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arXiv:quant-ph/0307209 · Optics Letters

Enhanced nonlinear generation in a three-level medium with spatially dependent coherence

Emmanuel Paspalakis, Z. Kis

Published Oct 15, 2002• 16 citations
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Abstract

We consider a method for efficient parametric generation of a laser pulse. A single laser field is injected into a three-level medium that has two lower states and one excited state. The lower states are initially prepared in a position-dependent coherent superposition state. It is shown that, by proper choice of the position dependence of the superposition along the direction of propagation, the incoming field can be completely converted to a new field.

DOI
10.1364/ol.27.001836

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We consider a method for efficient parametric generation of a laser pulse. A single laser field is injected into a three-level medium that has two lower states and one excited state. The lower states are initially prepared in a position-dependent coherent superposition state. It is shown that, by proper choice of the position dependence of the superposition along the direction of propagation, the incoming field can be completely converted to a new field.
We explore the laser-pulse propagation dynamics when one, two, or three pulses resonantly drive a coherently prepared four-level medium in a tripod configuration. If the system is prepared in a coherent superposition of two of the lower levels, we show that two incident resonant pulses can parametrically generate a third pulse in the medium. Over short distances, the propagation of this generated pulse can be partially controlled by varying the Rabi frequency of one of the driving fields. For a medium prepared in a coherent superposition of the three lower levels, we obtain a general expression for a three-photon Beer's length. Under specific conditions, the medium can either become completely opaque or completely transparent to three incident resonant pulses. Moreover, a single incident pulse can be used to parametrically generate two additional pulses. Finally, a general relationship is found that links the amplitudes of the initial superposition of states and the amplitudes of the pulses at large distances in the medium, implying that the initial superposition can be used to engineer the amplitudes of the exiting pulses.
We consider pulse propagation in a $\ensuremath{\Lambda}$-type medium with spatially dependent coherence. It has been shown in previous works that it is impossible to get complete nonlinear energy conversion between an injected pulse and a generated pulse for homogenous coherence distribution. The aim of our work is to achieve unity conversion efficiency. We show by analytic considerations and numerical simulations that this can be achieved only if the propagation satisfies the conditions of adiabaticity in the local frame on the position domain. We also derive an exact analytic model for pulse propagation in our $\ensuremath{\Lambda}$-type medium, which is valid even if adiabaticity is not satisfied.
A solution is obtained for the system of Maxwell-Schrödinger equations describing the propagation of a laser pulse through a three-level Λ medium in which the initial atomic populations are in a specially prepared coherent superposition of low-energy states. This solution describes a new type of transparency which is characterized by the presence of conversion of the frequency of the incident pulse and can be used, specifically, to produce “optical keys” and frequency converters for laser radiation.
Traditional schemes for coherent population transfer or generation of coherent superposition states in multilevel atoms or molecules usually utilize two or more laser beams with radiation bandwidth smaller than the frequency interval between the working levels. We show the possibility of creation of the coherent superposition of three metastable states of a four-level atom with tripodlike level structure using a single short frequency-chirped laser pulse. The bandwidth of the pulse envelope (without chirp) must be comparable to or exceed the frequency distance between the two metastable levels. No appreciable excitation of the atom takes place during the creation of the coherent superposition state, thus diminishing significantly the effect of decoherence due to the spontaneous decay of the excited state. The proposed method of creation of superposition states is robust against variations in the laser pulse parameters. Since this method does not require maintaining steady resonance with the atomic transitions (owing to the frequency chirp of the laser pulse), it is effective both in homogeneously and inhomogeneously broadened media.