Control-objective dependence of nonclassical-state preparation

Determine which of the conventional LQG control objective—cooling and localization with respect to a fixed spatial reference point while penalizing feedback displacement—or the redesigned LQG control objective—cooling with respect to the feedback-shifted trapping potential—is more favorable for preparing nonclassical motional states, including macroscopic quantum superpositions, entangled states, and Fock states, according to the requirements of the relevant state-preparation protocol.

Background

The paper compares two LQG formulations for feedback cooling of a continuously monitored quantum harmonic oscillator whose trapping-potential minimum is shifted by feedback. The conventional cost function evaluates oscillator energy relative to a fixed origin and separately penalizes the displacement of the potential minimum, whereas the redesigned cost function evaluates energy relative to the instantaneous feedback-shifted potential. These costs therefore encode different physical control objectives rather than alternative implementations of the same optimization problem.

The authors establish that the redesigned LQG controller achieves lower steady-state phonon occupation than low-pass-filter feedback for the cooling objective studied. However, they do not determine which control objective is preferable when the goal is preparing nonclassical motional states. The unresolved comparison is explicitly stated to depend on the requirements of the particular state-preparation protocol and is left for future work.