Ultracold atoms realize synthetic quantum systems at the intersection of condensed matter physics and quantum information science. With the advent of quantum gas microscopy, it has become possible to probe systems with condensed matter-like Hamiltonians at the level of individual particles. This offers exciting prospects for probing many-body systems with tools and protocols from few-mode quantum optics.

### Quantum gas assembly

Conventionally, ultracold gases are prepared via evaporative cooling, which has led to record low temperatures. However, typical entropies are still too large to observe some of the most interesting phases predicted to occur in optical lattice systems. Moreover, full control over which quantum state to initialize is still a challenge and sample preparation is slow.

We are pursuing alternative routes towards low-temperature phases via *quantum gas assembly. *Starting from individually cooled atoms, we will assemble lattice systems one-by-one with precise control over atomic density and spin configurations. We anticipate that this will open new avenues for the study of out-of-equilibrium scenarios and provide a testbed for recent theory advances. We also hope to reduce the time it takes to prepare an ultracold lattice system in order to provide better statistics for correlation observables.

**Random unitaries**

We are interested in new connections between quantum information theory and condensed matter physics. It has become clear that concepts originating from quantum information, for example entanglement entropy and the dynamics of quantum information, can generate new insights when applied to many-body systems. Cold atoms are the perfect experimental platform to explore these emerging connections.

An exciting way forwards is given by measurements in random bases: It turns out measuring a system in many different, randomly chosen bases and recording correlations between the outcomes can be a very effective way of probing many-body states. We are excited about implementing such random unitary protocols in optical lattice systems.