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We propose an experimental setup of ultracold fermions in an optical lattice to determine the pairing gap in a superfluid state and the spin ordering in a Mott-insulating state. The idea is to apply a periodic modulation of the lattice potential and to use the thereby induced double occupancy to probe the system. We show by full time-dependent calculation using the adaptive time dependent density-matrix renormalization group method that the position of the peak in the spectrum of the induced double occupancy gives the pairing energy in a superfluid and the interaction energy in a Mott-insulator, respectively. In the Mott-insulator we relate the spectral weight of the peak to the spin ordering at finite temperature using perturbative calculations.
Understanding the magnetic response of the normal state of the cuprates is considered a key piece in solving the puzzle of their high-temperature superconductivity. The essential physics of these materials is believed to be captured by the Fermi-Hubb
The study of superfluid fermion pairs in a periodic potential has important ramifications for understanding superconductivity in crystalline materials. Using cold atomic gases, various condensed matter models can be studied in a highly controllable e
Observation of topological phases beyond two-dimension (2D) has been an open challenge for ultracold atoms. Here, we realize for the first time a 3D spin-orbit coupled nodal-line semimetal in an optical lattice and observe the bulk line nodes with ul
We demonstrate a probe for nearest-neighbor correlations of fermionic quantum gases in optical lattices. It gives access to spin and density configurations of adjacent sites and relies on creating additional doubly occupied sites by perturbative latt
The exchange coupling between quantum mechanical spins lies at the origin of quantum magnetism. We report on the observation of nearest-neighbor magnetic spin correlations emerging in the many-body state of a thermalized Fermi gas in an optical latti