  Phase-sensitive optical parametric amplification of squeezed states helps to
overcome detection loss and noise and thus increase the robustness of
sub-shot-noise sensing. Because such techniques, e.g., imaging and
spectroscopy, operate with multimode light, multimode amplification is
required. Here we find the optimal methods for multimode phase-sensitive
amplification and verify them in an experiment where a pumped second-order
nonlinear crystal is seeded with a Gaussian coherent beam. Phase-sensitive
amplification is obtained by tightly focusing the seed into the crystal, rather
than seeding with close-to-plane waves. This suggests that phase-sensitive
amplification of sub-shot-noise images should be performed in the near field.
Similar recipe can be formulated for the time and frequency, which makes this
work relevant for quantum-enhanced spectroscopy.
