  We experimentally demonstrate a nonlinear detection scheme exploiting
time-reversal dynamics that disentangles continuous variable entangled states
for feasible readout. Spin-exchange dynamics of Bose-Einstein condensates is
used as the nonlinear mechanism which not only generates entangled states but
can also be time reversed by controlled phase imprinting. For demonstration of
a quantum-enhanced measurement we construct an active atom SU(1,1)
interferometer, where entangled state preparation and nonlinear readout both
consist of parametric amplification. This scheme is capable of exhausting the
quantum resource by detecting solely mean atom numbers. Controlled nonlinear
transformations widen the spectrum of useful entangled states for applied
quantum technologies.
