Coherent spectroscopy

In PC IV you have learnt about Bloch equations, Rabi oscillations and pulse sequences as an approach to extracting useful information on the structural and dynamical properties of matter based on the coherent interaction between nuclear or electronic spins and radio waves. In principle these approaches can be transferred to the domain of optical spectroscopy for the same purposes. Unfortunately, at optical frequencies one has to deal with different and much faster relaxation processes that destroy coherence. For example, in NMR, spontaneous emission is very slow, because of the ν3 scaling (where ν is the emitted frequency), such that its contribution to bringing the spin system into thermal equilibrium is negligible. On the contrary, at optical frequencies, spontaneous emission is one of the most important sources of decoherence. Nonetheless, progress in laser sources and techniques has provided a great deal of possibilities in the coherent manipulation of atoms and molecules that nowadays have important applications in areas as diverse as quantum information science and femtochemistry. 1 Rabi oscillations Rabi oscillations are a fundamental consequence of coherent light-matter interaction. In this context the term coherent implies that the light field has a well-defined temporal phase ωt+φ. Nowadays this is most commonly realized using laser light sources. Being able to observe Rabi oscillations in an experiment is a clear signature of strong light-matter interaction. (a) Consider Eqs. (1.96) and (1.97) from the lecture notes. These equations describe the temporal behaviour of a driven quantum mechanical system. Show that the equations can be reformulated as i dc1 d