Molecular photodissociation: Quantum calculations, nonlinear dynamics, chaos and phase space control.
A well-known issue in physics is understanding theoretically and quantitatively the various aspects of the correspondence between classical and quantum mechanics. The validity of this type of understanding is enhanced when real physical systems rather than simple models - albeit mathematically convenient- are the objects of investigation.
In this context, we have been studying the dynamics of laser-induced time-dependent multiphoton dissociation of the diatomic Morse molecule by advanced methods and analysis of both classical (CM) and quantum mechanics (QM). Our approach is to solve the equations of Schrodinger and of Hamilton nonperturbatively. The first task is carried out by implementing the state-specific expansion approach (SSEA), where the scattering continuum is included explicitly [1, 2]. The solution includes all the physically important information. A number of results concerning multiphoton dissociation as a function of laser pulse parameters are obtained . These are then used as reference data not only for experiment but also for the study of the same problems in terms of CM.
As regards the CM calculations and analysis [2, 3], the key idea is to employ the changes in the classical phase space of laser-driven diatomic molecules in order to achieve understanding, (and, therefore, control), of the process of photodissociation. To this end, we aim at uncovering the degree of the connection of the phenomenology of classical calculations with the phase space modifications and the basic periodic orbits that structure the phase space.
Certain of the findings from the above studies are as follows [2-5]:
1. Both CM and QM show that for long pulses (>100 cycles) the dissociation probability of a monochromatically driven molecular bond is sensitive to the initial phase of the external laser field. An explanatory CM mechanism was proposed, based on the effects of the initial phase on the fundamental periodic orbits of the system.
2. In the two-frequency driven Morse molecule, it is demonstrated that addition of the second laser leads to suppression of dissociation probability (meaning stabilization), when the intensity of the first laser is kept constant just above or below the single laser dissociation threshold. This ''chemical bond hardening'' diminishes as the phase of the pulse increases. These effects are investigated and interpreted in terms of modifications in phase-space topology. Variations of the phase as well as of the intensity of the second laser may cause appearance/disappearance of the stability island corresponding to the common resonance with the lowest energy and deformation and movement of the region of Kolmogorov-Arnold-Moser tori that survive from the undriven system. The latter is the main origin in phase space of stabilization and phase-dependence. Finally, it is shown that the use of short laser pulses enhances both effects.
3. Regarding the effects of laser frequency, a well-established quantum and classical result is that for laser intensities of the order of 1014 W/cm2 the dissociation probability presents a maximum at the frequency ýmax~ 0.80-0.90ý01, where ý01 is the transition frequency from the ground to the first excited vibrational state ('redshift' phenomenon). In this work, we have gone further, by exploring the quantum and classical effects of radiation at the optimum frequency ýmax on the overall vibrational excitation and dissociation dynamics. The below figure shows the quantal and classical survival probabilities as a function of the interaction time for different laser frequencies and intensity of 30 TW/cm2.
The final aim is to link the quantum behavior with properties of the periodic orbits, thereby making simpler and faster study of the control of the photodissociation of diatomic bonds through field and potential parameters.
 Th. Mercouris, Y. Komninos, S. Dionissopoulou and C. A. Nicolaides, ''Computation of strong-field multiphoton processes in polyelectronic atoms. State-specific method and application to H and Li- '', Phys. Rev. A 50, 4109 (1994).
 K. I. Dimitriou, V. Constantoudis, Th. Mercouris, Y. Komninos, and C. A. Nicolaides
''Quantum and classical dynamics of a diatomic molecule in laser fields with frequency in the region producing maximum dissociation'', Phys. Rev. A 76, 033406 (2007)
 V. Constantoudis and C. A. Nicolaides, ''Stabilization and relative phase effects in a dichromatically driven diatomic Morse molecule: Interpretation based on nonlinera classical dynamics'', J. Chem. Phys. 122, 084118 (2005).
. V. Constantoudis, L. P. Konstantinidis, K. I. Dimitriou, Th. Mercouris, and C. A. Nicolaides, ''Classical Chaos and Its Relation to Quantum Dynamics in the Case of Multiphoton Dissociation of the Morse Oscillator'', Nonlinear Phenomena in Complex Systems, 11, 292 (2008).
 L.P. Konstantinidis, Master's thesis, School of Applied Mathematical and Physical Sciences, National Technical University of Athens, ''Effects of laser initial phase on the dissociation of diatomic molecules using methods of classical dynamics'' (2007).