Uhlmann number of mixed states in circuit QED

Inspired by the recent experimental realization of topological transitions in circuit quantum electrodynamics and the research interest in the generalization of mixed states of topological geometric phases, we propose a scheme for probing topological phase transitions at finite temperature, which consists of two transmon qubits. Measurements of the mixed geometry phase shift, i.e. 2 pi-discontinuous Uhlmann phase jumps, can verify the Uhlmann number of the simulated mixed state. By adjusting the systematic parameters, we are able to engineer a topological transition n(U) = 1 -> 0 at finite temperature before allowing the degeneracy in the Hamiltonian to pass from inside to the outside of the manifold. According to our estimates based on conservative experimental parameters, the measurements are experimentally solvable.

Automated summary

This study proposes a scheme for probing topological phase transitions at finite temperature using two transmon qubits. The Uhlmann number of the simulated mixed state can be verified by measuring the mixed geometry phase shift, which exhibits 2pi-discontinuous Uhlmann phase jumps. Based on estimates using conservative experimental parameters, the measurements are experimentally solvable.