  We explore the possibility to overcome the standard quantum limit (SQL) in a
free-fall atom interferometer using a Bose-Einstein condensate (BEC) in either
of the two relevant cases of Bragg or Raman scattering light pulses. The
generation of entanglement in the BEC is dramatically enhanced by amplifying
the atom-atom interactions via the rapid action of an external trap focusing
the matter-waves to significantly increase the atomic densities during a
preparation stage -- a technique we refer to as delta-kick squeezing (DKS). The
action of a second DKS operation at the end of the interferometry sequence
allows to implement a non-linear readout scheme making the sub-SQL sensitivity
highly robust against imperfect atom counting detection. We predict more than
30 dB of sensitivity gain beyond the SQL for the variance, assuming realistic
parameters and $10^6$ atoms.
