The Time Evolution And The Quantum Fluctuation For The Second-Order Nonlinear Optical Frequency Conversion System With Coupling Of Two-Mode Quantum Field

Second-order nonlinear optical frequency conversion system (i.e. second-order parametric process) is a powerful tool for generating tunable coherent radiation, squeezed vacuum state, squeezed coherent state, squeezed Fock state and other kinds of nonclassical states of light. It mainly consists of harmonic generation, sum-frequency generation, difference-frequency generation, optical parametric oscillation and etc. In general, typically no more than one of these nonlinear optical processes will be present with any appreciable intensity in a nonlinear crystal. The reason for this behavior is that the nonlinear interaction can efficiently implemented only if the photon energy conservation and phase matching conditions are satisfied, and usually these conditions cannot be satisfied for more than one parametric process. So in the past, one mainly needs to treat single parametric process. With the development of the Quasi-phase matching technology, today we can realize efficiently several parametric processes in a quasiperiodic optical superlattice. It is valuable to study further the general second-order parametric processes.In this paper the development of nonlinear optical frequency conversion technique and the advances in researches for squeezed states are reviewed at first, then the quantization of the electromagnetic field, the properties of the basis quantum states, a one-photon device and a two- photon device, the effect of some simple nonlinear processes as well as the Hamiltonians describing the general second-order parametric processes are also described. In order to solve the complex time-dependent system, the Lewis–Riesenfeld invariant theory is discussed. Depending on these bases, we place the emphasis on exploration of the time evolution and quantum fluctuation for the complex second-order nonlinear optical frequency conversion...