsive regime

We review various unitary time-dependent perturbation theories and compare them formally and numerically. We show that the Kolmogorov-Arnold-Moser technique performs better owing to both the superexponential character of correction terms and the possibility to optimize the accuracy of a given level of approximation which is explored in details here. As an illustration, we consider a two-level system driven by short pulses beyond the sudden limit.Comment: 15 pages, 5 color figure

Light and nitrogen nutrition regulate apical control in Rosa hybrida L.

Apical control is defined as the inhibition of basal axillary bud outgrowth by an upper actively growing axillary axis, whose regulation is poorly understood yet differs markedly from the better-known apical dominance. We studied the regulation of apical control by environmental factors in decapitated Rosa hybrida in order to remove the apical hormonal influence and nutrient sink. In this plant model, all the buds along the main axis have a similar morphology and are able to burst in vitro. We concentrated on the involvement of light intensity and nitrate nutrition on bud break and axillary bud elongation in the primary axis pruned above the fifth leaf of each rose bush. We observed that apical control took place in low light (92 μmol m−2 s−1), where only the 2-apical buds grew out, both in low (0.25 mM) and high (12.25 mM) nitrate. In contrast, in high light (453 μmol m−2 s−1), the apical control only operates in low nitrate while all the buds along the stem grew out when the plant was supplied with a high level of nitrate. We found a decreasing photosynthetic activity from the top to the base of the plant concomitant with a light gradient along the stem. The quantity of sucrose, fructose, glucose and starch are higher in high light conditions in leaves and stem. The expression of the sucrose transporter RhSUC2 was higher in internodes and buds in this lighting condition, suggesting an increased capacity for sucrose transport. We propose that light intensity and nitrogen availability both contribute to the establishment of apical control

Nitrogen deficiency increases basal branching and modifies visual quality of the rose bushes

Rosebush architecture resulting from the spatial organisation of the plant axes induces plant shape and consequently within ornamental horticulture context, its visual quality and commercial value. This architecture can be modulated by environmental conditions, particularly in the horticulture context in which the possibilities to control growing conditions are numerous. The objectives of the study were to determine, in young rose bushes, (1) whether short periods of nitrogen deficiency affect branching and (2) whether this effect is sufficient to modify the visual quality of the plant in a sustainable manner. Between vegetative bud burst and the petal colour visible stage of the generated primary branch, young rooted cuttings of bush rose (cv Radrazz) were subjected to one of three nitrogen regimes: (1) no nitrogen deficiency, (2) continuous nitrogen deficiency, i.e. 35 days of N deficiency, and (3) nitrogen deficiency restricted to the flowering stages, i.e. 18 days of N deficiency. After the petal colour visible stage, all three groups of plants were supplied continuously with nitrogen. We observed the morphology of the axes and the kinetics of axillary bud burst. Twelve weeks after the petal colour visible stage, the visual quality of the rose bushes was evaluated by an expert jury. We found that nitrogen deficiencies (1) increased bud burst ratios in the medial and basal zones of the primary branch, (2) delayed the bud burst in the apical zone of the primary branch and (3) had long-term effects on plant visual quality. The continuous nitrogen deficiency regime produced flatter, more asymmetric and less vigorous rose bushes than the no nitrogen deficiency regime. By contrast, nitrogen deficiency during the flowering stages only resulted in more symmetric, taller and more vigorous rose bushes than the no nitrogen deficiency regime. Based on these results, the role of nitrogen on bud burst was discussed and candidate processes at the origin of the visual quality modification were suggested. This new approach combining ecophysiology and sensory assessment of ornamental plants enabled the identification of some early architecture components to be correlated with later visual quality characteristics and then to better target the physiological processes of interest