Quantum sensor network metrology with bright solitons

TL;DR

This paper explores quantum metrology with bright soliton networks, introducing a new fundamental limit and proposing a three-mode soliton Josephson junction system to enhance multiparameter estimation in quantum sensor networks.

Contribution

It introduces the General Heisenberg Limit for soliton-based quantum metrology and proposes the TMSJJ system as a novel platform for improved multiparameter quantum sensing.

Findings

The GHL characterizes fundamental measurement limits in soliton networks.

TMSJJ system exhibits sharp phase transitions towards entangled N00N states.

Weak losses allow TMSJJ to approach optimal scaling near the GHL.

Abstract

We consider multiparameter quantum metrology problem with bright soliton networks in the presence of weak losses. We introduce General Heisenberg Limit (GHL) $\sigma_{\boldsymbol{\chi}}=1/N^k$ that characterizes fundamental limitations for unknown parameter measurement and estimation accuracy $\sigma_{\boldsymbol{\chi}}$ within linear ($k=1$) and nonlinear ($k=3$) quantum metrology approaches to solitons. We examine multipartite $N00N$ states specially prepared for the improvement of multiparameter estimation protocols. As a particular example of producing such states, we propose the three-mode soliton Josephson junction (TMSJJ) system as a three mode extension for the soliton Josephson junction (SJJ) bosonic model, which we previously proposed. The energy spectrum of the TMSJJ exhibits sharp phase transition peculiarities for the TMSJJ ground state. The transition occurs from a Gaussian-like (coherent) state to the superposition of entangled Fock states, which rapidly approach the three-mode $N00N$ state. We show that in the presence of weak losses, the TMSJJ enables saturate scaling relevant to the optimal state limit close to the GHL. Our findings open new prospects for quantum network sensorics with atomtronic circuits.