Lagrangian descriptor and escape time as tools to investigate the dynamics of laser-driven polar molecules.

We consider the nonlinear dynamics of a diatomic polar molecule under a linearly polarized laser field. We assume a model in which the molecule dipole is coupled with a time-dependent electric field. This system presents a bound energy region where the atoms are bound, and a free-energy region where the atoms are dissociated. Due to the nonalignment between the dipole axis and the laser direction, and the time dependence of the external field, this system presents two and a half degrees of freedom, namely the vibrational degree, the rotation degree, and the time. To investigate the system dynamics, instead of using the Poincaré surface-of-section technique, we propose the use of the Lagrangian descriptor associated with the escape times. The Lagrangian descriptor is a quantity that reveals complex structures in the phase space, whereas the escape times are the time span in which a trajectory is initially in the bound region before escaping to the unbound region. The combination of these two quantities allows us to distinguish between real stability regions from other complex structures, including stickiness regions, and a different formation, which we call escape islands. With the help of these tools, we find that for high-field amplitudes the inclusion of rotation leads to an increase of the stability regions, which implies a decrease of the dissociation in comparison with the one-dimensional case.

Nonlinear photoassociation through exotic orbits.

We investigate the effects of a particular kind of orbits, which we call exotic orbits, on the process of classical molecular photoassociation. As a starting model system, we consider the process described by the Morse potential with a time-dependent perturbation consisting of the interaction of an external laser field with the molecular dipole. When the external perturbation is turned off, the bound molecular states are classically represented by librational motion, whereas the unbound, the collisional states, are represented by unbound motion, and in both cases, the energy is a constant of motion. When the perturbation is turned on, the total energy is no longer a constant of motion and initial conditions in the unbound region can reach the bound region, and vice versa, through chaotic orbits. Alternatively, we have found that the connection between the bound and unbound sectors can be achieved through exotic orbits, which are comprised by librationlike parts, a localized chaotic region, and an unbounded constant-energy part. Thus, if a colliding atomic pair is in an exotic orbit, it penetrates a chaotic region coming from the unbound sector, subsequently performing librationlike motion, during which the molecule with constant bound energy is formed. Afterwards, the molecule returns to the chaotic region and from this region, it can either access a distinct bound energy or dissociate. We call this phenomenon, in which a metastable molecule is formed, intermittent photoassociation. We show that the key for the emergence of exotic orbits is the relatively short range of the dipole as compared to the interacting potential range. In order to further verify our results, we have considered realistic forms for the potentials and dipole functions of several molecules and found the emergence of exotic orbits, and consequently of intermittent photoassociation, for the MgLi and SrLi molecular parameters.

Nonchaotic laser pulse dissociation through deformed tori.

We consider the nonlinear classical dynamics of a diatomic molecule under the action of a laser field in the framework of the driven Morse oscillator model. We investigate the influence of the dipole function and the laser field on the deformations of the surviving, invariant tori. For intense and high-frequency fields, some invariant tori traverse the separatrix of motion, visiting both the bound and unbound regions of the interatomic potential. Based on this fact, we propose the use of appropriately designed laser pulses to induce dissociation of trajectories on such invariant tori. This mechanism constitutes a controlled nonchaotic route for dissociation, which is an alternative to chaotic multiphoton dissociation and to chirped pulse dissociation.