## Dynamics and Characterization of Composite Quantum SystemsThis thesis sheds new light on the fascinating properties of composite quantum systems. Quantum systems of different sizes, ranging from small bipartite systems to large many-body ensembles, can be studied with the help of modern quantum optical experiments. These experiments make it possible to observe a broad variety of striking features, including nonclassical correlations, complex dynamics and quantum phase transitions. By adopting the complementary perspectives of quantum information theory, quantum chemistry and many-body theory, the thesis develops new methods for the efficient characterization and description of interacting, composite quantum systems. |

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### Contents

1 | |

2 Local Detection of Correlations in Composite Quantum Systems | 69 |

Behavior of Correlated Quantum States | 129 |

4 Quantum Phase Transition in a Family of Quantum Magnets | 151 |

5 Multidimensional Nonlinear Spectroscopy of Controllable Quantum Systems | 201 |

6 Open Quantum Systems of Identical Particles | 257 |

7 Summary and Conclusions | 311 |

Appendix A Derivation of the Bosonic Master Eq 6151 | 315 |

Appendix B Representation of DoubleCommutator Terms in a Larger Basis | 331 |

Appendix C Transformation Properties of InteractionPicture Operators | 334 |

Appendix Curriculum Vitae | 344 |

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### Common terms and phrases

ansatz approximation arbitrary atoms bipartite Bose–Einstein condensate bosonic Breuer Buchleitner classical Cohen-Tannoudji collective dephasing Composite Quantum Systems contributions controllable quantum systems coupling decay decoherence degrees of freedom density matrix dephasing dephasing operation described detection discussed distribution dynamics effective eigenbasis electronic entanglement environment evolution expectation value experimental experiments ferromagnetic frequency function Gessner ground Häffner Hamiltonian Hilbert space incoherent induced initial interaction laser Lett limit magnetic field master equation mean-field measurement methods modes multipartite N-particle nonlinear spectroscopy nonzero observable obtain open quantum systems oscillations parameters partial trace particles photon Phys population potential pulses quantum coherence quantum coherence signal quantum computations quantum discord quantum information quantum mechanical quantum optical quantum phase transition quantum simulations qubit readout resonances Schlawin Sect semiclassical sideband single quantum coherence single-particle spectral spin subspace subsystem symmetric theoretical theory trace distance trapped ions trapped-ion two-particle yields