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Optics and Spectroscopy

Nonlinear optical properties of a medium with M-configuration of atomic levels

George P. Miroshnichenko, I. Yu. Popov, Alexander Trifanov

Published Sep 1, 2010• 2 citations
Publisher

Abstract

Nonlinear effects related to the resonant interaction of electromagnetic fields that act on four transitions of a five-level M scheme of atomic levels in the stationary limit are studied. Eight stationary solutions that depend on the state of circular polarizations of three operating classical modes of the field are found for the atomic density matrix. To decrease the absorption of the fields on the atomic transitions, the regime of electromagnetically induced transparency is used. The conditions under which the M scheme is close in its optical properties to two- or three-level schemes are found. Based on the obtained eight solutions, the total accumulated phase shifts of the working waves are calculated. It is shown that the M scheme can perform the operation of double controlled phase shift. Alternatively to the method proposed, this operation also can be carried out using five two-qubit operations, which reduces its noise immunity.

DOI
10.1134/s0030400x1009016x

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Nonlinear effects related to the resonant interaction of electromagnetic fields that act on four transitions of a five-level M scheme of atomic levels in the stationary limit are studied. Eight stationary solutions that depend on the state of circular polarizations of three operating classical modes of the field are found for the atomic density matrix. To decrease the absorption of the fields on the atomic transitions, the regime of electromagnetically induced transparency is used. The conditions under which the M scheme is close in its optical properties to two- or three-level schemes are found. Based on the obtained eight solutions, the total accumulated phase shifts of the working waves are calculated. It is shown that the M scheme can perform the operation of double controlled phase shift. Alternatively to the method proposed, this operation also can be carried out using five two-qubit operations, which reduces its noise immunity.
Possible optical implementation of CCNOT gate based on the M-configuration system of atomic levels is discussed. The semiclassical estimations of summary conditional phase shift for the corresponding Controlled Phase Shift (CPS) operator are got. To this end the nonlinear optical phenomena (such as EIT) connected with resonant interaction of electromagnetic field acting on the four transients of five level atomic system with M-configuration (in stationary operating mode) is investigated. It is shown that the M-scheme may be used for implementation of CCNOT gate.
The interaction of a five-level atomic system involving electromagnetically induced transparency with four light fields is investigated. Two different light-atom configurations are considered, and their efficiency in generating large nonlinear cross-phase shifts compared. The dispersive properties of those schemes are analyzed in detail, and the conditions leading to group velocity matching for two of the light fields identified. An analytical treatment based on amplitude equations is used in order to obtain approximate solutions for the susceptibilities, ehich are shown to fit well with the numerical simulations of the full Bloch equations in a large parameter region.
A polarization method has been proposed for transforming the nonlinear electromagnetically induced transparency resonance into the electromagnetically induced absorption resonance (and vice versa) in the Hanle configuration in the field of counterpropagating waves. Numerical calculations have been performed for the F g = 2 → F e = 1 and F g = 2 → F e = 3 transitions in the 87Rb atom. The qualitative analysis of the effect has been performed for the three-level Λ scheme of the atomic energy levels. The main theoretical conclusions are in qualitative agreement with our experimental data for 87Rb. The results can be applied in magnetometry and nonlinear optics.
In this work, we present an analytical method to achieve giant Kerr nonlinearity without absorption in a five-level atomic medium. By using iterative perturbation technique on density matrix equations, we have derived the analytical expressions of nonlinear susceptibility and Kerr nonlinear coefficient in the presence of spontaneously generated coherence (SGC) and relative phase between applied laser fields. It shows that, this five-level atomic medium exhibits multiple electromagnetically induced transparency (EIT) at three different frequencies, at the same time, the Kerr nonlinear coefficient is enhanced around three transparent spectral regions; in each such EIT region appears a pair of positive-negative peaks of Kerr nonlinear coefficient. In particular, these nonlinear peaks are moved to the center of the EIT windows via SGC. This means that the Kerr nonlinear coefficient is enhanced with completely suppressed absorption at different transparency frequencies. Furthermore, the magnitude and the sign of the Kerr nonlinear coefficient are easily controlled according to the SGC strength, the coupling laser intensity, and the relative phase between applied laser fields. Such a giant nonlinear medium can be useful for photonic devices working in the resonant frequency region without absorption. As a typical application, this giant Kerr nonlinear material has been applied to an interferometer for the formation of optical bistability, and showed the appearance of OB at the resonant frequency with significantly reduced threshold intensity and OB width.
We have studied nonlinear quantum optical effects in a doubly driven four-level atomic system in a homogeneously broadened regime. On application of two strong fields the system can be made to display double electromagnetically induced transparency (EIT) because of constructive quantum interference giving rise to nonlinear absorption at three-photon resonance condition. This fact may be used to obtain other phenomena like the effect of photon switching in a pulsed regime and large cross phase modulation (XPM) effect. We also show that the behaviour of spatial modulation of transparency of the weak probe beam in a three-level system interacted with a strong standing wave pump field can be dramatically changed in our four-level ladder type system. Here, strong coupling field acting on the uppermost transition is represented by a standing wave whereas strong pump and weak probe fields acting successively on the lower transitions are represented by travelling waves. The effect of double EIT on nonlinear light generation based on the four-wave-mixing (FWM) technique is also investigated. We have examined that the four wave mixing efficiency can be effectively controlled by varying the strength of the pump field.
Abstract We describe the linear and nonlinear optical properties of a four-level atomic system, after reducing it to an effective two-level atomic model under the condition of adiabatic shifting of resonances driven by two coherent off-resonant fields. The reduced form of the Hamiltonian corresponding to the two-level system is obtained by employing an adiabatic elimination procedure in the rate equations of the probability amplitudes for the proposed four-level model. For a weak probe field operating in the system, the nonlinear dependence of complex susceptibility on the Rabi frequencies and the detuning parameters of the off-resonant driving fields makes it possible to exhibit coherent control of single-photon and two-photon absorption and transparency, the evolution of enhanced Self-Kerr nonlinearity and noticeable dispersive switching. We have shown how the quantum interference results in the generic four-level model at the adiabatic limit. The present scheme describes the appearance of single-photon transparency without invoking any exact two-photon resonance.