报告摘要：

Large quantum superpositions carry great promise for enhancing
precision measurements but can be extremely fragile, currently
limiting the size of maximally entangled ``NOON'' states to 10
particles. The related mesoscopic superpositions of current states
with 10^9 Cooper pairs observed in superconducting rings have proven
more robust but their microscopic nature is debated. Here we present a
realistic microscopic model of ultra-cold atoms in a ring trap
analogous to superconducting rings. Most importantly, we show how
correlations in the strongly-interacting Tonks-Girardeau regime
produce superposition states of mesoscopic flow that are robust
against single-particle loss and excitation. These states are
experimentally accessible and adiabatically connected to NOON states,
thus providing a path to engineering larger NOON states.
We further show how strongly-correlated superposition states can be
used for Heisenberg-limited interferometry of rotational phase shifts.
Calculating the Fisher entropy reveals that phase sensitivity degrades
less under single-particle loss for these states than it does for NOON
states and that the performance is improved compared to classical
states.