Geometric Interpretation of Sum Photon Blockade

We present a geometric interpretation of the sum photon blockade effect in multimode quantum optical systems, such as semiconductor microresonators. The blockade condition (c^{(n)} \cdot v = 0) reflects the orthogonality of the (n)-photon amplitude vector to a target mode vector in an (N)-dimensional Hilbert space, visualized as the confinement of the state to a hyperplane. A key result is the calculation of the maximum probability of the system remaining in the blockade subspace under the influence of decoherence processes (in particular, dephasing), which determines the practical feasibility and robustness of the effect. This approach extends to higher-order correlators (g^{(2)}_Σ) and cross-correlations, enabling the design of scalable quantum devices. We introduce the concept of "dark-state typicality": as the number of modes (M) increases, the dark subspace annihilated by the collective mode operator asymptotically occupies a unit fraction of the (n)-boson Hilbert space. This allows the transition from fragile, finely tuned mechanisms to macroscopically robust non-classical light in large multimode bosonic architectures. We consider continuum collective modes, hypotheses on correlation zeros and invariant manifolds, as well as the relationship between blockade and entanglement.

Source: arXiv:2607.07591v1 - http://arxiv.org/abs/2607.07591v1 PDF: https://arxiv.org/pdf/2607.07591v1 Original Link: http://arxiv.org/abs/2607.07591v1