Adiabatic Ramsey Interferometry for Measuring Weak Nonlinearities with Super-Heisenberg Precision

TL;DR

This paper introduces an adiabatic Ramsey interferometry method using the quantum Rabi model to detect weak nonlinearities in trapped ions with super-Heisenberg precision, even under thermal and dephasing conditions.

Contribution

It presents a novel interferometry technique that achieves super-Heisenberg scaling without requiring entangled initial states or perfect coherence.

Findings

Spin signal amplification by mean-phonon excitations enhances measurement precision.

Super-Heisenberg scaling is achievable even with thermal initial states.

High-precision estimation remains robust against weak spin-dephasing.

Abstract

We propose an adiabatic Ramsey interferometry technique for detecting weak nonlinearities with trapped ions. The method relies on using the quantum Rabi model as a probe, which is sensitive to nonlinear symmetry-breaking perturbations. We show that the couplings which arise either from anharmonic terms of the trapping potential or due to higher order terms in the Coulomb interaction expansion can be efficiently estimated by measuring the spin state probabilities alone. We show that the spin signal is amplified by the mean-phonon excitations, which results in the estimation precision reaching the super-Heisenberg limit. Notably, achieving such high-precision estimation does not require specific entangled state preparation and can be reached even for initial thermal motion state. Furthermore, we show that the super-Heisenberg scaling can be observed even in the presence of weak spin-dephasing.