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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Transmission of dressed fields in three-level media

Joseph H. Eberly

Published Jun 1, 1995• 64 citations
Publisher

Abstract

The interaction of two incident laser pulses with a dielectric medium composed of three-level atoms is discussed. Particular attention is paid to various effects connected with the well known dark state or trapping state of lambda systems. Strong- and weak-field adiabatic processes are considered, taking note of the two-photon adiabatic criterion and counter-intuitive pulse sequencing. Results include two-photon absorption formulae two-photon soliton solutions, and graphs showing the propagation of the recently discovered two-photon trapping states of the field.

DOI
10.1088/1355-5111/7/3/013

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The interaction of two incident laser pulses with a dielectric medium composed of three-level atoms is discussed. Particular attention is paid to various effects connected with the well known dark state or trapping state of lambda systems. Strong- and weak-field adiabatic processes are considered, taking note of the two-photon adiabatic criterion and counter-intuitive pulse sequencing. Results include two-photon absorption formulae two-photon soliton solutions, and graphs showing the propagation of the recently discovered two-photon trapping states of the field.
Spatio-temporal dynamics of two short laser pulses propagating in an absorbing medium, which consists of one- and two-photon resonant (Lambda) -atoms, is investigated in the adiabatic approximation. We give an analytical solution and compare it with numerical simulations. It is shown that pulses may propagate in a medium, whose thickness is considerably greater than the length of the linear absorption of a single weak probe wave. Finally, full transfer of the probe pulse energy into the coupling pulse takes place. A vector model of the adiabatic interaction of two pulses with three-level atom is proposed.
We consider adiabatic interaction of five-level atomic systems and their media with four short laser pulses under the condition of all two-photon detunings being zero. We derive analytical expressions for eigenvalues of the system's Hamiltonian and determine conditions of adiabaticity for both the atom and the medium. We analyze, in detail, the system's behavior when the eigenvalue with nonvanishing energy is realized. As distinct from the usual dark state of a five-level system (corresponding to zero eigenvalue), which is a superposition of three states, in our case the superposition of four states does work. We demonstrate that this seemingly unfavorable case nevertheless completely imitates a three-level system not only for a single atom but also in the medium, since the propagation equations are also split into those for three- and two-level media separately. We show that, under certain conditions, all the coherent effects observed in three-level media, such as population transfer, light slowing, light storage, and so on, may efficiently be realized in five-level media. This has an important advantage that the light storage can be performed twice in the same medium; i.e., the second pulse can be stored without retrieving the first one, and then the two pulses can be retrieved in any desired sequence.
Propagation of a pulse pair in a nondissipative three-level medium is investigated in the adiabatic-following approximation to a trapped state. The general case of unequal oscillator strengths of two electric dipole transitions in an atom is studied analytically, and the adiabaticity criterion for the matter-field interaction is derived. It is shown that the interaction adiabaticity strongly depends on the relationship between oscillator strengths. A simple expression specifying the critical propagation length at which the stimulated Raman adiabatic passage process is still effective is derived. An estimate of the propagation distance at which a complete energy transfer from the pump pulse into the Stokes pulse occurs is made.
The features of spatial and temporal evolution of two short laser pulses propagating in three-level medium under conditions of coherent population trapping and adiabatic population transfer is investigated in adiabatic approximation. It is shown that in both cases pulses can penetrate into a medium at a distance considerably exceeding the length of linear absorption of a single weak probe pulse in absence of a coupling pulse at adjacent transition. The difference of spatial and temporal evolution of level populations in processes of coherent population trapping and adiabatic population transfer is demonstrated. Also we show that the concept of dressed-field pulses is consequence of Manley-Raw relation.
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.
We summarize recent developments in the area of the coherent propagation of laser pulses through dielectric media.We will show that the principle of dynamical adiabaticity opens new avenues to control the non-perturbative .and resonant interaction between two laser pulses and a three-level medium.Examples include the formation of stable wave forms that can travel through optical dielectric media in a loss-free manner with arbitrary pulse shapes, novel possibilities to store optical information in dielectric media in the form of spatially dependent excitations and techniques to exploit this information to control laser pulse envelopes.