We apply the techniques of control theory and of sub-Riemannian geometry to laser-induced population transfer in two-and three-level quantum systems. The aim is to induce complete population transfer by one or two laser pulses minimizing the pulse fluences. Sub-Riemannian geometry and singular-Riemannian geometry provide a natural framework for this minimization, where the optimal control is expressed in terms of geodesics. We first show that in two-level systems the wellknown technique of ''-pulse transfer'' in the rotating wave approximation emerges naturally from this minimization. In three-level systems driven by two resonant fields, we also find the counterpart of the ''-pulse transfer.'' This geometrical picture also allows one to analyze the population transfer by adiabatic passage.

We report a direct nonintrusive observation of alignment and planar delocalization of CO2 after an intense linearly polarized femtosecond laser pulse excitation. The effects are measured by a polarization technique involving a perturbative probe that itself does not induce appreciable alignment. We show that this technique allows one to measure a signal proportional to -1/3, with theta the angle between the molecular axis and the laser polarization. Simulations that support this analysis allow one to characterize the experimentally observed alignment and planar delocalization quantitatively.

No abstract

We present a strategy for post-pulse molecular orientation aiming both at efficiency and maximal duration within a rotational period. We first identify the optimally oriented states which fulfill both requirements. We show that a sequence of half-cycle pulses of moderate intensity can be devised for reaching these target states.PACS numbers: 32.80.Lg, 42.50.Hz Molecular orientation plays a crucial role in a wide variety of applications extending from chemical reaction dynamics, to surface processing, catalysis and nanoscale design [1,2,3,4]. Static electric field [5] and strong nonresonant long laser pulses [6,7] have been shown to yield adiabatic molecular orientation which disappears when the pulse is off. Noticeable orientation that persists after the end of the pulse (and even under thermal conditions) is of special importance for experiments requiring fieldfree transient orientation. It has recently been shown that very short pulses combining a frequency ω and its second harmonic 2ω excite a mixture of even and odd rotational levels and have the ability to produce such post-pulse orientation [8]. But even more decisive has been the suggestion to use half-cycle pulses (HCPs), that through their highly asymmetrical shape induce a very sudden momentum transfer to the molecule which orients under such a kick after the field is off [9,10]. Both the (ω + 2ω) and the kick mechanisms have received a confirmation from optimal control schemes [11]. The caveat is that the post-pulse orientation is maintained for only short times. Recently, the use of a train of kicks to increase the efficiency of the orientation has been suggested in optimal control strategies [11] and applied to molecular alignment [12] and orientation of a 2D rotor [13]. However, due to the strength of the kicks used, only the efficiency of the process has been optimized, its duration decreasing strongly. In the present letter, we propose a control strategy using specially designed series of kicks * Electronic address: dominique.sugny@u-bourgogne.fr † Electronic address: arne.keller@ppm.u-psud.fr ‡ Electronic address: ddaems@ulb.ac.be delivered by short HCPs, that allows to significantly enhance the duration of the orientation, maintaining a high efficiency. Our construction is first based on the identification of target states which fulfill the previous requirement. These states are characterized by the fact that they only involve a limited number of the lowest lying rotational levels and that they maximize the orientation efficiency within the corresponding restricted rotational spaces. At a second stage, we show that these selected states can be reached by a train of kicks, acting at appropriately chosen times. The choice of the strength of the pulses (taken equal for simplicity), together with the total number of kicks allow to approach these target states with good accuracy. The time evolution of the molecule (described in a 3D rigid rotor approximation) interacting with a linearly polarized field is governed by the time-dependent Schröding...