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Journal of Experimental and Theoretical Physics Letters

Generation of a pilot phase pulse during the propagation of slow elliptically polarized pulses in a medium under coherent population trapping

M. Yu. Basalaev, Denis V. Brazhnikov, Alexander S. Zibrov, A. V. Taǐchenachev, Anatolii M Tumaikin, Valeriy I. Yudin

Published Jul 1, 2012• 0 citations
Publisher

Abstract

Propagation of elliptically polarized light pulses in a medium of two-level atoms with degenerate energy levels under coherent population trapping has been studied within the density-matrix formalism and reduced Maxwell’s equation. It has been shown that ellipticity pulses and the orientation angle of the polarization ellipse move with a deceleration. The analytical expression for the group velocity of an arbitrary J → J dark transition ( J is an integer) has been derived. In addition, a previously unknown effect of forced phase modulation under the variation of the spatial orientation of the polarization ellipse has been discovered. This phase modulation includes a pilot pulse passing through the medium at the speed of light in vacuum and a slow pulse moving synchronously with the pulse of the orientation angle.

DOI
10.1134/s0021364012090032

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Propagation of elliptically polarized light pulses in a medium of two-level atoms with degenerate energy levels under coherent population trapping has been studied within the density-matrix formalism and reduced Maxwell’s equation. It has been shown that ellipticity pulses and the orientation angle of the polarization ellipse move with a deceleration. The analytical expression for the group velocity of an arbitrary J → J dark transition ( J is an integer) has been derived. In addition, a previously unknown effect of forced phase modulation under the variation of the spatial orientation of the polarization ellipse has been discovered. This phase modulation includes a pilot pulse passing through the medium at the speed of light in vacuum and a slow pulse moving synchronously with the pulse of the orientation angle.
We develop a general method allowing one to construct the consistent theory of light pulse propagation through an atomic medium in arbitrary nonlinear regime with respect to the field strength, taking into account the light polarization, temporal (frequency), and spatial dispersions. The method is based on the reduced Maxwell equation, atomic density matrix formalism, and adiabatic approximation. In order to demonstrate the efficiency of our method we investigate in detail the case of propagation of the pulses under conditions of coherent population trapping in a medium of two-level atoms with degenerate energy levels. Equations describing the evolution of various field parameters are derived. It is shown that pulses of ellipticity and spatial orientation of polarization ellipse propagate with slowing. Analytical expressions for the slowing factor are obtained. Previously unknown effects of the stimulated phase modulation and the generation of a phase pilot pulse by the variation of spatial orientation of the polarization ellipse are predicted.
We study the dynamics of the phase pulses of laser radiation with two resonant frequency components propagating in an atomic three-level Λ type medium under coherent population trapping. Using the density matrix adiabatic approach we show that the effect of a very large slowing down occurs not only for amplitude pulses, but also for phase pulses. The group velocity of phase pulses can be controlled by the amplitudes of resonant fields. The analytical solution describing the mutual influence of the phase modulation of one field component on another is obtained.
The elaborate linkage pattern of the interaction Hamiltonian descriptive of pulsed laser interaction of elliptically polarized light with a degenerate two-level system can, for coherent excitation, be reduced to sets of independent pairs of coupled two-state equations by means of the Morris-Shore transformation [Phys. Rev. A 27, 906 (1983)]. By extending the earlier defining work, which dealt only with time-independent interactions, to consider various pulse shapes, one can obtain exact analytic solutions to various multilevel linkages. We use these to find the conditions on the interaction parameters (e.g., the ellipticity) leading to various population transfer schemes, for example, to achieve either population inversion or orientation. We illustrate these with the M and W linkages amongst magnetic sublevels of J=1J=1J=1 or J=2J=2J=2 excited by elliptically polarized light.
Coherent population trapping (CPT), under the resonant interaction of elliptically polarized light with atoms having degenerated energy levels, is analytically treated without the use of a specific coordinate frame. Tensors describing dark states are presented in an explicit and invariant form for all atomic transitions, where CPT takes place. A correspondence between elliptical polarization vectors and pairs of unit spinors is established. It is shown that all dark states in the problem under consideration can be constructed from these spinors by taking multiple tensor products. In the case of an integer angular momentum, this general construction is reduced to a multiple tensor product of vectors.
The results of a theoretical investigation of the evolution of a probe pulse under electromagnetically induced transparency in the Λ -scheme of degenerated inhomogeneously broadened quantum transitions are presented. It supposed that the interacted light fields are elliptically polarized, and their influence on the medium can be either strictly resonant or quasiresonant. It is demonstrated that the probe pulse in the medium can be presented as the sum of two normal modes, i.e. quasi-monochromatic elliptically polarized fields propagating independently of each other. Due to the fact that velocities of normal mode pulses are different, a single probe pulse entering a medium splits into individual pulses inside of the medium, each of which transfers the energy of one of the normal modes. If normal modes are not phase modulated at the input surface, then in the case of quasi-resonance they become phase modulated during propagation in the medium, whereas this does not occur in the case of strict resonance. The total probe field, which is the sum of normal modes, has phase modulation before it splits into the mode pulses in cases of both strict resonance and quasi-resonance, even if it does not have it on the input surface.
An analytic solution is obtained for the self-consistent equations describing propagation of an ultrashort pulse in a resonant two-level medium. The first approximation in respect of the dispersion is used to allow for phase modulation and for the dependence of the group velocity on the intensity and on the running value of the frequency. The conditions for the formation of a shock wave are established. It is shown that asymmetric broadening of the spectrum of a pulse results in coherent absorption, as a result of which the propagation of this pulse in such a medium leaves behind a polarization at the atomic transition frequency responsible for the radiation represented by the pulse.