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Journal of Optics B Quantum and Semiclassical Optics

Transparency, slow light and enhanced nonlinear optics in a four-level scheme

Emmanuel Paspalakis

Published Aug 1, 2002• 124 citations
Publisher

Abstract

We analyse the interaction of three laser fields with a four-level quantum system in a tripod configuration. We obtain an analytical expression for the steady state linear susceptibility of a probe laser field and show that the system can exhibit double electromagnetically induced transparency with controlled group velocity. We also show that a coherently prepared tripod scheme can be used for efficient nonlinear generation of new laser fields.

DOI
10.1088/1464-4266/4/4/322

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We analyse the interaction of three laser fields with a four-level quantum system in a tripod configuration. We obtain an analytical expression for the steady state linear susceptibility of a probe laser field and show that the system can exhibit double electromagnetically induced transparency with controlled group velocity. We also show that a coherently prepared tripod scheme can be used for efficient nonlinear generation of new laser fields.
We analyze the interaction of N laser fields with a (N+1)(N+1)(N+1)-level quantum system. A general analytic expression for the steady-state linear susceptibility for a probe-laser field is obtained and we show that the system can exhibit multiple electromagnetically induced transparency, with at most $N\ensuremath{-}1$ transparency windows occurring in the system. The group velocity of the probe-laser pulse can also be controlled.
The interaction of a weak probe laser with an inverted Y-type four-level atomic system driven by two additional coherent fields is investigated theoretically. Under the influence of the coherent coupling fields, the steady-state linear susceptibility of the probe laser shows that the system can have single or double electromagnetically induced transparency windows depending on the amplitude and the detuning of the coupling lasers. The corresponding index of refraction associated with the group velocity of the probe laser can be controlled at both transparency windows by the coupling fields. The propagation of the probe field can be switched from superluminal near the resonance to subluminal on resonance within the single transparency window when two coupling lasers are on resonance. We propose an atomic 87Rb system for experimental observation.
Abstract We consider propagation of a probe pulse in an atomic medium characterized by a combined tripod and Lambda (Λ) atom-light coupling scheme. The scheme involves three atomic ground states coupled to two excited states by five light fields. It is demonstrated that dark states can be formed for such an atom-light coupling. This is essential for formation of the electromagnetically induced transparency (EIT) and slow light. In the limiting cases the scheme reduces to conventional Λ- or N -type atom-light couplings providing the EIT or absorption, respectively. Thus, the atomic system can experience a transition from the EIT to the absorption by changing the amplitudes or phases of control lasers. Subsequently the scheme is employed to analyze the nonlinear pulse propagation using the coupled Maxwell–Bloch equations. It is shown that a generation of stable slow light optical solitons is possible in such a five-level combined tripod and Λ atomic system.
Abstract In this paper, linear and 3rd-order nonlinear group velocities of the probe laser field are investigated in a tripod-type four-level cylindrical quantum dot (TTFLCQD) with parabolic potential in electromagnetically induced transparency. The nonlinear refractive index for this system is calculated by obtaining the real part of the 1st and 3rd-order susceptibilities. Afterward, linear and 3rd-order nonlinear group velocities are found. The control lasers at z-polarization are applied to the system in order to investigate the linear and 3rd-order nonlinear group velocities and the results are discussed. The linear and 3rd-order nonlinear group velocities are compared at z-polarization. Furthermore, the effects of parameters of TTFLCQD and control lasers on linear and 3rd-order nonlinear group velocities are explored. Finally, 3rd-order nonlinear group velocity for z- and x-polarization is compared.
The optical properties of a five-level atomic system composed of a 'Lambda'-type four-level atomic and a tripod four-level atomic systems are investigated. It is found that the behaviors of electromagnetically induced transparency (EIT) and group velocity can be controlled by choosing appropriate parameters with the interacting dark resonances. In particular, when all the fields are on resonance, the slow light at the symmetric transparency windows with a much broader EIT width is obtained by tuning the intensity of the coupling field in comparison with its sub-system, which provides potential applications in quantum storage and retrieval of light.
A scheme for large enhancement of the third-order nonlinearity in a four-level system with double dark resonances is proposed. We obtain an analytical expression for the linear susceptibility and nonlinear susceptibility of a weak probe field and show that the properties of double electromagnetically induced transparency and the Kerr nonlinearity can be modified significantly by changing the ratio of the two coupling fields. A physical understanding of our numerical results using the dressed-state approach is presented. The obtained large nonlinearity with vanishing absorption can be used to generate optical solitons, polarization phase gates and optical Kerr shutters.