Enhanced nonlinear quantum metrology with weakly coupled solitons and particle losses

TL;DR

This paper proposes a novel interferometric method using soliton Josephson Junctions to achieve Heisenberg and super-Heisenberg scaling in quantum phase estimation, even with moderate particle losses, advancing quantum metrology.

Contribution

It introduces a new SJJ-based approach for generating entangled states that maintain high precision in lossy environments, surpassing previous limitations.

Findings

Achieves Heisenberg and super-Heisenberg scaling in phase estimation.

Demonstrates robustness of entangled states against moderate losses.

Provides a feasible pathway for experimental implementation with atomic condensates.

Abstract

The estimation of physical parameters with Heisenberg sensitivity and beyond is one of the crucial problems for current quantum metrology. However, unavoidable lossy effect is commonly believed to be the main obstacle when applying fragile quantum states. To utilize the lossy quantum metrology, we offer an interferometric procedure for phase parameters estimation at the Heisenberg (up to 1/N) and super-Heisenberg (up to 1/N^3) scaling levels in the framework of the linear and nonlinear metrology approaches, respectively. The heart of our setup is the novel soliton Josephson Junction (SJJ) system providing the formation of the quantum probe, i.e, the entangled Fock (N00N-like) state, beyond the superfluid-Mott insulator quantum phase transition point. We illustrate that such states are close to the optimal ones even with moderate losses. The enhancement of phase estimation accuracy remains feasible both for the linear and nonlinear metrologies with the SJJs, and allows further improvement for the current experiments performed with atomic condensate solitons with a mesoscopic number of particles.