  Atomic nonlinear interferometry has wide applications in quantum metrology
and quantum information science. Here we propose a nonlinear time-reversal
interferometry scheme with high robustness and metrological gain based on the
spin squeezing generated by arbitrary quadratic collective-spin interaction,
which could be described by the Lipkin-Meshkov-Glick (LMG) model. We optimize
the squeezing process, encoding process, and anti-squeezing process, finding
that the two particular cases of the LMG model, one-axis twisting and two-axis
twisting outperform in robustness and precision, respectively. Moreover, we
propose a Floquet driving method to realize equivalent time reverse in the
atomic system, which leads to high performance in precision, robustness, and
operability. Our study sets a benchmark in achieving high precision and
robustness in atomic nonlinear interferometry.
