提出了一种通过建立双线性二次哈密顿量在量子腔中实现参量上转换和下转换的方案.通常在非线性过程中，介质本身不参与能量的净交换，但光波频率可以发生转换的作用称为参量转换作用.此方案建立在一个四能级原子同时与两经典场和两量子场相互作用的基础上，理论属于非线性光学四波混频范畴.将原子制备在合适的能级上，经典光场与相应的能级发生共振，而同时量子光场与相应的能级产生大失谐相互作用，在强相互作用区域内，原子和腔场失耦合，进而实现腔模的参量转换.根据所制备初始能级的不同以及光场激发能级的差异，分别实现了参量上转换和参量下转换.在利用参量下转换制备压缩算符后，对实验的可行性进行了讨论，并且给出了理论值.结果表明: 在级联三能原子中采用一个级联双光子过程代替了原来的两个偶极禁戒跃迁间的经典驱动，可以保证高的不同频率之间的转换效率,并且用于光的量子操控和量子信息处理.

A scheme was proposed to construct bilinear and quadratic Hamiltonians for frequency up- and down-conversions in cavity quantum electrodynamics (QED). Generally, in nonlinear optics, the interaction that the energe swaps between different optic modes without atomic transition is named frequency conversion. The proposed scheme was based on the interactions of a single four-level atom simultaneously with two classical driving fields and a two-mode cavity field, which is in the domain of four-wave mixing . By initially preparing the atom in a suitable state, each pump light was resonant with its transition, and two quantum modes were large tune to the other two transition, respectively, In the strong laser regime, the atomic degrees of freedom could be decoupled from the cavity degrees of freedom and the frequency conversion could be realized for the cavity modes. Due to the different initial states and interactions between optic fields and atom, frequency up- and down-conversions arose, respectively. After the preparation of squeezed operation respect to Frequency down-conversion, a discussion on the feasibility of experiment was given and the theoretical value was obtained. The advantage of this proposal is to realize the transition using two cascade photons, which is dipole-forbidden in a cascade structure atom, with high efficiency. The proposal will be useful for optical quantum control and fundamental tests of quantum theory.