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Physical Review A

Enhanced frequency conversion of nonadiabatic resonant pulses in coherently prepared Λ systems

A. Eilam, A. D. Wilson‐Gordon, Harry Friedmann

Published May 5, 2006• 12 citations
Publisher

Abstract

We show that nonadiabatic, resonant amplitude- and phase-modulated pulses can be frequency converted with greater efficiency than adiabatic resonant pulses in a coherently prepared $\ensuremath{\Lambda}$ system. Indeed, conversion efficiencies close to unity, similar to those achieved using highly detuned pulses, can been obtained by using highly nonadiabatic resonant pulses. Moreover, by solving the Maxwell-Bloch equations using Fourier transforms, we derive analytical expressions for the probe and the generated four-wave mixing (FWM) pulses as a function of time and propagation distance. From these expressions, which are valid for either adiabatic or nonadiabatic pulses, we derive the result that starting from a nonadiabatic probe pulse, an asymptotically matched probe-FWM pulse pair with the same shape as the initial probe pulse is obtained. In addition, we show that, starting with a nonadiabatic matched pulse pair or a pair of matched pulse trains, we obtain propagation of these pulses without either deformation or losses.

DOI
10.1103/physreva.73.053805

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We show that nonadiabatic, resonant amplitude- and phase-modulated pulses can be frequency converted with greater efficiency than adiabatic resonant pulses in a coherently prepared \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ system. Indeed, conversion efficiencies close to unity, similar to those achieved using highly detuned pulses, can been obtained by using highly nonadiabatic resonant pulses. Moreover, by solving the Maxwell-Bloch equations using Fourier transforms, we derive analytical expressions for the probe and the generated four-wave mixing (FWM) pulses as a function of time and propagation distance. From these expressions, which are valid for either adiabatic or nonadiabatic pulses, we derive the result that starting from a nonadiabatic probe pulse, an asymptotically matched probe-FWM pulse pair with the same shape as the initial probe pulse is obtained. In addition, we show that, starting with a nonadiabatic matched pulse pair or a pair of matched pulse trains, we obtain propagation of these pulses without either deformation or losses.
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We derive an analytic solution for pulsed frequency conversion based on electromagnetically induced transparency or maximum coherence in resonant atomic vapors. In particular, drive-field and coherence depletion are taken into account. The solutions are obtained with the help of a Hamiltonian approach, which in the adiabatic limit allows one to reduce the full set of Maxwell-Bloch equations to simple canonical equations of Hamiltonian mechanics for the field variables. Adiabatic integrals of motion can be obtained and general expressions for the spatiotemporal evolution of field intensities derived. Optimum conditions for maximum conversion efficiency are identified and the physical mechanism of nonlinear conversion in the limit of drive-field and coherence depletion discussed.
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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.
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The interaction of a pair of copropagating pulses with three-level \ensuremath{\Lambda}-type atoms is discussed in terms of time-dependent coupled and decoupled superpositions \ensuremath{\Vert}\ifmmode\pm\else\textpm\fi{}〉 of the lower levels. Due to the explicit time dependence of these states there is a nonadiabatic coupling between the ``bright'' state \ensuremath{\Vert}+〉 and the ``dark'' state \ensuremath{\Vert}-〉 in addition to the strong coupling between \ensuremath{\Vert}+〉 and the upper level \ensuremath{\Vert}a〉 . We show that under quasiadiabatic conditions and in the presence of decay from the upper level this coupling can be treated perturbatively and the Maxwell-Bloch equations can be solved analytically. With the help of such a perturbation approach, coherent population transfer and formstable laser pulse propagation are studied. \textcopyright{} 1996 The American Physical Society.