Optimal measurement precision of a nonlinear interferometer

TL;DR

This paper investigates the fundamental limits of measurement precision in a nonlinear bosonic interferometer, showing that the Heisenberg limit can often be maintained despite nonlinear interactions and tunneling effects.

Contribution

It introduces time independent perturbation theory to analyze measurement precision in a nonlinear interferometer, demonstrating conditions under which the Heisenberg limit is preserved.

Findings

Heisenberg limit scaling is often maintained despite nonlinearity and tunneling.

Perturbation theory effectively analyzes measurement precision in complex quantum systems.

Optimal measurement precision can be achieved without violating fundamental quantum limits.

Abstract

We study the best attainable measurement precision when a double-well trap with bosons inside acts as an interferometer to measure the energy difference of the atoms on the two sides of the trap. We introduce time independent perturbation theory as the main tool in both analytical arguments and numerical computations. Nonlinearity from atom-atom interactions will not indirectly allow the interferometer to beat the Heisenberg limit, but in many regimes of the operation the Heisenberg limit scaling of measurement precision is preserved in spite of added tunneling of the atoms and atom-atom interactions, often even with the optimal prefactor.