Integrable active atom interferometry

TL;DR

This paper presents an exact analysis of an active atom interferometer using a spinor Bose-Einstein condensate, revealing its phase sensitivity and performance without idealized assumptions.

Contribution

It provides exact eigenstates and eigenvalues for the Hamiltonian using Bethe Ansatz, enabling precise evaluation of interferometer performance.

Findings

Exact eigenstates and eigenvalues derived

Interferometer's phase sensitivity expressed in Bethe rapidities

Performance studied under full Hamiltonian without approximations

Abstract

Active interferometers are designed to enhance phase sensitivity beyond the standard quantum limit by generating entanglement inside the interferometer. An atomic version of such a device can be constructed by means of a spinor Bose-Einstein condensate with an $F=1$ groundstate manifold in which spin-changing collisions create entangled pairs of $m=\pm1$ atoms. We use Bethe Ansatz techniques to find exact eigenstates and eigenvalues of the Hamiltonian that models such spin-changing collisions. Using these results, we express the interferometer's phase sensitivity, Fisher information, and Hellinger distance in terms of the Bethe rapidities. By evaluating these expressions we study scaling properties and the interferometer's performance under the full Hamiltonian that models the spin-changing collisions, i.e., without the idealising approximations of earlier works that force the model into the framework of SU(1,1) interferometry.