Measuring second Chern number from non-adiabatic effects

Abstract

The geometry and topology of quantum systems have deep connections to quantum dynamics. In this paper, I show how to measure the non-Abelian Berry curvature and its related topological invariant, the second Chern number, using dynamical techniques. The second Chern number is the defining topological characteristic of the four-dimensional generalization of the quantum Hall effect and has relevance in systems from three-dimensional topological insulators to Yang-Mills field theory. I illustrate its measurement using the simple example of a spin-3/2 particle in an electric quadrupole field. I show how one can dynamically measure diagonal components of the Berry curvature in an over-complete basis of the degenerate ground state space and use this to extract the full non-Abelian Berry curvature. I also show that one can accomplish the same ideas by stochastically averaging over random initial states in the degenerate ground state manifold. Finally I show how this system can be manufactured and the topological invariant measured in a variety of realistic systems, from superconducting qubits to trapped ions and cold atoms.

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Cited by in corpus (19)

• Geometry and non-adiabatic response in quantum and classical systems
• Thouless pumping and topology
• Observation of a non-Abelian Yang Monopole: From New Chern Numbers to a Topological Transition
• Adiabatic Perturbation Theory and Geometry of Periodically-Driven Systems
• Second Chern Number and Non-Abelian Berry Phase in Topological Superconducting Systems
• A comprehensive review on developments of synthetic dimensions
• Emergence of non-abelian magnetic monopoles in a quantum impurity problem
• Non-Abelian tensor Berry connections in multi-band topological systems
• Direct measurement of quantum Fisher information
• Non-Abelian monopoles in the multiterminal Josephson effect
• Topology of a dissipative spin: dynamical Chern number, bath induced non-adiabaticity and a quantum dynamo effect
• Extracting non-Abelian quantum metric tensor and its related Chern numbers
• Counterdiabatic control of transport in a synthetic tight-binding lattice
• Superfluid Vortices in Four Spatial Dimensions
• Non-Abelian quantum geometric tensor in degenerate topological semimetals
• Topological Electromagnetic Effects and Higher Second Chern Numbers in Four-Dimensional Gapped Phases
• Yang monopoles and emergent three-dimensional topological defects in interacting bosons
• Curved vortex surfaces in four-dimensional superfluids: I. Unequal-frequency double rotations
• Curved vortex surfaces in four-dimensional superfluids: II. Equal-frequency double rotations