Statistics of tens-of-photons states scattered by optical cavities, two-level atoms, and Jaynes-Cummings emitters

Quantum technology is highly relevant to manipulating photon states, for which the quantum waveguide serves as a primary building block. It is a vital task to explore the statistics of tens-of-photons states in quantum waveguides coupled to quantum emitters, such as optical cavities (OCs), two-level atoms (TLAs), and Jaynes-Cummings emitters (JCEs). However, the related theoretical framework has not been established. Here, we use matrix-product-state theory and show that although OCs do not change the second-order photon-photon correlation ${g}^{(2)}$, they can tune the occupation ratio of bunching photons $\ensuremath{\eta}$. What is more, the states scattered by TLAs and JCEs exhibit extremely different statistical behaviors in tens-of-photons cases with respect to those in few-photon ones. The scattering effects from JCEs tend to those from OCs as photon number $n\ensuremath{\rightarrow}\ensuremath{\infty}$, and photon-photon correlation due to JCEs reaches a maximum value as $n$ increases. We anticipate these distinguishable results for tens-of-photons states will be a starting point for multiphoton manipulation in quantum waveguides.