# Light mediated non-Gaussian atomic ensemble entanglement

## TL;DR

This paper extends the analysis of light-mediated entanglement between atomic ensembles by solving the exact time evolution without the Holstein-Primakoff approximation, revealing non-Gaussian states at longer interaction times.

## Contribution

It provides an exact solution for the entanglement dynamics, showing the transition from Gaussian to non-Gaussian states over time, beyond the standard approximation.

## Key findings

- Short entangling times produce two-mode squeezed states.
- Longer times lead to non-Gaussian entangled states.
- Exact evolution reveals deviations from Holstein-Primakoff predictions.

## Abstract

We analyze a similar scheme for producing light-mediated entanglement between atomic ensembles, as first realized by Julsgaard, Kozhekin and Polzik [Nature {\bf 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 this produces a state with similar characteristics as a two-mode squeezed state, in agreement with standard predictions. For long entangling times, the state evolves into a non-Gaussian form, and the two-mode squeezed state characteristics 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 non-local entanglement between the ensembles. We compare and connect several quantities obtained using the Holstein-Primakoff approach and our exact time evolution methods.