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arXiv:quant-ph/0203125 · Physical Review A

Studies of group-velocity reduction and pulse regeneration with and without the adiabatic approximation

M. G. Payne, Lu Deng, Chris Schmitt, Shannon Anderson

Published Oct 4, 2002• 7 citations
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Abstract

We present a detailed semiclassical study of the propagation of a pair of optical fields in resonant media with and without the adiabatic approximation. In the case of near- and on-resonance excitation, we show detailed calculations, both analytical and numerical, of the extremely slowly propagating probe pulse and the subsequent regeneration of a pulse via a coupling laser. Further discussions of the adiabatic approximation provide much subtle understanding of the process, including the effect on the bandwidth of the regenerated optical field. We show that the adiabatic condition does not generally predict that the regenerated field will have the same bandwidth as that of the original probe pulse. Indeed, we show analytically that for a set of coupling pulses well satisfying the adiabatic conditions, the regenerated field usually has a different bandwidth from the original probe pulse. For very-far-off resonance excitations, we show that the analytical solution is nearly detuning independent, providing a simple condition is satisfied. This surprising result is vigorously tested and compared to numerical calculations with very good agreement.

DOI
10.1103/physreva.66.043802

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We present a detailed semiclassical study of the propagation of a pair of optical fields in resonant media with and without the adiabatic approximation. In the case of near- and on-resonance excitation, we show detailed calculations, both analytical and numerical, of the extremely slowly propagating probe pulse and the subsequent regeneration of a pulse via a coupling laser. Further discussions of the adiabatic approximation provide much subtle understanding of the process, including the effect on the bandwidth of the regenerated optical field. We show that the adiabatic condition does not generally predict that the regenerated field will have the same bandwidth as that of the original probe pulse. Indeed, we show analytically that for a set of coupling pulses well satisfying the adiabatic conditions, the regenerated field usually has a different bandwidth from the original probe pulse. For very-far-off resonance excitations, we show that the analytical solution is nearly detuning independent, providing a simple condition is satisfied. This surprising result is vigorously tested and compared to numerical calculations with very good agreement.
We show both analytically and numerically that photons from a probe pulse are not stored in several recent experiments. Rather, they are absorbed to produce a two-photon excitation. More importantly, when an identical coupling pulse is re-injected into the medium, we show that the regenerated optical field has a pulse width that is very different from the original probe field. It is therefore, not a faithful copy of the original probe pulse. Recent experiments [1,2] on the extremely slow propagation of a pair of optical pulses in a resonant medium and the subsequent coherent regeneration of the “probe ” pulse have generated much excitement in the fields of optical computing and quantum optics. The physical explanation offered to these extraordinary phenomena rests on the adiabatic theory developed a decade ago by Eberly and coworkers[3]. To a large degree, the “dark-state polariton” theory [4] and all other recent works formulated around it are basically a field theoretical reformulation of the adiabatic approximation of pulse pair propagation in resonant media originally studied reasonably complete in the early 90’s. These new treatments have provided some further understanding of the process, especially from the view point of atomic spin wave excitation and atomic coherence. Two main results of the these works, however, do not, in our view, accurately describe the physical picture of such a highly nonlinear excitation process. In this letter, we show, based on the adiabatic theory, that the claim of the “revival of the probe pulse ” in recent experiments [1,2,5] is not accurate.
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.
Short pulses of narrow-line low-intensity dye-laser light nearly resonant with the Zeeman-split 2P12^{2}P_{\frac{1}{2}}2P21​​ resonance line (7948 \AA{}) of rubidium were observed to propagate through dilute rubidium vapor as slowly as (114)c(\frac{1}{14})c(141​)c. These slow pulse velocities showed that most of the energy in the propagating wave was contained by the vapor as coherent atomic excitation. The observed pulse velocities vp{v}_{p}vp​ are in good agreement with the equation ${v}_{p}=\frac{d\ensuremath{\omega}}{\mathrm{dk}}$ for the group velocity obtained from linear-dispersion theory. Also, the experimental results are quantitatively explained by adiabatic following, in which the pseudomoments of the atoms remain aligned along the effective field of the laser light. The adiabatic-following model allows for a direct comparison of our results with the work on self-induced transparency. For high-intensity light, adiabatic following predicts a nonlinear pulse velocity and the possibility of observing self-steepening.
We investigate the problem of propagation of three-component resonant light pulses with adiabatically varying amplitudes through a medium consisting of atoms with the tripod level configuration. By means of both analytic and numerical methods we find the two modes of shape-preserving pulse propagation. The pulse propagation velocity of the fast mode is equal to the speed of light in vacuum, whereas the group velocity of the other (slow) mode is significantly slowed down. These two modes represent a general asymptotic solution of the problem of adiabatic pulse propagation, i.e., a pulse of any shape, which is consistent with the adiabaticity conditions, and a finite duration evolves at large propagation distances (and, correspondingly, at large times of interaction with the medium) to a well-separated pair of fast and slow pulses. The experimental requirements for adiabatic pulse propagation in a tripod medium are similar to that needed for observation of slow light propagation in a medium with the $\ensuremath{\Lambda}$ configuration of levels. However, the tripod scheme offers a different possibility, which is absent in the $\ensuremath{\Lambda}$-medium case: collisions of fast and slow pulses. It is found numerically that after such a collision the shapes of the pulses change, so these pulses do not match the classical definition of a soliton.
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.
We report on experimental investigation of optical-pulse group-velocity reduction and probe-pulse ``regeneration'' using a Raman scheme. This scheme, which does not rely on the commonly used on-one-photon-resonance electromagnetically induced transparency (EIT) process, has many advantages over the conventional method that critically relies on the transparency window created by an EIT process. We demonstrate significant reduction of the group velocity, less probe-field loss, reduced probe-pulse distortion, and high probe-pulse regeneration efficiency.