Executive Summary : | The study of attosecond laser induced electron correlation driven dynamics in many electron systems is a topic of significant relevance. This is primarily because electronic motion forms the basis of controlling a chemical reaction, preparing qubits for quantum computation or building solar cells. In this spirit, we would like to further probe into the electron dynamics by studying non-linear quantum optical interactions in the attosecond regime. In the current proposal, we would like to theoretically investigate electron correlation driven dynamics, within the attosecond regime, by using a conventional non-linear optical spectroscopic techniques like four wave mixing (FWM). The proposal focuses on two important aspects. Firstly, to theoretically investigate the effects of different types of electron dynamics on the FWM signal. Secondly, how FWM may influence the electron dynamics through the multiple couplings associated with this technique. Based on the two-fold perspective, we would address to few pertinent issues. It would be a matter of interest to study the effects of core-excited state wavepackets on FWM spectra and to explore the possibility of manipulating the time evolution and constitution of decaying core-excited state wavepackets using FWM. Our work will probe into the effects of non-adiabatic (NA) interaction between excited vibronic states on FWM spectra. In the attosecond regime intense laser induced Rabi oscillations causes dynamic interference between electrons released into the continuum at two different times. The possibility of both probing and manipulating dynamic interference using FWM spectroscopy is a pertinent issue to be addressed. Due to the broad bandwidth of the attosecond pulses probability of excitation of non-resonant states are high and the effects of these non-resonant states are manifested through Stark shift in the electron spectra. It would be of interest to look for signatures of this dynamic shift in the FWM signal and make a reasonable estimation of this dynamic Stark shift. Manipulation of quantum coherence in atomic and molecular systems continues to be an attractive research problem. Investigation of quantum coherence induced Electro magnetically induced transparency (EIT) under an attosecond pulse set up is not thoroughly studied and exploration of this can lead us to rich Physics. To theoretically model these important issues both Essential states as well as density matrix-based methods are to be implemented. The project involves creation and manipulation of coherent superpositions, monitoring the evolution and transfer of coherence etc. These aspects are widely significant from the context of both controlling chemical reactions as well as creating qubits for quantum information processing. Moreover, the study of quantum optical effects like EIT and EIA in the ultrashort time scale can have potential applications in optical switches. |