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Accueil > Équipes scientifiques > Systèmes Moléculaires, Astrophysique et Environnement (SYSTEMAE) > Offres de stages, thèses et post-docs > Optima control theory applied to molecular alignement

Master internship (theory)

Optima control theory applied to molecular alignement

Master internship

The strong electric field of a laser [1] allows us to manipulate molecular degrees of freedom. For instance, the external degrees of freedom corresponding to overall rotation can be altered. In the case of a linear molecule, when the coupling with the electric field of the laser involves the polarizability tensor, alignment is observed [2]. A non-resonant laser pulse with a picoseconds duration (10-12 s), a TW/cm2 intensity, and polarized along of the laboratory-fixed Z axis makes it possible to align the molecule along this axis and to change its direction cosine squared (ΦZz)2. When this becomes close to 1, the molecule is almost parallel to the laboratory-fixed Z axis. Maximum actual values of (ΦZz)2 are on the order of 0.8 [3].

Increased molecular alignment, without a higher intensity of the laser pulse, can be achieved using pulse shaping [4] in conjunction with optimal control theory [5]. A laser pulse allowing us to maximize the alignment at time T can thus be designed.

This internship will first focus on modeling the effects of a non-resonant laser pulse in the case of an isolated linear molecule. Starting from the Stark coupling Hamiltonian written with the polarizability tensor, the time-dependent Schrödinger equation will be solved taking into account the shape of the laser pulse. In a second step, the shape of the laser pulse leading to a maximum alignment will be deduced solving optimal control theory equations [6]. This internship is essentially theoretical and will consist in writing the computer codes aimed at modeling the effects of the pulse and solving optimal control theory equations.

References :

[1] Stapelfeldt and T. Seideman, Rev. Mod. Phys. 75 (2003) 543
[2] Normand, Lompré, and C. Cornaggia, J. Phys. B : At., Mol. Opt. Phys. 25 (1992) L497
[3] Sakai et al., J. Chem. Phys. 110 (1999) 1
[4] Weiner, Opt. Commun. 284 (2011) 3669
[5] Werschnik and Gross, J. Phys. B 40 (2007) R175
[6] Lapert, Tehini, Turinici, and Sugny, Phys. Rev. A 78 (2008) 023408

Contact : Laurent Coudert

Voir en ligne : Equipe Systèmes Moléculaires, Astrophysique et Environnement