Planar quantum squeezing and atom interferometry

TL;DR

This paper introduces a new planar uncertainty relation for spin components, explores the properties of states that saturate it, and demonstrates their potential for enhanced atom interferometry and quantum information applications.

Contribution

It presents a novel planar quantum squeezing concept, derives the properties of the associated states, and shows their experimental realization and practical advantages.

Findings

Planar quantum squeezed states reduce phase noise at all angles.

Ground states of Bose-Einstein condensates can achieve planar squeezing.

The approach enables improved one-shot interferometric phase measurements.

Abstract

We obtain a lower bound on the sum of two orthogonal spin component variances in a plane. This gives a novel planar uncertainty relation which holds even when the Heisenberg relation is not useful. We investigate the asymptotic, large $J$ limit, and derive the properties of the planar quantum squeezed states that saturate this uncertainty relation. These states extend the concept of spin squeezing to any two conjugate spin directions. We show that planar quantum squeezing can be achieved experimentally as the ground state of a Bose-Einstein condensate in two coupled potential wells with a critical attractive interaction. These states reduce interferometric phase noise at all phase angles simultaneously. This is useful for one-shot interferometric phase-measurements where the measured phase is completely unknown. Our results can also be used to derive entanglement criteria for multiple spins $J$ at separated sites, with applications in quantum information.