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Manipulating photon states serves as a primary requirement for variousoptical devices and is of high relevance for quantum information technology.Nevertheless, the fundamental theoretical framework for tens-of-photon stateshas not been established. This study successfully establishes thematrix-product-state theory to explore the statistics of the tens-of-photonstates scattered by optical cavities (OCs), two-level atoms (TLAs), andJaynes-Cummings emitters (JCEs) in waveguide-QED systems. Taking 10-photonstates as an example, we reveal some novel physical results that differ fromthose for few-photon cases. We verify that OCs do not change the statistics ofthe incident photon states, being independent of the photon number. However,for the TLAs and JCEs, the photon number strongly impacts the photon bunchingand anti-bunching behaviors. As the photon number increases, there exists amaximum strength for the photon-photon correlation induced by the JCE.Especially, the scattered waves by the TLA (or JCE) exhibit extremely differentstatistics behaviors for the 10-photon cases from those for the bi-photon.These distinguishable conclusions for the tens-of-photon states and thematrix-product-state theory pave the way for the multi-photon manipulation.

Statistics of tens-of-photon states scattered by optical cavity, two-level atom and Jaynes-Cummings emitter