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Atom-by-Atom Quantum Control of Fermions in Arbitrary Potentials

Periodic Reporting for period 1 - FermiTrap (Atom-by-Atom Quantum Control of Fermions in Arbitrary Potentials)

Reporting period: 2016-04-01 to 2018-03-31

Understanding quantum mechanical systems of many particles is one of the big challenges in physics, with implications for chemistry, material design, condensed matter and information processing. Experiments with ultracold atoms enable us to experimentally create, manipulate and probe quantum many-body systems. Such experiments serve as important benchmarks for theories and thus underpin our fundamental understanding of quantum mechanics. The technological developments associated with the experiments also enable new practical use cases and devices, for example in atomic clocks, quantum sensing, cryptography and information processing. Our overall goal is to further push the experimental control over quantum many-body systems and utilize this control to harness quantum effects for new materials, devices etc.

The main result of the action is the development of novel methods to image and characterize quantum states on the single-particle level. By now, many groups have been successful in imaging quantum gases with single-particle resolution, typically in optical lattices. Such measurements come with significant technical difficulties and only give access to position ordering of the underlying particles - one obtains a snapshot of the instantaneous distribution of particles. For many physical phenomena, most notably superfluidity, it is not the positions but rather the velocities (or momenta) or the particles that encode the crucial information about the quantum state, which is lost with conventional imaging methods.

Our new approach enables to image both the position as well as the velocity distribution of individual particles in a quantum state in a technically much more straightforward manner. This technique makes microscopic access to quantum states available to many more groups working in the field and gives new observables for quantum states of itinerant particles. In particular, we showed that it is possible to access the entanglement properties of the Fermi-Hubbard dimer through spin-resolved correlation measurements in momentum and position space.

Our results fit within the broader framework of simulating quantum materials with ultracold atoms, where the microscopic ingredients are highly controlled and understood. Eventually, such approaches will lead to new materials and coherent control of their properties, which may for example be relevant for improved speed of information storage in memory.
I worked on the implementation of highly controlled few-fermion systems on the lithium 6 machine in the group of Prof. Selim Jochim.

The first component of the work consisted of implementing highly tunable optical potentials in tweezer configurations. An SLM-based setup was realized in a test setup and incorporated into a lithium machine to generate arrays of optically defined microtraps. The full calibration of the setup is ongoing. We also realized time-dependent rotating trap based on interference of frequency-mismatched custom shaped laser beams. This work is aimed at creating fractional quantum Hall states of fermions and was performed by the Masters student Lukas Palm under my supervision. There are no publications related to this work yet.

The second component of the work concerns single-particle resolved detection of correlations in cold atom systems. We developed a technique to image individual lithium atoms in fluorescence imaging in free space. This method is much simpler than previously developed schemes and enables new ways of probing quantum gases. In particular, single atoms can be imaged in a spin-resolved way without any confining potentials, such that single-particle detection in time-of-flight becomes possible. Many-body systems can thus be characterized via their spin-resolved momentum correlation functions. This work is published in PRA (Phys. Rev. A 97, 063613 (2018))

We used this technique to probe equilibrium states of a Fermi Hubbard dimer in position and momentum space with access to its entanglement properties. The key result of our work is the particle-resolved detection of a quantum state in conjugate bases, position and momentum. We observe the emergence of entanglement in a simple model system (the Fermi Hubbard dimer) with repulsive and attractive interactions and clarify the dependence of entanglement on the chosen partitioning scheme. Our work is currently under peer review and available on the preprint server arXiv.org at https://arxiv.org/abs/1807.06405

We are already implementing our new imaging technique in a second experiment and anticipate that it will be widely used for atomic superfluids, where coherence properties are uniquely encoded in momentum correlations.

One of the most fruitful applications of our detection scheme will be qualitatively new studies of the BEC-BCS crossover regime, where strongly interacting fermions form different types of superfluids. As an outcome of the action, we will be able to study such systems in the few-body regime in the future and we have already performed several preparatory experiments in the many-body regime in quasi-two-dimensional Fermi gases. We experimentally explored the regime of strong interactions in two dimensions using RF spectroscopy, revealing the presence of many-body pairs above the critical temperature for superfluidity (Science, 359, 452 (2018)). We observed the breaking of scale invariance in the frequency of the breathing mode (arXiv:1803.08879 (2018)) and its momentum space dynamics (arXiv:1805.04734 (2018)).

Throughout the action, I continued a theoretical collaboration initiated during my PhD with Yannick Meurice and co-workers on measurements of the central charge of the Bose-Hubbard model. This work is published in PRA (Phys. Rev. A, 96, 023603 (2017)).

In a broader context, I was involved in the activities of the Heidelberg Center for Quantum Dynamics by hosting the colloquium series for one year and co-organizing the interdisciplinary conference Beyond Digital Computing in Heidelberg.
I accumulated teaching experience by leading two seminar courses on AMO methods at the masters level and participated as a lecturer at a winter school.

We do not foresee commercial applications of our methods, but have shared our results widely with colleagues through conference talks and journal articles.
We have developed new methods to probe ultracold atoms on the single-atom level. Our approach will enable a simpler and more robust realization of quantum many-body systems for basic and applied research. In the long run, this will increase our understanding of quantum mechanics and help to develop new tools and materials based on quantum effects. Our approach, which makes single atoms and their correlations visible in raw images, also give very visual access to quantum mechanical phenomena and may help attract the broader public to basic research in quantum science.
A setup to detect individual lithium atoms in free space through fluorescence imaging