Generation of energy-entangled W states via parametric fluorescence in integrated devices

Tripartite entangled states, such as Greenberger-Horne-Zeilinger and W states, are typically generated by manipulating two pairs of polarization-entangled photons in bulk optics. Here we propose a scheme to generate W states that are entangled in the energy degree of freedom in an integrated optical circuit. Our approach employs photon pairs generated by spontaneous four-wave mixing in a microring resonator. We also present a feasible procedure for demonstrating the generation of such a state, and we compare polarization-entangled and energy-entangled schemes for the preparation of W states.

Figure 1

Analogies between optical elements employed in bulk optics for schemes involving polarization-entangled states (on the left) and the corresponding integrated optical elements for the scheme introduced here involving energy-entangled states (on the right). Note the absence of an analog for the $\lambda /2$ wave plate.

Figure 2

Scheme for generating energy-entangled W states. $S$—Microring resonator for the production of photons pairs by SFWM. $A{D}_1$—Add-drop filter extracting only the red and blue photons. $A{D}_2$—Add-drop filter routing the red and blue photons to different target detectors. The $D{C}_i\mathrm{s}$ are directional couplers, characterized by real-valued transmission and reflection coefficients $t_i$ and $r_i$, respectively.

Figure 3

Schematic representation of the detection setup. Here, as an example, we sketch a threefold coincidence measurement revealing the $|\mathit{BBR}\rangle$ state in the output channels. All these measurements are subject to the simultaneous detection of a red photon by $T_1$ (see Fig. 2). Note that not all of the detectors represented are actually required; the density matrix of the state can be fully reconstructed using four detectors.