Utilizing the normal and antinomal product representative of exponential quadrat ic operator　in multi－dimensional phase space we give the exact expressions of matrix element for arbitrary exponential quadratic operator. Thus we derive the partition function and wave function of the system of quadratic Hamiltonian with out the knowledge of energy spectrum and eigenfunctions.

A new kind of four-mode continuous variable coherent-entangled state is proposed in the Fock space by using the technique of integration within an ordered product, which exhibits both the properties of a coherent state and an entangled state, and spans a complete and orthonormal representation. The conjugate state of the four-mode continuous variable coherent-entangled state is derived by using the Fourier transformation. Moreover, a simple experimental protocol of generating a four-mode continuous variable coherent-entangled state is proposed by using beam splitters. As applications of this four-mode continuous variable coherent-entangled state, a four-mode entangled state and a four-mode squeezing-Fresnel operator are constructed.

A two-level atom drvien by a strong classical field interacts with a single-mode light field, and the interaction between the atom and the light field can turn into an effective anti-Jaynes-Cummings model under the conditions of strong driving and large detuning. In this paper, we mainly study the two-mode entangled coherent light field in this model, in which one mode of the entangled coherent light field interacts with a two-level atom driven by a strong classical field. During the evolution of the total system, we make a selective measurement on the atom. Through tuning the evolution time and the parameter of the coherent field, we can easily control the quantum statistical properties of the other mode of the entangled light fields and generate the expected non-classical light field in a longer interaction time and a wider region of coherent parameter.

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Recently, newly created unnatural fluorescent nucleobase analogs have gained increasing attention. In the present work, a comprehensive theoretical study on the structural, electronic, and excited-state properties of y-guanine (yG-t1) and its five possible tautomers (yG-t2, yG-t3, yG-t4, yG-t5 and yG-t6) is performed. Tautomerization analysis reveals that the canonical form of yG is not the most stable tautomer in the gas phase since it has three tautomers with the same stabilities. The spectroscopic properties are investigated: It is found that these tautomers have different absorption spectra, and so we can distinguish them by their spectroscopic signatures. In addition, effects of methanol solution and hydrogen bonding with cytosine on the absorption and emission spectra are examined. The methanol solution is found to red-shift both the absorption and emission maxima of the studied bases except for yG-t1, for which the absorption and emission maxima have blue-shifts after solvation. On the other hand, hydrogen bonding with cytosine is found to are blue-shifted both the absorption and emission maxima of yG-t1, yG-t2, yG-t5, and yG-t6. Theoretical predictions here are helpful for the investigation of the tautomerism of yG and the optical properties of yDNA.