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Physical Review A

Effect of the upper-level decay on the resonantly enhanced four-wave mixing in a modified double- Λ system

Fam Le Kien, K. Hakuta

Published Apr 14, 2004• 6 citations
Publisher

Abstract

We study the continuous resonant four-wave mixing in a medium of atoms with a modified double-$\ensuremath{\Lambda}$ level configuration. Under the far-off-resonance condition for a pair of levels, we reduce the five-level scheme to an effective three-level scheme, with a two-photon coupling between the two lower levels. We derive the exact steady-state solution to the density-matrix equations for the reduced scheme and obtain the wave-mixing equations for the fields in the continuous-wave regime. We show that the upper-level decay may substantially affect the resonantly enhanced wave-mixing process. We demonstrate that this decay shortens the conversion cycle rather than prolongs it.

DOI
10.1103/physreva.69.043811

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We study the continuous resonant four-wave mixing in a medium of atoms with a modified double-\ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ level configuration. Under the far-off-resonance condition for a pair of levels, we reduce the five-level scheme to an effective three-level scheme, with a two-photon coupling between the two lower levels. We derive the exact steady-state solution to the density-matrix equations for the reduced scheme and obtain the wave-mixing equations for the fields in the continuous-wave regime. We show that the upper-level decay may substantially affect the resonantly enhanced wave-mixing process. We demonstrate that this decay shortens the conversion cycle rather than prolongs it.
Using Schrödinger–Maxwell formalism, we propose and analyse a cw four-wave mixing (FWM) scheme for the generation of coherent light in a five-level double-Λ atomic system based on electromagnetically induced transparency. We derive the corresponding explicit analytical expressions for the generated FWM field. The influence of hyperfine sublevel on the amplitude of the generated FWM field is predicted in detail. We also give a brief discussion on the experimental realization of the proposed scheme.
Using Schroedinger-Maxwell formalism, we propose and analyse a cw four-wave mixing (FWM) scheme for the generation of coherent light in a five-level double-∧ atomic system based on electromagnetically induced transparency. We derive the corresponding explicit analytical expressions for the generated FWM field. The influence of hyperfine sublevel on the amplitude of the generated FWM field is predicted in detail. We also give a brief discussion on the experimental realization of the proposed scheme.
Using Schrodinger–Maxwell formalism, we propose and analyse a continuous-wave four-wave mixing (FWM) scheme for the generation of coherent light in a five-state double-Λ atomic system with or without spontaneously generated coherence (SGC) based on electromagnetically induced transparency (EIT). We derive the corresponding explicit analytical expressions for the generated FWM field under the steady-state condition. The influence of hyperfine sublevel and SGC effect on the amplitude of the generated FWM field is predicted in detail via the derived analytical expressions. We also give a brief discussion on the experimental realization of the proposed scheme.
We present a theory of a continuous-wave light propagation in a medium of atoms with a double-$\ensuremath{\Lambda}$ configuration of levels. This is a configuration with a closed cycle of radiation-induced transitions. An interference of excitation channels in such closed-loop systems leads to a strong dependence of the atomic state on the relative phase and the relative amplitudes of applied electromagnetic waves. Therefore, the medium response may be controlled by the phases. On the other hand, the phases themselves change during the propagation. Thus the state of the medium and all the field parameters are tightly coupled to each other in the present problem. We consider the propagation of four-frequency laser radiation through the double-$\ensuremath{\Lambda}$ medium for two situations. At resonant or near-resonant excitation of atoms, both the medium and the field evolve into a nonabsorbing state. This state implies specific coherent superposition for atoms (``dark state''), and particular relations for the field phases, amplitudes, and frequencies. In this way, the propagation results in the phase, amplitude, and frequency matching of the laser waves. In the second case, one $\ensuremath{\Lambda}$ system in double-$\ensuremath{\Lambda}$ atoms is excited resonantly, while the second $\ensuremath{\Lambda}$ system is far off resonance. Such an excitation scheme ensures the preparation of atoms in the nearly dark state throughout the medium. Therefore, the total light energy is dissipated very weakly, whereas each individual laser wave can vary considerably along the propagation path. We have found that the resonant fields change as much as the far-detuned ones. The intensities oscillate sinusoidally with the optical length, with the energy being transferred back and forth between two waves in each frequency pair, resonant and far detuned. This gives the possibility for an almost lossless amplification of two of the laser waves, or an even generation of one of them.
Electromagnetically-induced-transparency-based four-wave mixing (FWM) in a resonant four-level double-Λ system has a maximum conversion efficiency (CE) of 25% due to spontaneous emission. Herein, we demonstrate that spontaneous emission can be considerably suppressed by arranging the applied laser beams in a backward configuration. With the backward double-Λ FWM scheme, we observe a CE of 63% in cold rubidium atoms with an optical depth (OD) of 48. To the best of our knowledge, this is the first observation of a CE exceeding the conversion limit in resonant FWM processes. Furthermore, we present a theoretical model that includes the phase-mismatch effect in the backward double-Λ FWM system. According to the theoretical model, the present scheme can achieve 96% CE using a medium with a large OD of 200 under ideal conditions. Such an efficient frequency conversion scheme has potential applications in optical quantum information technology.