## Final Report Summary - YTTERBIUMSPINLATTICE (Ultracold atoms in state-dependent optical lattices for realizing novel classes of interacting spin systems and artificial gauge fields)

Ultracold atoms in optical lattices are a novel method of approaching many-body systems of strongly correlated particles, a scenario usually encountered in the context of interacting electrons in condensed matter systems. Many of these complex many-body states are notoriously hard to study, as strong interactions and correlations make a general theoretical description impossible. Ultracold atoms in lattices serve as model systems with a well-known Hamiltonian on the microscopic level, allowing for a careful analysis of those types of interacting systems for which a suitable Hamiltonian can be implemented.

In this project, significant progress has been made towards the expansion of the range of phenomena accessible for implementation with ultracold atoms. Our strategy is to combine a setup of ultracold ytterbium atoms with state-dependent optical lattice potentials. The electronic structure of ytterbium gives rise to an extremely long-lived excited state and a high degree of decoupling of the nuclear spin from the electronic states (see Figure 1). These two properties are central for several new approaches to implement new classes of quantum systems. Our experiment is focused on three specific systems, which are so far not reachable by using the current state of the art implementations with Alkali atoms: (1) to realize a Kondo model, relevant for example for heavy-fermion materials, which exhibit complex phase diagrams which are not yet fully understood (2) realizing a many body system with particles of half-integer spin larger than 1⁄2, exhibiting enlarged SU(N) symmetry, with complex spin-correlated quantum phases which are as yet inaccessible, often even by theoretical methods, and (3) to enable the creation of strong artificial gauge fields in optical lattices while avoiding the heating effects present in Alkali atom implementations. Artificial gauge fields are important for quantum simulation, as they can provide effective magnetic fields for neutral atoms, which is necessary to investigate any phenomenon analog to electrons in magnetic fields.

The main part of the project consisted of building the experimental setup for generating and controlling a cloud of ultracold ytterbium atoms and the generation of suitable optical potentials. The most notable experimental achievements are:

1) Building of an experimental setup capable of trapping and cooling any stable isotope of ytterbium.

2) Generating a Bose-Einstein condensate from a cloud of ytterbium-174 atoms.

3) Generating a Fermi-degenerate gas of ytterbium-173 atoms.

4) The implementation of a 3D optical lattice suitable for ytterbium atoms.

5) Measurement of the nuclear-spin state of ytterbium using an optical-Stern-Gerlach technique.

6) Control of the nuclear spin states via optical pumping.

7) The construction of a laser with ultra-narrow linewidth (~60Hz) for exciting the long-lived 3P0 transition.

8) Nunclear-spin state selective excitation to 3P0 states.

9) Inducing coherent oscillations on the 3P0 state (also nuclear-spin state selective).

These ingredients form the main part of the technical requirements for the target experiments mentioned above (Kondo lattice, SU(N) symmetry, gauge fields).

Another important prerequisite for these experiments is the determination of some (fundamental) properties of ytterbium itself, as some of these had never been investigated before. For our proposed experiments the spin-exchange interaction (Vex) between ytterbium atoms in the 3P0 state and the 1S0 state plays an important role. In the course of our investigations we discovered that Vex for ytterbium-173 is remarkably high compared to most other atoms. It is in fact so high that it might have a serious impact on the experimental strategy how to use the Vex for implementing the desired Hamiltonians. As this was the first direct observation of Vex for ytterbium, or even for any quantum gas, and that the result can have a large impact on the experimental strategies of our and other groups, we spent a large amount of time characterizing this specific property.

For this result, experimentally we measured directly the spin-exchanging interactions in a two-orbital SU(N)-symmetric quantum gas of ytterbium in an optical lattice. The two orbital states are represented by two different (meta-)stable electronic configurations of fermionic ytterbium-173. A strong spin-exchange between particles in the two separate orbitals was mediated by the contact interaction between atoms, which we characterized by clock shift spectroscopy in a 3D optical lattice. We found the system to be SU(N)-symmetric within our measurement precision and characterized all relevant scattering channels for atom pairs in combinations of the ground and the excited state. Elastic scattering between the orbitals is dominated by the antisymmetric channel, which leads to the strong spin-exchange coupling. The exchange process was directly observed, by characterizing the dynamic equilibration of spin imbalances between two large ensembles in the two orbital states, as well as indirectly in atom pairs via interaction shift spectroscopy in a 3D lattice. The realization of a stable SU(N)-symmetric two-orbital Hubbard Hamiltonian has now opened the route towards experimental quantum simulation of condensed-matter models based on orbital interactions, such as the Kondo lattice model.

