Laying a theoretical groundwork for quantum many-body systems under feedback control

Benjamin Lev, Professor of Physics and Applied Physics
Surya Ganguli, Associate Professor of Applied Physics, Senior Fellow at the Stanford Institute for HAI, and Associate Professor, by courtesy, of Neurobiology and of Electrical Engineering
Vedika Khemani, Associate Professor of Physics and Associate Professor, by courtesy, of Applied Physics
Hideo Mabuchi, Professor of Applied Physics and Denning Family Director, Stanford Arts Institute

Summary: Most technologies exist out of thermal equilibrium. This is trivially so in the context of electrically driven devices, but can result in quite sophisticated nonequilibrium situations when observation and actuation combine in a feedback loop. Feedback can create emergent capabilities of a dynamic system that would otherwise fall into boring or tragic equilibrium states. For example, consider the Air Force’s F-22, the first ‘supermaneuverable’ all-stealth fighter jet available to the US. The F-22 was purposefully designed to be aerodynamically unstable like the F-16 but even more so. The instability allows for rapid and extreme maneuvers, but the plane can- not stay aloft without feedback stabilization: A sophisticated interpretation of flight dynamics and actuation of control surfaces prevents crashes while enabling enhanced maneuverability.

We understand how ‘closing the feedback loop’ in the classical world can create novel dynamics and robust performance. However, much remains unknown about what feedback could do when applied to systems in the many-body quantum world. To enable the entanglement-based quantum engineering of tomorrow, learning to feedback-engineer quantum many-body systems is an important step we must begin to take.

Our collaboration will begin the search for answers to the following questions. How can we use feedback to create effective closed-loop (Hamiltonian or Lindbladian) dynamics with many-body properties not permitted in equilibrium contexts? In what way might such systems exhibit novel ‘nonequilibrium’ phase transitions, phases, or even classes of phases? Could feedback-engineered quantum dynamics prove advantageous for the processing or protection of quantum information? Could the many-body entanglement exhibited by these new phases be harnessed for remote sensing or the simulation of quantum materials and chemistry? We will benchmark this nascent theory using a multimode cavity QED apparatus, highlighting the dual theory/experiment nature of this new collaboration.