Light-mediated non-Gaussian entanglement of atomic ensembles
Olov Pettersson, Tim Byrnes · Physical Review A · 2017
We analyze a similar scheme for producing light-mediated entanglement between atomic ensembles, as first realized by Julsgaard, Kozhekin, and Polzik [Nature (London) 413, 400 (2001)]. In the standard approach to modeling the scheme, a Holstein--Primakoff approximation is made, where the atomic ensembles are treated as bosonic modes, and is only valid for short interaction times. In this paper, we solve the time evolution without this approximation, which extends the region of validity of the interaction time. For short entangling times, we find that this produces a state with characteristics similar to those of a two-mode squeezed state, in agreement with standard predictions. For long entangling times, the state evolves into a non-Gaussian form, and the characteristics of the two-mode squeezed state start to diminish. This is attributed to more exotic types of entangled states being generated. We characterize the states by examining the Fock-state probability distributions, Husimi $Q$ distributions, and nonlocal entanglement between the ensembles. We compare and connect several quantities obtained by using the Holstein--Primakoff approach and our exact time evolution methods.