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It can be shown that when the driving field is very weak, the pump field is strongly absorbed, leading to a partially incoherent excitation of state |3〉 a situation that must be avoided in coherent multi-wave mixing. See also Ref. [6]
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10444249187
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1τ ≤ 1 indicate a system with a maximum and persisted Raman coherence. Such a persistent Raman coherence gives the generated field described here both the characteristics of a conventional FWM and hyper-Raman radiation
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For a review see: E. Arimondo E. Wolf Progress in Optics 1996 Elsevier Science Amsterdam 257; K. Bergmann, H. Theuer, and B.W. Shore Rev. Mod. Phys. 70 1998 1003
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10444231555
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note
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1 will be small
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32
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10444263360
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note
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We note that approximations made in obtaining Eqs. (4)-(6) are not necessary conditions for the destructive interference to occur. Extensive numerical calculations have shown that effective three-photon destructive interferences can be established without making any approximation other than neglecting the depletions of states |0〉 and |1〉. Experimental and theoretical studies on this and other nonlinear optical processes including hyper-Raman, parametric FWM, etc. using ladder and double-Λ schemes with prepared states are in progress
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33
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10444244459
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note
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We note that once the conditions leading to Eqs. 5(a) and (b) are satisfied, the resulting multi-photon destructive interferences described here are very robust and immune to power fluctuation of the control and auxiliary fields. In fact, these destructive interferences can be maintained in a broad range of density, propagation distance and driving field strengths
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34
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10444266884
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note
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a| → 0 limit, the peak in the center of Fig. 3(a) disappears and we recover the transparency window of a conventional 3-level EIT scheme
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G.M. Meyer Quantum Optics 6 1994 231; M.A.G. Martinez Phys. Rev. A 55 1997 4483
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