Quantum geometry and non-adiabatic response

In this talk I will review the basic notions of quantum geometry encoded in the Berry curvature and the Fubini-Study metric tensor as well as the topological invariants associated with them: the Chern number and the Euler characteristic. I will discuss how the Berry curvature emerges as a Lorentz type force in an arbitrary parameter space, where parameters like e.g. components of the magnetic field play the role of coordinates, and constitutes a dynamical Hall type response. This allows one to measure it and hence the Chern number directly in a wide class of systems interacting or not. I will show recent experiments, which observe topological phase diagram in superconducting qubits based on these ideas, which can be mapped to the Haldane model (single qubit) and a more complicated four band model (two coupled qubits). Finally I will discuss that the metric tensor is closely related to the basic concept of the mass tensor for any type of motion and hence can be also directly measured.

Host: Victor Galitski