Lez #43+44 IRS signal. RRS under different pulse temporal profile

 We investigated the IRS1 response under various resonance conditions, demonstrating that the resulting lineshapes - positive, negative or dispersive - depend on the Raman pump wavelength relative to the sample's absorption and the probed vibrational mode.

Then, we derived an expression for the RRS signal as a function of arbitrary spectral profiles of the Raman pump and probe pulses. This formula was then used to numerically evaluate the Raman gain under different experimental conditions, specifically varying the pump pulse temporal profile and its relative delay with respect to the probe.

Lez #41+42 DephasingII SRS blue side

 Final considerations on dephasing. Homogeneous and inhomogeneous limits (fast and slow modulation regimes) and motional narrowing. Spectral line shapes: Lorentzian, Gaussian, and Voigt. Derivation of the SRS response in the blu side (IRS diagram) for a monochromatic pump and a generic Stokes beam

Lez #39+40 Dephasing

We discussed from a microscopic point of view how out-of-diagonal elements of the density matrix are damped due to the interaction with the environment. As a reference, you can use chapter 5 of the “Principles of Nonlinear Optical Spectroscopy: A Practical Approach” by P. Hamm

Lez #37+38 FSRS I: Heme proteins and molecular movies

 We introduced the Femtosecond Stimulated Raman Scattering (FSRS) experimental scheme, where SRS is exploited to track the evolution of a system upon the photoexcitation of an Actinic pump pulse, preceding the Raman and Stokes pair. The experimental layout has been introduced and the temporal/spectral resolutions of FSRS have been compared with the time-resolved spontaneous Raman counterpart. Then we started to discuss the paradigmatic case of Myoglobin, where FSRS has been exploited to: i) interpret transient absorption experiments to discriminate between two possible contrasting scenarios related to the existence of transient electronic states vs vibrational cooling. ii) determine how the absorbed photon energy, initially stored in delocalized low frequency heme modes, is very efficiently funneled into specific high frequency modes prior to slow dissipation through the protein 

Lez #35+36 SRS signals

 We evaluated the SRS (RRS1 diagram) response in resonant and non resonant case, for monochromatic Raman pump and probe beams.

Lez #33+34 Diagrams for 3rd order processes: pump-probe and stimulated Raman

We re-discussed the pump probe response (stimulated emission (SE), bleaching and excited state absorption (ESA)) commenting on the differences between bleaching and SE. 

We then derived the double sided Feynman diagrams associated with stimulated Raman processes, i.e. for a three level systems (2 electronic states, with the ground state having 2 vibrational levels) in presence of two different pulses, namely the Raman pulse and the Stokes pulse, detecting the heterodyne response arising on top of the stokes beam.

Lez #31+32 Double sided Feynman diagrams: linear absorption and introduction to 3rd order

 We introduced the double sided Feynman diagrams to describe the perturbative expansion of the polarization, end explicitly evaluated the linear absorption of a two level system.

We started to extend the same approach to third order processes. Among them, pump-probe experiments with the first 2 simultaneous interactions with the pump, and the third interaction with a probe.

Lez #29+30 Radiation - matter, rabi oscillations, perturbative expansion

  Today we recalled the basic concepts of quantum mechanics, introducing the density matrix. We stressed the importance  of density matrix to describe statistical mixtures, and how this is not possible through an eigenstates superposition (for instance a two level system).

We discussed how to solve Bloch equation and Rabi oscillation, introducing the rotating wave approximation to neglect some terms in the integration.

We then introduced Shroedinger, Heisenberg and Interaction schemes (in this latter both eigenfunctions and operators evolve, and the temporal evolution related to the unperturbed Hamiltonian is removed from the wavefunction). Then it makes sense a perturbative expansion of the eigenfunctions and of the density matrix in the Interactions scheme. Finally, we went back to the Shroedinger scheme.

Please refer to the first part of the notes added to classroom.