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Abstract
The preparation of excited many-body eigenstates is a central challenge in quantum simulation. In the Fermi–Hubbard model, the double well constitutes a local building block of a many body extended system. In this thesis, a controlled scheme for preparing two-particle eigenstates of a repulsively interacting fermions in a double-well system is developed and experimentally characterised using ultracold 40K atoms in an optical superlattice.
The preparation protocol exploits the use of varying Potential offset between the double well sites dynamically to prepare target eigenstates of the tilted double-well spectrum which is achieved by ramping the superlattice lattice phase and controlling optical lattice depths. This approach enables the preparation of the ground state |E₁⟩, the antisymmetric doublon |E₃⟩, which corresponds to a local η-pair, and the symmetric doublon |E₄⟩.
To quantify the quality of the preparation, a detection scheme based on resolved site occupation combined with dedicated reference measurements to account for detection offsets and residual imperfections. Repeated traversals of the avoided crossings amplify small preparation errors, while bootstrap resampling is used to determine the statistical uncertainties of the resulting fidelity estimator. The measured per-ramp fidelities are close to unity for all four investigated ramp configurations.
The resulting state-preparation fidelities are 0.998 ± 0.001 for |E₁⟩, 0.994 ± 0.002 for |E₃⟩, and 0.996 ± 0.002 for |E₄⟩. These results demonstrate high-fidelity control of two-particle eigenstates in the repulsive double-well system and establish the double-well eigenstates as well-controlled local building blocks for future preparation of extended η-paired states in optical lattices.