Proportional–integral–derivative (PID) control is the workhorse of classical feedback electronics, used to hold a quantity at a set value. Alberto Hijano and Tero Heikkilä of QMAT's Condensed Matter Theory group at the University of Jyväskylä have extended quantum feedback theory to include the derivative and integral terms, and studied their effect in an optomechanical system.

They show how these terms shape both the transient and the steady-state amplitude and squeezing of a mechanical quadrature. Unlike standard proportional feedback, derivative feedback affects both conditional and unconditional squeezing. Feedback can also make a mechanical quadrature track a desired reference signal. The results suggest new routes to better quantum state control and measurement precision.

The preprint has not yet been peer reviewed.

Image: QMAT