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Measuring the Second Chern Number from Nonadiabatic Effects.

Michael Kolodrubetz1

  • 1Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA; Department of Physics, University of California, Berkeley, California 94720, USA; and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.

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Summary
This summary is machine-generated.

This study introduces dynamical methods to measure the non-Abelian Berry curvature and the second Chern number in quantum systems. These topological invariants are crucial for understanding quantum Hall effects and topological insulators.

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Area of Science:

  • Quantum Physics
  • Condensed Matter Physics
  • Quantum Information

Background:

  • Quantum geometry and topology are intrinsically linked to quantum dynamics.
  • Topological invariants like the second Chern number characterize exotic quantum phenomena.

Purpose of the Study:

  • To develop and demonstrate dynamical techniques for measuring non-Abelian Berry curvature.
  • To extract the second Chern number, a key topological invariant, using quantum dynamics.

Main Methods:

  • Utilizing dynamical measurements of Berry curvature components in a degenerate ground state space.
  • Employing stochastic averaging over random initial states for topological invariant extraction.
  • Illustrating the method with a spin-3/2 particle in an electric quadrupole field.

Main Results:

  • Successfully demonstrated dynamic measurement of non-Abelian Berry curvature.
  • Showcased the extraction of the second Chern number via dynamical techniques.
  • Validated the measurement approach in a simplified quantum system.

Conclusions:

  • Dynamical methods offer a viable pathway to measure topological invariants in quantum systems.
  • The proposed techniques are applicable to realistic systems like superconducting qubits, trapped ions, and cold atoms.
  • This work bridges the gap between quantum topology and experimental measurement through dynamics.