Quantum control spectroscopy denotes the combination of optical quantum coherent control with femtosecond spectroscopy.

The molecular response to a photo induced process,

controlled by shaped ultrashort light pulses,

carries information about the system and the induced chemical reaction

not obtainable by unshaped pulses.

In this work quantum control spectroscopy is used to investigate the photochemical process of

beta-carotene during its first few hundred femtoseconds, which are important in the photosynthesis

of light harvesting complexes.

A special class of shaped pulses, called pulse trains, are investigated.

Pulse trains are obtained from Fourier limited pulses, by modulation with a

sinusoidal phase mask $\phi(\omega) = a \sin(b\omega_0+c)$,

leading to a sequence of three or more phase stabilized Gaussian shaped pulses in the time domain.

The intensities of these pulses are defined by a, they are separated by

equal interpulse distances b and have a distinct phase relation which is defined by c.

In this work it will be shown that it is possible

to draw a very unique relation between molecular properties and

the molecular response to the electrical field in dependance of these parameters.

In terms of quantum coherent control, sinusoidal modulated pulse trains

have attracted special attention in the context of mode selectivity.

In a series of experiments it was observed that pulse train excitation can suppress spectral features in the detection signal when the

interpulse distance is adjusted to molecular characteristics like vibrational frequencies.

Furthermore, in many control experiments aiming to steer a chemical reaction,

the use of learning loops for field optimization leads to pulse shapes

that could be reduced to sequences of pulses, comparable to the pulse trains introduced.

Replacement of optimized light fields by appropriate adjusted pulse trains were successful in experiments controlling the energy flow in a light harvesting complex.

Control could be obtained by variation of the phase parameter c, suggesting that the achieved effect was of coherent origin.

The assumption that the carotene units in LH2 were responsible for the successful control,

was the motivation for the presented work of quantum control spectroscopy

of beta-carotene.

Although many efforts have been made to understand

the non-linear effects induced by pulse trains,

the underlying mechanism is not yet clear.

Neither the background of mode selectivity nor the mechanism of chemical reaction control

could be deciphered satisfactorily.

For spectroscopical investigations, however, the knowledge of the

underlying process and its connection to the molecular response is inevitable and are

analyzed in detail.

Starting with a simple model of bound states in a diatomic molecule,

the induced dynamics of the molecular system and the characteristics

of the response field are analyzed.

First phenomenological investigations of the pulse train induced wave packet dynamics

show dependancies between the populations and coherences of the generated molecular state

and the choice of the sinusoidal mask parameters.

Further investigations imply a mechanism connecting the outcome of the control experiment

with the pulse train parameters and the molecular properties which is

confirmed by derivation of a formula based on time dependent perturbation theory.

The proposed mechanism leads to results which are in accordance with

many experimentally observed effects.

It is found that pulse train excitation generates vibrational wave packets that can exhibit symmetric phase space structures.

Comparable structures appear during long time evolution after excitation with Fourier limited pulses

and are known as partial revival states.

Experimentally observed effects, like annihilation of spectral signals, are attributed to temporal interference effects between phase shifted vibrational coherences of these symmetr