In this paper, we investigate the behaviour of the geometric phase of a more generalized nonlinear system composed of an effective two-level system interacting with a single-mode quantized cavity field. Both the field nonlinearity and the atom-field coupling nonlinearity are considered. We find that the geometric phase depends on whether the index k is an odd number or an even number in the resonant case. In addition, we also find that the geometric phase may be easily observed when the field nonlinearity is not considered. The fractional statistical phenomenon appears in this system if the strong nonlinear atom-field coupling is considered. We have also investigated the geometric phase of an effective two-level system interacting with a two-mode quantized cavity field.
This paper theoretically studies the effects of the vacuum-induced coherence on one- and two-photon absorption in a four-level atomic medium. It finds that the one- and two-photon absorption and amplification properties are quite sensitive to the vacuum-induced coherence. It is also shown that the one- and two-photon absorption spectra can be dramatically affected by modulating the relative phase of the applied fields, With the proper choice of the relative phase, the amplification without inversion for the probe field can be realized.
