Enhanced third-order cross-nonlinearity in four-level and three-level systems

Alexandre V. Kats, В. М. Конторович, A. V. Nikolaev

Hamid Reza Hamedi, Gediminas Juzeliūnas

The third-order susceptibility is investigated in a five-level atomic system in which the laser beams couple the ground state to a four-level closed-loop system. It is found that under the condition of the multiphoton resonance, one can enhance the Kerr nonlinearity of such a medium by properly adjusting the amplitudes and phases of the applied fields. In this case, the linear and nonlinear absorption reduce considerably in a region with a positive group velocity. It is demonstrated that the third-order susceptibility is very sensitive to the relative phase of the applied fields. An analytical model is presented to elucidate such phase control of the Kerr nonlinearity. A comparison is also made between the Kerr-nonlinear indices for the five-, four-, and three-level systems. It is realized that the magnitude of the Kerr nonlinearity for the five-level system is larger than that of the three- and four-level counterparts. Finally, it is shown that effect of Doppler broadening can lead to an enhanced Kerr nonlinearity while maintaining linear and nonlinear absorption.

J.N. Elgin, LI Fu-li

Hong, T, Jack, M W, Yamashita, M +1 more

Enhancement of optical Kerr nonlinearity for self-action by electro-magnetically induced transparency in a four-level atomic system including dephasing between the ground states is studied in detail by solving the density matrix equations for the atomic levels. We discern three major contributions, from energy shifts of the ground states induced by the probe light, to the third-order susceptibility in the four-level system. In this four-level system with the frequency-degenerate probes, quantum interference amongst the three contributions can, not only enhance the third-order susceptibility more effectively than in the three-level system with the same characteristic parameters, but also make the ratio between its real and imaginary part controllable. Due to dephasing between the two ground states and constructive quantum interference, the most effective enhancement generally occurs at an offset that is determined by the atomic transition frequency difference and the coupling Rabi frequency.

Govind Prasad Agrawal

Liu Zhi-Yuan, Yupeng Duan, Ying-Jie Du

Abstract We theoretically investigate the self-nonlinear and cross-nonlinear responses of the Λ-type, V-type, and ladder-type three-level atomic systems. The analytical solutions of the cross-nonlinearity are obtained by using an iterative method. These analytical expressions reveal that the atomic decay rates and two-photon resonance are closely related to the cross-nonlinear response. For the Λ-type system, the relaxation rate between the ground-state sublevels determines the amplitude and linewidth of the cross-nonlinearity. For the ladder-type system, the lifetime of the upper excited state governs the amplitude and linewidth of the cross-nonlinearity. In both systems, the amplitude of the cross-nonlinearity is significantly enhanced, and the linewidth is greatly compressed simultaneously. In contrast, for the V-type three-level system, the amplitude and linewidth of the cross-nonlinearity are related to the spontaneous emission rate of the excited states, where neither the amplitude enhancement nor the linewidth compression is observed. We conclude that the cross-nonlinear response can reach or even exceed the linear response in the Λ-type system when the relaxation rate between the ground states is sufficiently small, or in the ladder-type system when the spontaneous emission rate of the upper excited state is sufficiently small. Compared with the crossnonlinearity, the self-nonlinearity is related to the Rabi frequency and detuning of the coupling field. Its amplitude decreases with the increase of the coupling Rabi frequency, while it can be increased to a certain extent with the increase of the coupling detuning. Our results provide a theoretical basis for the optimization and application of strong nonlinear effects in three-level atomic systems.