  Although SU(1,1) interferometry achieves Heisenberg-limited sensitivities, it
suffers from one major drawback: only those particles outcoupled from the pump
mode contribute to the phase measurement. Since the number of particles
outcoupled to these `side modes' is typically small, this limits the
interferometer's absolute sensitivity. We propose an alternative `pumped-up'
approach where all the input particles participate in the phase measurement,
and show how this can be implemented in spinor Bose-Einstein condensates and
hybrid atom-light systems - both of which have experimentally realized SU(1,1)
interferometry. We demonstrate that pumped-up schemes are capable of surpassing
the shot-noise limit with respect to the total number of input particles and
are never worse than conventional SU(1,1) interferometry. Finally, we show that
pumped-up schemes continue to excel - both absolutely and in comparison to
conventional SU(1,1) interferometry - in the presence of particle losses, poor
particle-resolution detection, and noise on the relative phase difference
between the two side modes. Pumped-up SU(1,1) interferometry therefore pushes
the advantages of conventional SU(1,1) interferometry into the regime of high
absolute sensitivity, which is a necessary condition for useful
quantum-enhanced devices.
