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Optics and Spectroscopy

Nonlinear regimes of propagation of resonant pulses in multilevel quantum media

С. В. Сазонов

Published Oct 1, 2003• 9 citations
Publisher

Abstract

An approximate operator approach that is equivalent to the mathematical Wentzel-Kramers-Brillouin method and allows one to solve the set of constitutive equations for an N -level quantum medium resonantly interacting with multifrequency optical pulses is proposed. The transitions occurring via a common level with the ordinal number j are considered in detail. It is shown that, for j =1, the self-induced transparency regime is realized, whereas, at j=N , the regime of electromagnetically induced transparency is realized. Within the framework of the WKB approximation, an expression that represents the area theorem for multifrequency resonant pulses is derived.

DOI
10.1134/1.1621448

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An approximate operator approach that is equivalent to the mathematical Wentzel-Kramers-Brillouin method and allows one to solve the set of constitutive equations for an N -level quantum medium resonantly interacting with multifrequency optical pulses is proposed. The transitions occurring via a common level with the ordinal number j are considered in detail. It is shown that, for j =1, the self-induced transparency regime is realized, whereas, at j=N , the regime of electromagnetically induced transparency is realized. Within the framework of the WKB approximation, an expression that represents the area theorem for multifrequency resonant pulses is derived.
We study theoretically the phenomenon of self-induced transparency for ultrashort pulses (videopulses) propagating in a multilevel quantum medium under conditions in which the method of slowly varying amplitudes and phases breaks down and the pulse spectrum substantially overlaps the quantum transitions. A special class of transitions with one common level is considered. We find that the dynamics of the videopulses in such a medium is described by a double sine-Gordon equation. We establish the conditions under which steady-state traveling 0 π -, 2 π -, and 4 π -videosolitons are formed. It is found that 4 π -videosolitons can propagate both in equilibrium media and in some nonequilibrium media, while 0 π -videosolitons can propagate only in nonequilibrium media. We study amplification processes in highly nonequilibrium systems and show that, depending on the initial state of the medium, 2 π -and qπ -pulses (0< q <1) with increasing amplitudes may be formed. We conclude that the amplification of an ultrashort pulse occurs due to an increase in the photon number density and to an increase in the frequency of each photon. Finally, we study the possibility of an electromagnetic autosoliton being formed in a nonequilibrium dissipative medium.
We investigate short pulses propagation through multilevel atomic vapors. The medium is composed of an ensemble of four atomic levels generated by the hyperfine structure of the D1 transition in Rubidium-87 atoms. The pulses are resonant to their respective optical transitions, in order to have a well-defined pulse area definition. We discuss local stabilization of the pulse area with or without energy stabilization and as a function of the prolonged distance. Furthermore, we explore some new features for the propagation dynamics in multilevel atomic media which are beyond the traditional framework of McCall and Hahn area theorem and self-induced transparency.
The propagation of ultrashort coherent light pulses through a resonant atomic medium, modelled by a two-quantum level of absorbers, is studied including the effects of level degeneracy. The governing equations, a sequence of n-tuple sine-Gordon (SG) equations, are solved by quadrature for the Q-transition, with an approximate method indicated for the (mathematically) more difficult P- and R- transitions. It is shown, in particular, that there is a surprisingly close relation between the usual SG equation and the double SG equation. A simple theorem is proved which shows that each travelling wave solution of the former immediately leads to a solution of the latter, which thus admits a restricted Backlund transformation. This direct solution of nonlinear dispersive equations, which apparently cannot be solved by the inverse method, has an interesting by-product: an approximate method for finding travelling wave solutions of relatively arbitrary Klein-Gordon equations.
We introduce a notion of ``matrix potential'' to nonlinear optical systems. In terms of a matrix potential ggg, we present a gauge-field-theoretic formulation of the Maxwell-Bloch equation that provides a semiclassical description of the propagation of optical pulses through resonant multilevel media. We show that the Bloch part of the equation can be solved identically through ggg and the remaining Maxwell equation becomes a second-order differential equation with a reduced set of variables due to the gauge invariance of the system. Our formulation clarifies the (non-Abelian) symmetry structure of the Maxwell-Bloch equations for various multilevel media in association with symmetric spaces G/HG/HG/H. In particular, we associate the nondegenerate two-level system for self-induced transparency with G/H=SU(2)/U(1)G/H=\mathrm{SU}(2)/\mathrm{U}(1)G/H=SU(2)/U(1) and three-level $\ensuremath{\Lambda}$ or VVV systems with G/H=SU(3)/U(2)G/H=\mathrm{SU}(3)/\mathrm{U}(2)G/H=SU(3)/U(2). We give a detailed analysis for the two-level case in the matrix potential formalism, and address various properties of the system including soliton numbers, effective potential energy, gauge and discrete symmetries, modified pulse area, conserved topological, and nontopological charges. The nontopological charge measures the amount of self-detuning of each pulse. Its conservation law leads to a different type of pulse stability analysis that explains earlier numerical results.
A review is given of recent theoretical investigations on coherent propagation and nonlinear interaction of multifrequency ultrashort radiation pulses in resonantly absorbing media. An analysis is made of frequency conversion by parametric interaction and stimulated Raman scattering of laser pulses in resonant three-level media. New ways of controlling the parameters of coherent pulses and the use of multifrequency pulses in the spectroscopy of multilevel media are discussed. The experimental capabilities of the investigated effects are considered.
(Submitted 14 February 1986) Zh. Eksp. Teor. Fiz. 92,46-55 (January 1987) The coherent resonant interaction between multifrequency light and a multilevel system is considered together with the N-wave interaction of wave packets in a medium with a quadratic nonlinearity. The Lax representation of the self-consistent set of Maxwell-Bloch equations for this interaction is found. Soliton solutions resulting from the parametric transformation of ultrashort pulses in three- and four-level system (N = 3, and N