Dynamical entanglement as a signature of chaos in the semiclassical limit

International audienceThe relationship between classically chaotic dynamics and the entanglement properties of the corresponding quantum system is examined in the semiclassical limit. Numerical results are computed for a modified kicked top, keeping the classical dynamics constant while investigating the entanglement for several versions of the corresponding quantum system characterized by a different value of the effective Planck constant ℏ eff. Our findings indicate that as ℏ eff → 0, the apparent signatures of classical chaos in the entanglement properties, such as characteristic oscillations in the time-dependence of the linear entropy, can also be obtained in the regular regime. These results suggest that entanglement is not a universal marker of chaotic dynamics of the corresponding classical system

Survey of correlation properties of polyatomic molecules vibrational energy levels using FT analysis

International audienceIn the last few years molecular spectroscopists have begun to study the highly excited vibrational levels of polyatomic molecules. In this high energy regime vibrational quantum numbers can no longer be intrinsically assigned (in contrast to vibrational levels at low energy). One can only characterize these levels by their correlation properties. The authors consider: short range correlations which are characterized by the next neighbor distribution, (NND). These correlations range from a Poisson (random or uncorrelated spectra) to a Wigner distribution (which shows 'level repulsion'); (ii) long range correlations are characterized by the$\mathrm{\Sigma ^{2}}$(L) and$\mathrm{\Delta _{3}}$(L) function. They describe the behavior which ranges from an uncorrelated spectra (Poisson statistic) to a spectra with 'spectral rigidity'

Complex trajectory method in semiclassical propagation of wave packets

International audienceWe propose a semiclassical wave packet propagation method relying on classical trajectories in a complex phase space. It is based on the Schrödinger wave equation and the usual expansion with respect to ℏ, except that the amplitude of the wave packet is taken into account at the very zeroth order, unlike in the usual WKB method where it is treated as a corrective or first order term. Formally, it amounts to making both the wavelength and the width of the wave packet tend to zero with ℏ. The action and consequently the classical trajectories derived are complex. This method is tested successfully in many cases, analytically or numerically, including the bounce and even the splitting of the wave packet. Our method appears to be much more accurate than the WKB method while less computationally demanding than the Van-Vleck formula. Moreover, it has a particularly interesting property: the singularities (caustics) of the usual semiclassical theories do not appear in this formalism in all cases tested

Coupled modes semiclassical treatment of nonadiabatic transitions

International audienceWe analyse the Schrödinger wave equation of a two-level or spinorial Hamiltonian, from a classical point of view. An iterative scheme, the coupled mode semiclassical formalism, is proposed, allowing us to deal with the nonadiabatic transfer. As the WKB expansion, it allows the one-dimensional Schrödinger equation to be integrated by successive quadratures. Finally, we show that time-dependent information can be drawn from the previous, purely stationary, analysis by extending the notion of group velocity. The proposed formalism is thus coherent with an image of multiple trajectories, conforming more to physical behaviour than a single trajectory

Unified theory of bound and scattering molecular Rydberg states as quantum maps

Using a representation of multichannel quantum defect theory in terms of a quantum Poincar\'e map for bound Rydberg molecules, we apply Jung's scattering map to derive a generalized quantum map, that includes the continuum. We show, that this representation not only simplifies the understanding of the method, but moreover produces considerable numerical advantages. Finally we show under what circumstances the usual semi-classical approximations yield satisfactory results. In particular we see that singularities that cause problems in semi-classics are irrelevant to the quantum map

The microlocal Landau-Zener formula

International audienceWe describe the space of microlocal solutions of a 2 \Theta 2 system of pseudo­differential operators (PDO) on the real line near an avoided cross­ ing (2­levels system). We prove Landau­Zener type formulae in the adiabatic case with avoided crossings and for the classical limit of coupled Schr¨odinger operators (Born­Oppenheimer approximation). The formulae that we get are uniform in the set of small parameters (Planck constant and coupling constant), they admits an uniquely determined complete asymptotic expansion and allow to access simply to phases which are needed in order to derive quantization conditions. The present paper is an expanded version of results already ob­ tained by Joel Pollet in his PhD thesis [22]. Quantization conditions will be described in [5], following the techniques of [8]. See also [25] concerning the scattering matrix. An extension to time dependent Schr¨odinger equation close to the work by Hagedorn [13] and Hagedorn­Joye [14] and based on [20], [10] and [27] is also in preparation

Orientation of Hydrogenic Levels by Stark Effect and sp Coherence Resulting from Direct Excitation or Molecular Dissociation

International audienceWe have measured the predicted orientation induced by first-order Stark effect on sp coherent levels of He+ and H excited by a 100-keV Na+ beam impinging on a cell filled with He or H2. We discuss the mechanism of production of sp coherence by dissociative excitation of H2

Coherently excited atoms in external electric fields

International audienceVarious manifestations of coherent mixtures of even- and odd-parity eigenstates of collision-excited atomic hydrogen in external electric fields are discussed on general grounds. We show that when even-and odd-parity states are coherently excited, application of an electric field perpendicular to the velocity axis induces orientation in the originally unoriented atoms. Circular polarization of the decay radiation is an observable consequence of the orientation

Nonadiabatic effects in two-level systems: A classical analysis

International audienceOur aim in this paper is to study classical dynamics in two-level molecular systems. We first derive, through the Wigner phase-space transform, a classical limit that reduces unfortunately to the adiabatic approximation. This lead us to develop a one-center quantal approximation whose variables can be interpreted in a fully classical Hamiltonian scheme. As a prominent feature, this Hamiltonian couples polarization and spatial motion. We apply it successfully to the Rosenthal-Stückelberg oscillations. We analyze one-dimensional diffusion similar to a molecular reaction, it appears to exhibit chaotic behavior

Weak hyperfine structure measurement using the magnetic repolarization effect: Application to N = 1 v = 1 (1s 3d)1Σ level of H2

International audienceThe magnetic repolarization effect is studied in the case where the hyperfine structure (AI . J) of the considered excited atomic or molecular level is weaker than the natural width Γ. General expressions are given. It is shown that the amplitude of this effect varies as (A/Γ)2 and that its value permits the determination of A when one compares the magnetic repolarization and depolarization effects. Such an effect is experimentally studied in the N = 1, v = 1 (1s 3d)1Σ level of H2. A value of A = 1+/-0.17) MHz is deduced, corresponding to A/Γ = 0.15