Event time:
Friday, August 1, 2025 - 11:00am to 12:00pm
Audience:
YQI Researchers
Event description:
Quantum Morse-Smale topology for Kerr-Cat qubits
We bring the classical nonlinear vector flow topology to the quantum realm. In this talk, I show how the topological features of classical nonlinear flows persist in the quantum regime of driven- dissipative systems. Using the master equation description, spectral theory of Liouvillians, and quantum trajectory unravelings, we uncover how quantum steady states retain signatures of the underlying topological flow through long-lived Liouvillian eigenmodes. This dynamical topology perspective reveals fundamental differences between unraveled and ensemble-averaged descriptions, uncovering the topological origin of phase transitions—even without Liouvillian gap closure. We further discuss the intriguing interplay between topological structure and multiphoton resonances, a purely quantum effect with no classical analog. This work bridges classical and quantum perspectives, offering a new framework for identifying and classifying nonequilibrium quantum phases.
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