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Journal of Shaanxi Normal University

Effective cross-Kerr nonlinearity in a Raman resonant of four-level atom

Li Yongfang

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

A theoretical investigation is put forward for obtaining effective cross-Kerr nonlinearity of the four-level atom interacting with three electromagnetic fields.Using density-matrix equations and perturbation iterative method,the variation dependence of the third-order susceptibility on the detunings of the applied electromagnetic fields is derived.The results show that a large cross-Kerr nonlinearity can be generated when the detunings of the two weak probe fields are Raman resonant,and the corresponding linear susceptibility and self-Kerr interactions vanish.The realization of the effective Kerr nonlinearity with vanishing absorption is possible in a Raman resonant four-level system.

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A theoretical investigation is put forward for obtaining effective cross-Kerr nonlinearity of the four-level atom interacting with three electromagnetic fields.Using density-matrix equations and perturbation iterative method,the variation dependence of the third-order susceptibility on the detunings of the applied electromagnetic fields is derived.The results show that a large cross-Kerr nonlinearity can be generated when the detunings of the two weak probe fields are Raman resonant,and the corresponding linear susceptibility and self-Kerr interactions vanish.The realization of the effective Kerr nonlinearity with vanishing absorption is possible in a Raman resonant four-level system.
We derive an effective cross-Kerr Hamiltonian for the four-level atom interacting with three electromagnetic fields in the NNN configuration. When the atom has relaxed into the ground state, a cross-Kerr nonlinearity arises between two weak probe fields. As a development on earlier work, we derive the form of the atom-field interaction for all detunings and include the spontaneous decay of the upper atomic levels. In general, the atom will also display a linear and self-Kerr response, but if certain resonance conditions are satisfied then only the cross-Kerr interaction will remain. We consider the application of our theory to cold four-level rubidium atoms. The electrical susceptibilities of the probe transitions are explored, and it is shown that a large, pure cross-Kerr nonlinearity can be generated with vanishing absorption of both probe fields.
We derive a cross-Kerr type effective Hamiltonian for the four-level atom interacting with three electromagnetic fields in the N-configuration. When the atom has relaxed into the ground state a cross-Kerr nonlinearity arises between two weak probe fields. As a development on earlier work we show in general that the atom will also display a linear and self-Kerr response. However, if certain resonance conditions are satisfied then the linear and self-Kerr interactions will vanish. The electrical susceptibilities of the probe transitions are also explored and it is shown that a large, pure cross-Kerr nonlinearity can be generated with vanishing absorption of both probe fields.
We derive the form of the cross-Kerr interaction in a four-level atomic system in an N configuration. We use time-independent perturbation theory to calculate the eigenenergies and eigenstates of the Schr\"odinger equation for the system. The system is considered as a perturbation of a Raman-resonant three-level $\ensuremath{\lambda}$ scheme for which exact solutions are known. We show that within the strong control field limit the cross-Kerr interaction can arise between two weak probe fields. The strength of this nonlinear coupling is several orders of magnitude larger than that achievable using optical fibres.
A theoretical scheme for enhanced Kerr nonlinearity is proposed in a four-level ladder-type atomic system based on double dark resonances (DDRs). We solve the relevant density matrix equations in steady state and utilize the perturbation theory to obtain the analytical expressions for the third order susceptibility of the atomic system. The influence of system parameters on behavior of the first and third order susceptibilities is then discussed. In particular, it is found that an enhanced Kerr nonlinearity with reduced linear and nonlinear absorption is obtained around zero probe detuning under the slow light condition through proper adjusting the laser field intensity and frequency detuning of driving fields. The dressed state analysis is employed to explain the physical origin of the obtained result. The obtained results may be important for all-optical signal processing and quantum information technology.
A theoretical investigation was carried out into the program for enhancing the Kerr nonlinearity by interacting double dark states resonances.Using density-matrix equations and perturbative iterative method,the dependence of the real part of the third-order susceptibility on the variation of the additional coherent driving field detuning was derived.It is found that the maximal Kerr nonlinearity induced by interacting dark resonances increases with increment of the detuning and enters gradually the electromagnetically induced transparency window,in which the corresponding linear absorption vanishes,moreover,by utilizing the dressed state theory,physical mechanisms for the results were presented.The realization of the giant Kerr nonlinearity with vanishing absorption is possible in a generic four-level system with double dark resonances.
Abstract We propose to utilize a five-level Λ − Ξ system to achieve large self-Kerr nonlinearity under multiphoton resonance conditions. Using a density matrix formulation along with an iterative perturbation technique, analytic expressions of linear and nonlinear susceptibilities are derived for stationary as well as for moving atoms. Variation of first- and third-order susceptibilities with respect to frequency and intensity of switching field is then discussed. The dressed-state picture is employed to explain the amplitude and position of each peak in linear and nonlinear absorption profiles. It is found that under slow light conditions, large controllable Kerr nonlinearity with reduced linear and nonlinear absorption is achieved by properly adjusting the strength and detunings of strong electromagnetic (e.m.) fields. Our numerical results also reveal that the Kerr nonlinear index of our considered system is greater than that of existing three-level Λ and four-level N systems. Finally, it is substantiated that self-Kerr nonlinearity is proliferated by taking the Doppler effect into account.