Quantum simulators for relativistic quantum fields in curved spaces with defective optical lattices and graphenes

• Applicant: Dr. Nikodem Szpak
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields ; Theoretical Condensed Matter Physics
• Term: from 2013 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 242272380

In this project, we plan to design new types of quantum simulators for relativistic quantum fields living in curved spaces. They will be based on discrete physical systems like crystals or optical lattices containing structural and topological defects. Formulation of their effective models in terms of continuous fields, obtained by the application of discrete differential geometry and continuous theory of defects, will lead to various types of quantum fields coupled to emergent curvature and torsion. The natural areas of their application are ultra-cold atoms in optical lattices and electrons in graphene. The design of defective optical lattices and their application as simulators for curved spaces presents a completely new idea, whereas in the case of graphene, the geometric interpretation of defects has already been considered but requires further research. The key benefits of this project are expected to be threefold: First, to provide an efficient and easy-to-use geometric language for the classification, description and modeling of various types of lattice irregularities (defects, strain, etc.) and of phenomena appearing due to the curved lattice geometry (scattering, bound states, etc.). Second, to relate these models to the field theories of fundamental physics which, in this way, can be simulated using present-technology lattice devices with specially prepared geometries (e.g., coupling of quantum fields to torsion is still under debate and is not accessible experimentally otherwise). Third, to obtain an improvement in the general understanding of the implications of defects in crystalline structures on their physical properties and of the purposive use of the defects in the engineering of new materials.Furthermore, we also plan to consider time-dependent lattice deformations, especially in optical lattices, which should facilitate the simulation of lower dimensional analogs of gravitational (metric) waves. This will open the way for the proposal of a first-of-a-kind simulator of quantum geometry for quantum fields. The project should also generally contribute to a better understanding of the fundamental properties of matter through the study of conceptual questions related to the emergence of the relativistic behavior, mass and spin in lattice systems with variable structure.

• DFG Programme: Research Grants