杰尼斯-康明斯模型中的非经典光相关性

D. V. Maslennikov, V. Yu. Shishkov, E. S. Andrianov
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摘要

光谱滤波器对光的量子特性的影响问题最近在量子密码学和量子数据传输方面引起了极大关注。在本文中,我们在杰恩斯-康明斯模型的框架内考虑了光谱滤波器对共振模式场和两级原子的二阶相干函数的影响。由于共振模式场和原子算子的海森堡方程可以精确求解,因此可以得到共振模式和两级原子算子动态的精确分析傅里叶变换。我们证明了共振模和两级原子的二阶相干函数在算子振荡频谱的所有可能频率上都等于零。我们找到了傅立叶频谱不同频率之间的束间二阶相干函数,并证明在大量量子的情况下,它的取值范围从零到二。因此,发射光的傅立叶光谱中的某些频率之间形成了非经典的相关性。我们证明,在谐振器模式中存在大量量子的情况下,当滤波器将谐振器特征频率附近的频率相加时,谐振器模式场的二阶相干函数不会受到与两级原子相互作用的影响。
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Non-classical correlations of light in the Jaynes-Cummings model
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.
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