Progress towards quantum-enhanced interferometry with harmonically trapped quantum matter-wave bright solitons

We model the dynamics of attractively interacting ultracold bosonic atoms in a quasi-one-dimensional wave guide with additional harmonic trapping. Initially, we prepare the system in its ground state and then shift the zero of the harmonic trap and switch on an additional narrow scattering potential near the center of the trap. After colliding with the barrier twice, we propose to measure the number of atoms opposite the initial condition. Quantum-enhanced interferometry with quantum bright solitons allows us to predict detection of an offset of the scattering potential with considerably increased precision as compared to single-particle experiments. In a future experimental realization this might lead to measurement of weak forces caused, for example, by small horizontal gradients in the gravitational potential-with a resolution of several micrometers given essentially by the size of the solitons. Our numerical simulations are based on the rigorously proved effective potential approach developed in previous papers [Phys. Rev. Lett. 102, 010403 (2009) and Phys. Rev. Lett. 103, 210402 (2009)]. We choose our parameters such that the prerequisite of the proof (that the solitons cannot break apart, for energetic reasons) is always fulfilled, thus exploring a parameter regime inaccessible to the mean-field description via the Gross-Pitaevskii equation due to Schrodinger-cat states occurring in the many-particle quantum dynamics.