A nonlinear Ramsey interferometer operating beyond the Heisenberg limit

TL;DR

This paper demonstrates that a nonlinear Ramsey interferometer based on a two-mode Bose-Einstein condensate can surpass the Heisenberg limit in measurement precision for interatomic interactions, using realistic quantum states.

Contribution

It introduces a method to realize a nonlinear Ramsey interferometer with a TBEC that exceeds the Heisenberg limit for certain parameter estimations.

Findings

Measurement uncertainty for phase scales as 1/√N.

Uncertainty for scattering strength scales as 1/N^{7/5}.

Surpasses the Heisenberg limit of 1/N.

Abstract

We show that a dynamically evolving two-mode Bose-Einstein condensate (TBEC) with an adiabatic, time-varying Raman coupling maps exactly onto a nonlinear Ramsey interferometer that includes a nonlinear medium. Assuming a realistic quantum state for the TBEC, namely the SU(2) coherent spin state, we find that the measurement uncertainty of the ``path-difference'' phase shift scales as the standard quantum limit (1/N^{1/2}) where N is the number of atoms, while that for the interatomic scattering strength scales as 1/N^{7/5}, overcoming the Heisenberg limit of 1/N.