Beating Heisenberg limit with moving matter-wave solitons

In current quantum technologies estimation of some phase-dependent parameters with so-called super-Heisenberg (SH) sensitivity that is beyond Heisenberg limit (HL) represents one of the principal problem. We propose to use weakly coupled quantum bright solitons for this aim. We demonstrated that these solitons allow to form specific entangled Fock states providing accuracy up to the HL for soliton parameters estimation even in the presence of weak losses.