# Ultracold Fermions in optical lattices

We study the physics of ultracold fermionic atoms in optical lattices. Our experimental apparatus is a highly controllable and versatile quantum simulator. Using this we emulate strongly correlated condensed-matter systems that are neither accessible for conventional experimental platforms nor computable.

For example, we simulate the Hubbard-Model, which offers an approach to the dynamics of many-body states in periodic potentials by breaking their behaviour down into two fundamental processes: The tunneling of particles to neighbouring lattice sites (t) and the interaction of two particles which occupy the same lattice site (U).

## Experimental setup

In our setup, we use the potassium isotope K40 in its lowest two hyperfine states to emulate spin-1/2 particles. This cloud of atomic vapor is cooled from room temperature to several nK using various cooling techniques. The resulting quantum degenerate gas is then loaded into a three-dimensional optical lattice, which is well described by a stack of two-dimensional Hubbard models. Finally, individual planes are observed using high-resolution absorption imaging combined with radio-frequency spectroscopy.

Using this detection scheme we are able to resolve the in-situ density distribution determining the equation of state for a single realization of the Hubbard model. By additionally varying the repulsive interaction strength using Feshbach resonances, we are able to detect the transition from a metal to a Mott insulator [10.1103/Phys-RevLett.116.175301].

## Bilayer Hubbard Model

The lattice structure of real materials such as bilayer graphene is composed of coupled layers. To investigate the effect of finite tunnel coupling to a neighbouring plane, we impose a superlattice along the vertical direction. Using the phase of the superlattice and both lattice depths as free parameters, we control the filling of each layer and the tunneling between the two coupled layers. By tuning the coupling strength inside each layer relative to the coupling strength between the two layers, we can control a crossover from a planar antiferromagnetically ordered Mott insulator to a band insulator of spin-singlets along the bonds between the layers [10.1038/s41586-020-03058-x].

## Student Projects

### Imprinting spin spirals into an ultracold Fermi gas (Nicola Wurz, Master Thesis, November 2016)

In this project Nicola developed a new experimental scheme to probe antiferromagnetic correlations in reciprocal space by imprinting periodic spin waves onto the atoms. To analyze the effect of the Ramsey-type sequence in a magnetic field gradient, she carried out numerical simulations of the one-dimensional Hubbard model with four sites. These showed that the SU(2)-symmetry of the initial state is an important prerequisite to fully unwind the antiferromagnetic order. In the second part of her project, the wavevector describing the periodic spin pattern was carefully adjusted to the diagonal of the two-dimensional lattice unit cell.

### Cavity design for high-power frequency doubling (Nick Klemmer, Bachelor Thesis, July 2018)

In his Bachelor thesis project, Nick designed and set up a cavity for high-power frequency doubling of an ultra-narrow-linewidth infrared laser. For this purpose, a LBO crystal is pumped in a monolithic bow-tie cavity that can be used as a narrow-linewidth high-power laser source of green light. This green laser was used in his following Master thesis to create and characterize an in-plane superlattice which can be used in the future to create topological or Floquet-driven systems.