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International Journal of Theoretical Physics

Wigner-function Evolution and Photon-number Decay of Quantum States in a Laser Cavity with the Kerr Medium

Meng-Yan Wu, Heng-Yun Lv, Ji‐Suo Wang, Bao‐Long Liang, Xiang‐Guo Meng

Published Nov 16, 2019• 2 citations
Publisher
DOI
10.1007/s10773-019-04328-9

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Abstract We have studied the photon statistics of a nondegenerate two-photon laser with a medium that has both self- and cross-Kerr interactions as well as intensity-dependent atom–field coupling in the Hamiltonian. The density matrix equation of the atoms and two-mode cavity fields was derived using the standard Scully–Lamb approach and numerically solved. Under certain conditions, the photon distribution function equation was derived and solved analytically. The first few moments of photon numbers were calculated in the region above the lasing threshold. Nonclassicality of the fields was investigated by means of the Mandel Q parameter, second-order correlation functions and the Cauchy–Schwarz inequality. The results are analyzed for a range of finite Kerr parameters. Intensity-dependent coupling suppresses the nonclassicality of the field. It pushes the statistics of the field towards super-Poissonian.The self- and cross-Kerr interactions have significant roles in the nonclassicality of the two-photon cavity field and its statistics. These results are interesting for the field of quantum nonlinear optics and useful in quantum communications.
Abstract A Wigner functional approach is used to derive an evolution equation for a photonic state propagating through a Kerr medium. The resulting evolution equation incorporates all the spatiotemporal degrees of freedom together with the photon-number degrees of freedom and thus allows thorough analyses of the effects of experimental parameters in physical quantum information systems. We then use the evolution equation to consider four-wave mixing as a spontaneous process and finally we impose some approximations to obtain an expression for the optical field due to self-phase modulation.
We study a simple version of the dynamical Casimir effect in a single electromagnetic cavity mode containing a Kerr medium. We obtain an approximate expression for the time evolution operator valid for short times and/or low average photon number. We have found that the generation of photons from quantum vacuum is strongly affected by the presence of the Kerr medium. In the time domain it shows strong oscillations, whose frequency increases with the intensity of the nonlinear medium, sharing physical features with the case of two two-level atoms in a cavity with oscillating walls. Using a semiclassical approach, we show that Kerr nonlinearity produces a faster decrease in the photon production rate than that reported in previous studies working on quasi-resonant nonstationary cavities. We also found that the initial vacuum state can evolve in a cat sate. We expect that these results could be relevant for any study involving the dynamical Casimir effect that is willing to incorporate Kerr nonlinearities.