Non-classical Effects For An Optical Frequency Lip-conversion With A Driving Term

The study of squeezed and entangled states of the Radiation field has attractedmuch interest due to their potential applications in optical communication, preciseoptical measurement and quantum information processing. Optical parametricdown-conversion has long been considered as an important source of the squeezed andentangled state of light and has been well investigated. However, for the frequencyup-conversion process, little attention seems to have been paid to the generation ofsqueezing and entanglement. A lot of effort has been focused on developing newnonlinear materials, extending the frequency conversion range, improving the powertransfer efficiency, and so on. Some work has been done on the quantum fluctuation,information transfer and time evolution in the single up-conversion. Most of thesemodels did not considered the influence of the driving term on the dynamic behaviorsof the coupled fields. The evolution of an up-conversion model with a driving termwas first studied by Prants. However, only an evolution operator under parameterresonance was derived. Therefore, it is necessary to carry out a further research onthis system, such as to explore the dynamics and non-classical effects of the systemunder frequency detuning.In this Master’s thesis, firstly, the research development of nonlinear opticalfrequency conversion technique is reviewed briefly, the quantum dynamical model offrequency up-conversion with a driving term, is introduced in detail. Then employinga similarity transformation of the linear combination of the signal and idler photonnumber operators, by a time-dependent unitary operator, we construct an invariant andderive corresponding auxiliary differential equations, for the parametricup-conversion system with a driving term. Using the Lewis-Riesenfeld quantuminvariant theory, an explicit analytical solution for the time evolution operator of thesystem is obtained. Then it is used to investigate mainly the influence of the initialsqueezed state, the frequency detuning, and the driving term, on the quantumfluctuations of the coupled fields. It is found that the quantum fluctuations of theoutput beams are independent of the driving term, but obviously dependent on theinitial states and the relative detuning parameterΓ. When the system is initially in atwo-mode coherent state, no squeezing occurs in the output fields for arbitrarydetuning. When the signal mode starts in a single-mode squeezed coherent state, the idler mode starts in a single-mode coherent or vacuum state, the maximum squeezingin the output signal field is the same as its input for arbitrary detuning, but themaximum squeezing for the output idler field decreases as the detuning increases.Therefore, only when a parameter resonance occurs, can the time evolution for thesystem effectively convert a low-frequency squeezed light into a high-frequencysqueezed light. In addition, we also find that the idler field, produced by the generalup-conversion, is entangled with the output signal field. In the case of no driving termand no detuning, the signal field starts in a single-mode number state, and the idlerfield starts in a vacuum state, the evolution of the usual simple frequencyup-conversion makes the entanglement degree between the two modes varyperiodically with interaction time. The output state is maximally entangled when thetwo-mode output photons are equal to each other. At last, it is worth mentioning thatour solution can also describe the quantum dynamical behavior of a cascadedquasi-phase-matching up-conversion. Therefore, our results could be useful for thestudies in the nonlinear optics and quantum optics.