Optimal quantum sensing of the nonlinear bosonic interactions using Fock states

TL;DR

This paper develops optimal quantum sensing strategies using Fock states to measure nonlinear bosonic interactions, achieving improved precision scaling and enabling new insights into nonlinear quantum dynamics.

Contribution

It introduces the first optimal measurement protocols for sensing trilinear nonlinear interactions with Fock states, achieving a $N^{-1/3}$ scaling in estimation errors.

Findings

Optimal strategies for nonlinear coupling estimation derived.

Estimation error scales as $N^{-1/3}$ with particle number.

Applicable to bosonic systems like trapped ions and superconducting circuits.

Abstract

Nonlinear processes with individual quanta beyond bilinear interactions are essential for quantum technology with bosonic systems. Diverse coherent splitting and merging of quanta in them already manifest in the estimation of their nonlinear coupling from observed statistics. We derive non-trivial, but optimal strategies for sensing the basic and experimentally available trilinear interactions using non-classical particle-like Fock states as a probe and feasible measurement strategies. Remarkably, the optimal probing of nonlinear coupling reaches estimation errors scaled down with $N^{-1/3}$ for overall $N$ of quanta in specific but available high-quality Fock states in all interacting modes. It can reveal unexplored aspects of nonlinear dynamics relevant to using such nonlinear processes in bosonic experiments with trapped ions and superconducting circuits and opens further developments of quantum technology with them.