  Strong nonlinear interactions between single photons have important
applications in optical quantum information processing. Demonstrations of these
interactions in cold atomic ensembles have largely been limited to exploiting
slow light generated using electromagnetically induced transparency (EIT).
However, these EIT implementations have limited achievable phase shifts due to
spontaneous emission. Here, we demonstrate and characterize a scheme free from
these limitations using gradient echo memory with inferred single photon phase
shifts of $0.07\pm0.02$ $\mu\text{rad}$. Excellent agreement with theoretical
modelling was observed. Degradation of memory efficiency was observed for large
phase shifts but strategies to overcome that are presented.
