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 symmetric phase space structures. Contribution of such temporal interference effects are found to be essential
for the signal interpretation in the case of time limited detection periods in the femtosecond regime.

From a detailed analysis rules are extracted which serve to predict and
to interprete the outcome of quantum control experiments using sinusoidally modulated pulse trains.
It is found that the degree of rotational symmetry of the generated phase space pattern is determined by the ratio of the classical oscillation period of a vibrational mode to the interpulse distance b.
In contrast, at a fixed value of b, the variation of the phase parameter c causes an
oscillatory exchange between phase shifted components of the generated phase space structures,
leading to an oscillatory disturbance of the phase space symmetry.
While the phase space symmetry induced by b leads to destructive interference of spectral signals,
this effect can be partially removed by c.
The resulting oscillations of the peak amplitudes with c reflect the symmetry of the
b-generated phase space structures.

In a next step the model is extended towards the description of
complex biological systems.
Investigated are environmental effects,
the model expansion to polyatomic molecules and the influence of
electronic coupling elements, leading to the participation of additional electronic states.
Using the density matrix description, the influence on the pulse train mechanism
of elastic and inelastic environmental processes is investigated.
Limits are figured out, defining the scope of the extracted rules for
the two mask parameters b and c in dissipative environment.
Increasing the dimensionality of the model, it is found that the derived mechanism still holds in polyatomic molecules. In accordance with experimental results, it is possible
to damp spectral signals of selective vibrational modes by the mentioned
destructive interference effects, adapting the interpulse distance to participating modes.
By combination of the effects of b and c it is even possible to selectively damp
near resonant modes.
To come closer to the description of
beta-carotene, the model system
is extended by an additional diabatically coupled electronic state.
Now the spectroscopic response function after Fourier limited excitation, recording
the evolution of the excited state population, comprises information exclusively
of the reactive coupling modes.
Thus, the electronic coupling process can be traced without disturbance of inreactive
spectator modes by detection of the excited state population, acting as a window to coupling modes.
Additionally it is shown, that the mechanism of pulse train excitation
found for bound state potentials still holds in the presence of electronic coupling.

The described interference effects appearing in the spectroscopical signals after pulse train excitation, show that a rethinking is required in the interpretation of pulse train control experiments.
On the other hand, the different aspects of pulse train control offer a manifold of
new applications in various fields of spectroscopy.
Parallels to experiments, applying pulse trains under different conditions,
like for example nonresonant excitation, lead to the assumption, that the introduced effects
are more general.
Pulse trains in spectroscopy may enhance the sensitivity and the selectivity of spectral features and could be applied to achieve higher contrast in coherent microscopy.
By selective damping of near-resonant modes, application of pulse trains in combination with transient spectroscopy could provide access to the direct observation of dynamical processes.
Furthermore, the characteristic response to parameter variations under pulse train excitation
can serve to differentiate between vibrational and electronic origins of spectral features.
It is this method, that is used in the present work
to apply quantum control spectroscopy
to the early steps of the photochemical process in beta-carotene, i.e. the energy loss channel due to quenching via a conical intersection.

Based on experimental observations,
by the described modular construction
a model system for beta-carotene is proposed, comprising the
key components of the induced photochemical energy transfer process during the first few hundred femtoseconds.
The outcome of quantum control experiments of beta-carotene could be predicted and interpreted.
By comparison with results of quantum control experiments on beta-carotene,
performed in the group of M.~Motzkus (Heidelberg University),
it is possible to verify the key assumptions made for the construction of the model system.
Observed spectral features in dependance of the parameters b and c can be definitely assigned to vibrational coherences,
indicating that a low frequency mode is responsible for the electronic coupling
between the excited states S2 and S1 of beta-carotene.
The achieved agreement between simulations and experimental results
allow to conclude that the process of investigation is described well within the constructed
beta-carotene model.
The photochemical quenching process takes place on solely two excited states and no further electronic state plays a mentionable role.