Measuring a topological transition in an artificial spin-1/2 system.

Area of Science:

• Quantum physics
• Condensed matter physics
• Superconducting circuits

Background:

• Topological properties in quantum systems are crucial for robust quantum information processing.
• Superconducting qubits offer a promising platform for exploring fundamental quantum phenomena.

Purpose of the Study:

• To measure the topological property, Chern number (C_{1}), of a two-level system Hamiltonian manifold using a superconducting qubit.
• To experimentally verify topological transitions in quantum systems.

Main Methods:

• Utilizing a superconducting qubit to form a two-level system.
• Manipulating Hamiltonian parameters along paths within a closed manifold.
• Extracting the Chern number (C_{1}) from the nonadiabatic response of the qubit.

Main Results:

• Observed a topological transition from C_{1}=1 to C_{1}=0 by adjusting the manifold.
• The measured Chern number (C_{1}) was quantized to within 2% accuracy on both sides of the transition.

Conclusions:

• Demonstrated experimental measurement of topological properties in superconducting qubits.
• Confirmed the ability to induce and observe topological transitions in a controlled quantum system.