In a similar manner, the coupled electron-photon excitation operator τ α ñ can be written, for example, as ĉ † a ĉi ( â † ) n for a one-electron electronic excitation coupled to an n th -level photonic excitation while ĉ † a ĉ † b ĉi ĉj ( â † ) n will provide the two-electron and n th -level photonic coupled excitations. Each of these excitation operators is connected with a unique cluster amplitude {t α , t n , t α, ñ }.