Natural Mode Entanglement as a Resource for Quantum Communication

Natural particle-number entanglement resides between spatial modes in coherent ultracold atomic gases. However, operations on the modes are restricted by a superselection rule that forbids coherent superpositions of different particle numbers. This seemingly prevents mode entanglement being used as a resource for quantum communication. In this Letter, we demonstrate that mode entanglement of a single massive particle can be used for dense coding and quantum teleportation despite the superselection rule. In particular, we provide schemes where the dense coding linear photonic channel capacity is reached without a shared reservoir and where the full quantum channel capacity is achieved if both parties share a coherent particle reservoir.

Figure 1

A double well potential forms the two spatial modes, $A$ and $B$. A BEC reservoir (depicted in red below the double well) shared between the two parties, is used to rotate the spatial modes away from the particle number basis. Steps in the dense coding protocol. Initialization, (a) the state is prepared in the symmetric ground state of the double well potential. Encoding, (b) the $\widehat{Z}$ operation is performed by adjusting the potential of mode $A$; the $\widehat{X}$ operation by exchanging particles with a reservoir BEC. Decoding, the four steps of the Bell state analysis are (c) ${\widehat{R}}_x(\pi /2)$ rotation on mode $B$ by coupling to the shared reservoir, (d) system is driven to strongly interacting limit and the wells are coupled so that the particle(s) exchange position, (e) ${\widehat{R}}_x(\pi /2)$ rotations on both modes, and (f) the number of particles, $n,m=01$, in each mode are readout.