Quantum optical implementations of gauge-invariant dynamics

Current technologies for realising small-scale quantum computing devices are quickly evolving, and the launch of a 1 billion European flagship funding scheme for quantum technologies in 2018 will provide an additional boost for this field. This rapid development calls for meaningful and practical applications for small to medium sized systems. The Elise Richter project advocates and explores the use of such platforms for quantum simulations of so-called gauge theories. Gauge theories play a central role in many branches of physics and describe the fundamental interactions between elementary particles (a prominent example is QCD - quantum chromodynamics which describes the interaction between quarks and gluons). Due to fundamental reasons, the calculation of dynamical processes within such theories is extremely hard. This difficulty limits simulations that can be performed on classical computers to date and inspired the idea to use quantum simulators to complement existing numerical methods. The Elise Richter project will take the endeavour to design quantum simulators for gauge theories from the realm of ideas and concepts to proof-of-principle realisations in the lab. The key-element for realising this critical step will be the hardware-adapted design of such quantum simulation schemes that are custom-tailored to specific platforms. Dedicated quantum optical methods developed by the PI will enable resource efficient experimental proposals that mesh with the available technology. In a recent collaboration with an experimental ion group in Innsbruck, such a hardware-adapted design developed by the PI led to the first proof-of-principle demonstration in this field [Nature 534, 516-519 (2016)], where a one-dimensional theory has been realised. While providing a first stepping stone in uncharted territory, it leaves grand challenges of the field open, including the quantum simulation of theories that include color- degrees of freedom (as in quantum chromodynamics) and realisations beyond one spatial dimension. The Elise Richter project will address these two major research objectives and open up qualitatively new areas compared to the first demonstration. The two main quantum optical systems under consideration are trapped ions and cold atoms in optical lattices. Besides the quest to find platform-specific solutions for realising different types of gauge theories, a complimentary research line of the proposed project aims at the development of suitable simulation software that can be used to emulate various dynamical effects.