Photonic Phase Gate via an Exchange of Fermionic Spin Waves in a Spin Chain

We propose a new protocol for implementing the two-qubit photonic phase gate. In our approach, the $\pi$ phase is acquired by mapping two single photons into atomic excitations with fermionic character and exchanging their positions. The fermionic excitations are realized as spin waves in a spin chain, while photon storage techniques provide the interface between the photons and the spin waves. Possible imperfections and experimental systems suitable for implementing the gate are discussed.

Figure 1

(a) Schematic diagram for the implementation of the photonic two-qubit phase gate. (b) The $\Lambda$-type atomic level diagram used for interfacing photons and spin waves. (c) The fermionic dispersion relation $ϵ(k)$ in units of $J$ (solid line), and, schematically, the amplitudes of the two spin waves in $k$ space (dashed lines).