## Quantum-Enhanced Nonlinear SpectroscopyThis 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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### Contents

1 | |

2 Nonlinear Optical Signals | 35 |

3 Excited State Distributions and Fluorescence Signals | 92 |

4 PumpProbe Measurements with Entangled Photons | 143 |

5 Interferometric Setups | 167 |

6 Frequency Conversion | 190 |

7 Trapped Ion Spectroscopy | 205 |

8 Conclusions and Outlook | 233 |

Appendix A Parametric Downconversion | 239 |

Appendix B The Bacterial Reaction Center of | 255 |

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### Common terms and phrases

absorption signal anharmonic beam Chem classical light coherent contribution coupling created de-excitation degrees of freedom denotes density matrix depicted derivation detected dipole discussion dispersed dissertation downconversion dynamics Dyson series electronic energy entangled photon pairs excitation pathways exciton f-state field correlation function final fluorescence signal four-point correlation function frequency correlations frequency domain Hamiltonian Hence Hermite functions Hilbert space interaction intermediate ion chain laser Lett light field loop diagrams matter correlation function matter system measurement molecular Mukamel nonlinear optical nonlinear signals nonlinear spectroscopy observe obtain off-resonant oscillations panel parameters phase photon number Phys probe pump bandwidth pump frequency pump pulse pump-probe signal quantum coherence quantum computation quantum optics quantum systems Raman pathways regime resonance sample system Schlawin Schmidt modes Sect setup simulations single-exciton ſº spectral superoperator transition amplitudes transport trapped ions two-dimensional two-exciton two-photon absorption ultrafast wavefunction wavepackets wsum