Many-photon processes with the participation of squeezed light
József Janszky, Yu. Ya. Yushin · Physical Review A · 1987
The description of an electromagnetic field of complicated statistics with noise, coherent, and squeezed features are discussed using the nondiagonal coherent-state representation of the density matrix and the normally ordered characteristic function derived therefrom. The quantity 〈(${a}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$${)}^{n}$${a}^{n}$〉 which plays a central role in the theory of many-photon processes is found for this field. Particular cases with dominant coherent signal, noise, or squeezing are discussed. It is found that the ratios 〈(${a}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$${)}^{n}$${a}^{n}$〉/(〈${a}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$a〉${)}^{n}$ for the coherent, the chaotic, and the strongly squeezed vacuum states are 1, n!, and (2n-1)!!, respectively. The value of 〈(${a}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$${)}^{n}$〉 related to the anomalous coherence function is considered. It is found that the noise does not influence 〈(${a}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$${)}^{n}$〉.