Non-classical correlations of light in the Jaynes-Cummings model

Abstract

The problems concerning the influence of spectral filters on the quantum properties of light have recently attracted great attention in connection with quantum cryptography and quantum data transmission. In this paper, we consider the influence of a spectral filter on the second-order coherence function of a field of a resonator mode and a two-level atom in the framework of the Jaynes-Cummings model. Since the Heisenberg equations for the operators of the field of the resonator mode and the atom can be solved exactly, it is possible to obtain exact analytical Fourier transformation of the dynamics of operators of the resonator mode and two-level atom. We demonstrate that the second-order coherence function of the resonator mode and the two-level atom is equal to zero for all possible frequencies in the spectrum of operator oscillations. We find the interbeam second-order coherence function between different frequencies of the Fourier spectrum and show that in the limit of a large number of quanta, it can take the values in the range from zero to two. Thus, non-classical correlations are formed between certain frequencies in the Fourier spectrum of emitted light. We demonstrate that in the limit of a large number of quanta in the resonator mode, when the filter sums up the frequencies near the resonator eigenfrequency, the second-order coherence function of the field of the resonator mode is not affected by the interaction with the two-level atom.