We define an N-order squeezing of the radiation field and study it in the M-photo interactions of a single-mode field with one atom and with two atoms. We present the general relation betwwn N and M for which squeezing of the field is possible.

We have studied squeezing of the field in the N-photon interaction of two two-Level atoms with the radiation field initially in a squeezed state.

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

We present the general quantum theory for the micromaser with ultra-cold A-type three-level atoms. We first derive the dressed states for the interaction of a A-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 tranmission coefficients in this process, and calculate the atomis emission probability.

We present an operational definition of the Wigner function. Our method relies on the Fresnel transform of measured Rabi oscillations and applies to motional states of trapped atoms as well as to field states in cavities. We illustrate this technique using data from recent experiments in iontraps [D. M. Meekhof et al., Phys. Rev. Lett. 76, 1796 (1996)] and in cavity QED [B. Varcoe et al., Nature 403, 743 (2000)]. The values of the Wigner functions of the underlying states at the origin of phase space are W1) (0)=+1.75 for the vibrational ground state and W1) (0)= -1.4 for the one-photon number state. We generalize this method to wave packets in arbitrary potentials.