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Physical Review A

Theory of shape-preserving short pulses in inhomogeneously broadened three-level media

Ashiqur Rahman, Joseph H. Eberly

Published Aug 1, 1998• 44 citations
Publisher

Abstract

We introduce an ansatz that permits a treatment of the effects of Doppler broadening in the theory of intense steady-state pulse pairs propagating in three-level (\ensuremath{\Lambda} or V) media. We have derived analytic solutions for pulse amplitudes, for group and phase velocities, and for the probability amplitudes of the atoms in the transmission medium. The solutions are different for the \ensuremath{\Lambda} and V cases.

DOI
10.1103/physreva.58.r805

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We introduce an ansatz that permits a treatment of the effects of Doppler broadening in the theory of intense steady-state pulse pairs propagating in three-level (\ensuremath{\Lambda} or V) media. We have derived analytic solutions for pulse amplitudes, for group and phase velocities, and for the probability amplitudes of the atoms in the transmission medium. The solutions are different for the \ensuremath{\Lambda} and V cases.
In a recent paper [Gorshkov et al., Phys. Rev. Lett. 98, 123601 (2007)] and in the two preceding papers [Gorshkov et al., this issue, Phys. Rev. A 76, 033804 (2006); 76, 033805 (2006)], we used a universal physical picture to optimize and demonstrate equivalence between a wide range of techniques for storage and retrieval of photon wave packets in homogeneously broadened $\ensuremath{\Lambda}$-type atomic media, including the adiabatic reduction of the photon group velocity, pulse-propagation control via off-resonant Raman techniques, and photon-echo-based techniques. In the present paper, we generalize this treatment to include inhomogeneous broadening. In particular, we consider the case of Doppler-broadened atoms and assume that there is a negligible difference between the Doppler shifts of the two optical transitions. In this situation, we show that, at high enough optical depth, all atoms contribute coherently to the storage process as if the medium were homogeneously broadened. We also discuss the effects of inhomogeneous broadening in solid state samples. In this context, we discuss the advantages and limitations of reversing the inhomogeneous broadening during the storage time, as well as suggest a way for achieving high efficiencies with a nonreversible inhomogeneous profile.
A steady-state solution that describes pulse propagation in inhomogeneously broadening two-level atoms embedded in a dispersive and nonlinear Kerr lossless host medium has been found. The solution is of an unchirped hyperbolic-secant form with a linear spatial phase delay. The features of the solution are (i) the group velocity, the amplitude, and the width of the pulse are uniquely determined for given parameters of the medium and the carrier frequency; (ii) the group velocity is independent of the density of the resonant atoms; and (iii) the solution can exist in the positive dispersion region.
The results are given of a theoretical investigation of the interaction between two ultrashort pulses J1 and J2 of frequencies ω31 and ω21 with a three-level amplifying medium. It is assumed that the signal J1 of frequency ω31 is a steady-state π pulse and the signal J2 is weak so that its influence on the level populations can be ignored. The case when the signal J2 has a steady-state amplitude profile and an exponential gain is considered. The analysis is made ignoring the group delay effects and also allowing for the mismatch of the group velocities of the signals. The results obtained can be used in studies of the amplification of ultrashort pulses in molecular media such as organic dyes or CO2 molecules.
We present an analytical theory of propagation of electromagnetic pulses through a Doppler-broadened medium in the adiabatic population transfer regime. We show that thermal motion of atoms causes a strong asymmetric distortion of the pulse shape. Two different kinds of pulse distortions are found to be relevant for cases of (a) nondegenerate and (b) degenerate atomic states between which the population is transferred adiabatically. In case (a) the forward front of the nonlinear electromagnetic wave becomes steeper; otherwise, in case (b) a trailing front sharpening takes place. To increase the effect in the degenerate atomic level configuration to an experimentally significant value, the ratio of the Doppler profile width to the Rabi frequency must be much higher than in case (a). \textcopyright{} 1996 The American Physical Society.