Fig. 1: Physical requirements for the cluster-state machine gun protocol.
From: Scalable spin–photon entanglement by time-to-polarization conversion
a Ideal level scheme for the protocol of Lindner and Rudolph. Simultaneous excitation of two energy-degenerate transitions creates photons of orthogonal polarizations. Starting the cycle in an equal superposition of the states \(\left|0\right\rangle\) and \(\left|1\right\rangle\) creates a spin-photon entangled state of the type \((\left|0,V\right\rangle +{e}^{i\phi }\left|1,H\right\rangle )/\sqrt{2}\) in the first iteration. b Simplified level scheme corresponding to the optical NV transitions. The emitter does not present the required energy-degenerate transitions with orthogonal photon polarization and undesired decay channels occur, particularly from the level \(\left|\pm1_{e}\right\rangle\), which can non-radiatively decay to the metastable state (MS). Radiative decay occurs via the zero-phonon line (ZPL), where spin–photon entanglement can be generated, and through the phonon-side band (PSB), which is used for spin state readout. c Photoluminescence excitation spectrum of the NV center used herein. The working transition (\(\left|0\right\rangle\) ↔ \(\left|0_{e}\right\rangle\) is far-detuned (by 0.87 GHz in this experiment) from other transitions, ensuring negligible cross-excitation.
