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This thesis focuses on nonlinear spectroscopy from a quantum optics
perspective. First, it provides a detailed introduction to
nonlinear optical signals; starting from Glauber's photon counting
formalism, it establishes the diagrammatic formulation, which forms
the backbone of nonlinear molecular spectroscopy. The main body of
the thesis investigates the impact of quantum correlations in
entangled photon states on two-photon transitions, with a
particular focus on the time-energy uncertainty, which restricts
the possible simultaneous time and frequency resolution in
measurements. It found that this can be violated with entangled
light for individual transitions. The thesis then presents
simulations of possible experimental setups that could exploit this
quantum advantage. The final chapter is devoted to an application
of the rapidly growing field of multidimensional spectroscopy to
trapped ion chains, where it is employed to investigate
nonequilibrium properties in quantum simulations.
This thesis focuses on nonlinear spectroscopy from a quantum optics
perspective. First, it provides a detailed introduction to
nonlinear optical signals; starting from Glauber's photon counting
formalism, it establishes the diagrammatic formulation, which forms
the backbone of nonlinear molecular spectroscopy. The main body of
the thesis investigates the impact of quantum correlations in
entangled photon states on two-photon transitions, with a
particular focus on the time-energy uncertainty, which restricts
the possible simultaneous time and frequency resolution in
measurements. It found that this can be violated with entangled
light for individual transitions. The thesis then presents
simulations of possible experimental setups that could exploit this
quantum advantage. The final chapter is devoted to an application
of the rapidly growing field of multidimensional spectroscopy to
trapped ion chains, where it is employed to investigate
nonequilibrium properties in quantum simulations.
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