Deterministic spin-wave interferometer based on the Rydberg blockade

The spin-wave (SW) $N$-particle path-entangled $|N,0\rangle +|0,N\rangle$ (NOON) state is an $N$-particle Fock state with two atomic spin-wave modes maximally entangled. Attributed to the property that the phase is sensitive to collective atomic motion, the SW NOON state can be utilized as an atomic interferometer and has promising application in quantum enhanced measurement. In this paper we propose an efficient protocol to deterministically produce the atomic SW NOON state by employing the Rydberg blockade. Possible errors in practical manipulations are analyzed. A feasible experimental scheme is suggested. Our scheme is far more efficient than the recent experimentally demonstrated one, which only creates a heralded second-order SW NOON state.

Figure 1

(a) An ensemble of $N$ atoms trapped in volume $V$. The atoms are coupled by four types of light pulses, propagating along two spatial modes $a,b$. (b) The double-$\Lambda$ type energy levels. An effective energy shift ${\Delta }_e$ is introduced because of the strong interaction between the atoms at the Rydberg states.

Figure 2

The figure demonstrates the error $E(\ell )$ versus the energy shift ${\Delta }_e$ under various order $\ell$ after generating the SW NOON state. The solid data and the open one respectively denote the lifetime of the Rydberg state with $\tau =300$ $\mu s$ and $\tau =400$ $\mu s$.