Mode structure of a broadband high gain parametric amplifier

A high gain parametric amplifier with a single-pass pulsed pump is known to generate broadband twin photon fields that are entangled in amplitude and phase but have complicated spectral correlation. Fortunately, they can be decomposed into independent temporal modes. However, the early treatment of the parametric interaction Hamiltonian at strong pumping does not consider the issue of the time-ordering problem of the interaction Hamiltonian and thus leads to the inaccurate conclusion that the mode structure and the temporal mode functions do not change as the gain increases. Recent studies have revealed the change of the spectrum with the gain of the process. In this paper we use an approach that is usually employed for treating nonlinear interferometers and avoids the time-ordering issue. This allows us to derive an evolution equation in differential-integral form. Numerical solutions for the high gain situation indicate a gain-dependent mode structure that has its mode distributions changed and mode functions broadened as the gain increases. This study will enable us to have a complete picture of the mode structure of parametric processes and produce high quality quantum sources for a variety of applications of quantum technology.