Entanglement on macroscopic scales in a resonant-laser-field-excited atomic ensemble

We show that two groups of slow two-level atoms in a weak resonant laser field are entangled. The considered groups can be separated by a macroscopic distance, and be parts of a larger atomic ensemble. In a dilute regime, for two very distant groups of atoms, in a plane-wave laser beam, we determine the maximum attainable entanglement negativity, and a laser intensity below which they are certainly entangled. They both decrease with increasing distance between the two groups, but increase with enlarging groups sizes. As a consequence, for given laser intensity, far separated groups of atoms are necessarily entangled if they are big enough.

Figure 1

Schematic representation of two subgroups of atoms, $A$ and $B$, of characteristic size $L$, and separated by a distance $D$, of a larger atomic ensemble, partially illuminated by a resonant laser beam. $A$ and $B$ are entangled, for $D\simeq 1$ m and $L\simeq 50\mu \mathrm{m}$; for example, see Sec. 4c.