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Strongly correlated fermions in optical lattices with single-site resolution

Final Report Summary - FERMISITE (Strongly correlated fermions in optical lattices with single-site resolution)

State of the art and project objectives:
Ultracold atoms in optical lattices have evolved over the last years into an interdisciplinary tool for many-body solid state and quantum physics. To fully exploit the potential of ultracold atoms in quantum simulations, it is essential to image the correlated many-body systems with single-atom and single-site resolution. In the last years, in-situ-imaging with single-atom resolution has become available for bosonic atoms, but an experimental approach to reach single-site-resolved detection of fermions in an optical lattice was missing at the beginning of this project. An objective of this project was to extend the experimental methods, which were previously developed for bosonic rubidium atoms, to fermionic potassium-40 (K40). The goal was to detect and to manipulate fermionic quantum systems in an optical lattice with single-site and single-atom resolution. The new possibility of probing and manipulating strongly correlated fermionic atoms in a 2D lattice will allow to further exploit the potential of ultracold atoms as a quantum simulator, especially for the Fermi-Hubbard model, which is conjectured to be one of the key models in condensed matter physics for high-temperature superconductivity.

Progress of the project:
Previous to the beginning of this project, we had implemented single-site resolved imaging for bosonic rubidium atoms. Our experimental apparatus, including the microscope objective, had demonstrated to be fully functional, and in particular, to allow for a diffraction limited resolution of single atoms. The first task during the project consisted in the set-up and optimization of pre-cooling techniques for K40. We decided to implement an all-optical cooling scheme to follow an initial cooling with a 2D- and a 3D-magneto-optical trap (MOT). We capture approximately 1x10^7 of the coldest atoms of the 3D-MOT in a large-volume optical dipole trap which is formed by two crossed laser beams (power 2x100 W, waist 300 µm), and we transfer the atoms in a strongly focused dipole trap with a translatable focus over a distance of 15 cm into another section of our vacuum apparatus, which provides superior optical access. A final cooling stage of forced evaporation in a crossed-beam dipole trap is followed by the transfer to a vertical 1D-lattice potential, which separates the cloud in approximately 40 independent horizontal layers. The selection of a single layer of atoms is achieved by a spatially selective microwave transition in a strong magnetic field gradient. We reach a consistent spatial resolution far below the lattice spacing for several hours.
Our approach for a single-site resolved detection of fermionic potassium atoms relies on two essential techniques. The atoms need to fluoresce to generate a sufficiently large number of photons which can be the detected by a CCD camera, and we need to provide a cooling mechanism to prevent the atoms from tunneling between lattice sites during the imaging phase. Our originally proposed cooling method, which was based on an optical molasses, provided insufficient cooling rates to keep the atoms at the same lattice site. We contribute this to additional heating effects caused by a strong tensor light shift of the excited state in the optical lattice and by the absence of cycling transitions due to a small excited state hyperfine structure. Both problems are intrinsic to our atomic species, K40, and they made it necessary to redesign our imaging technique. As a consequence, we changed the laser wavelength to utilize a more favorable optical transition (D1 line instead of D2) for the generation of fluorescence photons, and we implemented two alternative cooling methods, i.e. degenerate Raman sideband cooling and electromagnetically-induced-transparency (EIT) cooling. We found that the cooling rates of EIT cooling outperformed degenerate Raman sideband cooling for our setup.

Main results of the project and potential impact:
The main result of the project is a newly developed, lattice based imaging method with single-site-resolved resolution for ultracold fermionic atoms (E. Haller et al., arXiv:1503.02005). The method combines two previously known technologies, electromagnetically-induced-transparency cooling and fluorescence imaging with single site resolution. It allows us to detect on average 1000 fluorescence photons from a single atom within 1.5 s, while keeping it close to the vibrational ground state of the optical lattice. A typical fluorescence image is depicted in Figure 1 (see below). We determined the optical resolution from the point spread function of single atoms to be 580 nm, which is approximately the expected diffraction limited value.
Gaining access to the in-trap atom distribution of the fermions with single-atom resolution will enable the precise characterization of spatial order, temperature, and entropy distribution of fermionic many-body states, such as fermionic Mott insulators, Band insulators, metallic phases or Néel antiferromagnets. The newly developed imaging method in an optical lattice potential enables a very precise measurement of the trap densities and correlation functions with single particle resolution, and will allow us and researchers worldwide to investigate the effect of local perturbations on the system by spatially resolving the ensuing dynamical in-trap evolution.