This result should be considered the most important achievement of the Marie Curie project. It is submitted for publication, with a preprint available online. The project will continue after the end of the Marie Curie funding period to further pursue the original goals.

In this project, significant progress has been made towards the expansion of the range of phenomena accessible for implementation with ultracold atoms. Our strategy is to combine a setup of ultracold ytterbium atoms with state-dependent optical lattice potentials. The electronic structure of ytterbium gives rise to an extremely long-lived excited state and a high degree of decoupling of the nuclear spin from the electronic states (see Figure 1). These two properties are central for several new approaches to implement new classes of quantum systems. Our experiment is focused on three specific systems, which are so far not reachable by using the current state of the art implementations with Alkali atoms: (1) to realize a Kondo model, relevant for example for heavy-fermion materials, which exhibit complex phase diagrams which are not yet fully understood (2) realizing a many body system with particles of half-integer spin larger than 1⁄2, exhibiting enlarged SU(N) symmetry, with complex spin-correlated quantum phases which are as yet inaccessible, often even by theoretical methods, and (3) to enable the creation of strong artificial gauge fields in optical lattices while avoiding the heating effects present in Alkali atom implementations. Artificial gauge fields are important for quantum simulation, as they can provide effective magnetic fields for neutral atoms, which is necessary to investigate any phenomenon analog to electrons in magnetic fields.

The main part of the project consisted of building the experimental setup for generating and controlling a cloud of ultracold ytterbium atoms and the generation of suitable optical potentials. The most notable experimental achievements are:

1) Building of an experimental setup capable of trapping and cooling any stable isotope of ytterbium.

2) Generating a Bose-Einstein condensate from a cloud of ytterbium-174 atoms.

3) Generating a Fermi-degenerate gas of ytterbium-173 atoms.

4) The implementation of a 3D optical lattice suitable for ytterbium atoms.

5) Measurement of the nuclear-spin state of ytterbium using an optical-Stern-Gerlach technique.

6) Control of the nuclear spin states via optical pumping.

7) The construction of a laser with ultra-narrow linewidth (~60Hz) for exciting the long-lived 3P0 transition.

8) Nunclear-spin state selective excitation to 3P0 states.

9) Inducing coherent oscillations on the 3P0 state (also nuclear-spin state selective).

These ingredients form the main part of the technical requirements for the target experiments mentioned above (Kondo lattice, SU(N) symmetry, gauge fields).

Another important prerequisite for these experiments is the determination of some (fundamental) properties of ytterbium itself, as some of these had never been investigated before. For our proposed experiments the spin-exchange interaction (Vex) between ytterbium atoms in the 3P0 state and the 1S0 state plays an important role. In the course of our investigations we discovered that Vex for ytterbium-173 is remarkably high compared to most other atoms. It is in fact so high that it might have a serious impact on the experimental strategy how to use the Vex for implementing the desired Hamiltonians. As this was the first direct observation of Vex for ytterbium, or even for any quantum gas, and that the result can have a large impact on the experimental strategies of our and other groups, we spent a large amount of time characterizing this specific property.

For this result, experimentally we measured directly the spin-exchanging interactions in a two-orbital SU(N)-symmetric quantum gas of ytterbium in an optical lattice. The two orbital states are represented by two different (meta-)stable electronic configurations of fermionic ytterbium-173. A strong spin-exchange between particles in the two separate orbitals was mediated by the contact interaction between atoms, which we characterized by clock shift spectroscopy in a 3D optical lattice. We found the system to be SU(N)-symmetric within our measurement precision and characterized all relevant scattering channels for atom pairs in combinations of the ground and the excited state. Elastic scattering between the orbitals is dominated by the antisymmetric channel, which leads to the strong spin-exchange coupling. The exchange process was directly observed, by characterizing the dynamic equilibration of spin imbalances between two large ensembles in the two orbital states, as well as indirectly in atom pairs via interaction shift spectroscopy in a 3D lattice. The realization of a stable SU(N)-symmetric two-orbital Hubbard Hamiltonian has now opened the route towards experimental quantum simulation of condensed-matter models based on orbital interactions, such as the Kondo lattice model.

This result should be considered the most important achievement of the Marie Curie project. It is submitted for publication, with a preprint available online. The project will continue after the end of the Marie Curie funding period to further pursue the original goals.