We apply the concept of the mazer to the two-photon process and propose the idea of the two-photon mazer. We establish the general quantum theory of the two-photon mazer and calculate its emission probability in the special case of a mesa mode function. We study not only the case in which the cavity field is initially in a number state, but also the case in which the cavity field is initially in a coherent state. Under the condition of an initial coherent field, the emission probability shows the collapse-revival phenomena, which have different features in different regimes. In the thermal-atom regime, the collapse revivals are similar to that in the two-photon Jaynes-Cummings model. In the critical regime, the collapse revivals look like that in the one-photon Jaynes-Cummings model. In the ultracold-atom regime, the collapse revivals are different from those in the above two regimes. The reasons for these results have been analyzed.

The Hamiltonian is derived for the interaction of a Lambda-type three-level atom with a two-mode quantum cavity field from the general interaction Hamiltonian between a multi-level atom and a multi-mode radiation field, and it is reduced to an effective two-mode Raman-coupled model under a large detuning condition. We propose a modified effective Hamiltonian for the two-mode Raman-coupled model, find the time-dependent state vectors, and present the validity conditions for the involved interaction Hamiltonians. It is shown that in the study of the two-mode Raman-coupled model it is not enough to retain only the usually used effective Hamiltonian, one must also take into account the ac Stark shift of the atomic levels (at least one of the levels). Finally, we study the atomic dynamics in the interaction of a Lambda-type three-level atom with a two-mode quantum cavity field and in the two-mode Raman-coupled model. We find that the number of collapse-revivals, the collapse time and the revival time show new characteristics.

The idea of the two-photon mazer (microwave amplification via z-motion-induced emission of radiation) is put forward. The dressed states for the interaction of a cascade three-level atom with a quantum cavity field are derived. The general quantum theory of the two-photon mazer is established and its emission probability is studied. The effects of the atomic c.m. momentum and of the atom-field detuning are examined. It is found that the two-photon mazer shows new features that differ from both the one-photon mazer and the conventional two-photon micromaser.

We present the general quantum theory for the micromaser with ultra-cold Λ-type three-level atoms. We first derive the dressed states for the interaction of a Λ-type three-level atom with a quantum cavity field, then treat the interaction between the injection atom with the cavity field as a scattering process, find the reflection and transmission coefficients in this process, and calculate the atomic emission probability.

A quantization scheme for an RLC circuit with a source is proposed and the fluctuations of the charge and the magnetic flux of the circuit in several quantum states are studied. The equation of motion for the density operator of the circuit is established and solved. The solutions are discussed.

The time and frequency features of the fluctuations are studied for a pulsed squeezed state field generated by train of pulses produced by a mode-locked laser via degenerated four wave mixing. We propose an improved balanced homodyne detection scheme, which can be used to measure simultaneously the time variation and the frequency spectrum of the noise of in one quadrature component of the pulsed squeezed state field. The explicit expressions for the intensity and the noise as functions of time and frequency are derived. The features of the intensity and noise spectra are discussed. It is shown that the variation of noise with time exhibits a pulse train with reduced noise and the frequency spectrum of the noise displays some very interesting properties.

From the equation for the matrix elements of the field density in the two-photon process, with the aid of the generation function method, the exact analytical expressions of the amplitude N-power squeezing generating in two-photon absorption process are derived. The variation of the amplitude N-power squeezing with the diemensionless time τ, power exponent N, the phase θ and the average number of photons of the incident field are discussed. It have been shown that the amplitude N-power squeezing for different power exponents N is independent of each other, the two-photon absorption process is one of effective ways to generate the amplitude N-power squeezing.