Generation of total angular momentum eigenstates in remote qubits

We propose a scheme enabling the universal coupling of angular momentum of $N$ remote noninteracting qubits using linear optical tools only. Our system consists of $N$ single-photon emitters in a $\Lambda$ configuration that are entangled among their long-lived ground-state qubits through suitably designed measurements of the emitted photons. In this manner, we present an experimentally feasible algorithm that is able to generate any of the $2^N$ symmetric and nonsymmetric total angular momentum eigenstates spanning the Hilbert space of the $N$-qubit compound.

Figure 1

(Color online) Experimental setup for the angular momentum coupling of two atoms via projective measurements using optical fibers. In a successful measurement cycle, each atom emits a single photon and each detector registers exactly one photon. Note that the detectors cannot distinguish which of the atoms emitted a registered photon.

Figure 2

(Color online) Left: Extension of the setup shown in Fig. 1 capable of generating the state $|\frac{1}{2},1;0⟩\otimes |+⟩$. Right: configuration for the generation of the state $|\frac{1}{2},1;1⟩\otimes |-⟩$.

Figure 3

(Color online) Setup for the generation of the state $2|++-⟩-|+-+⟩-|-++⟩$. The blue dashed lines indicate the quantum path which leads to $2|++-⟩$, whereas the red solid labeled path leads to $-|+-+⟩-|-++⟩$. Please note that the different blue dashed and red solid lines leading from atom 1 (2) to detector $D_1$ are drawn to indicate the different quantum paths only. Physically, there is only one fiber from atom 1 (2) to detector $D_1$.

Figure 4

(Color online) Experimental setup for the spin-spin coupling of $N$ remote atoms via projective measurements.