Observation of cross phase modulation in cold atom gradient echo memory

Abstract: 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.