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Physical Review A

Adiabatic Following and Slow Optical Pulse Propagation in Rubidium Vapor

D. Grischkowsky

Published Jun 1, 1973• 138 citations
Publisher

Abstract

Short pulses of narrow-line low-intensity dye-laser light nearly resonant with the Zeeman-split $^{2}P_{\frac{1}{2}}$ resonance line (7948 \AA{}) of rubidium were observed to propagate through dilute rubidium vapor as slowly as $(\frac{1}{14})c$. 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 ${v}_{p}$ 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.

DOI
10.1103/physreva.7.2096

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This thesis presents theoretical models and results of numerical simulations describing the propagation of optical pulses through dense, thermal atomic vapours. In particular we investigate the nonlinear effects of optical solitons due to self-induced transparency (SIT) in two-level systems, optical simultons in V-type three-level systems and electromagnetically induced transparency (EIT) in Λ-type systems, including the storage and retrieval of dark-state polaritons. An investigation is made into two-photon excitation of the 5D states of rubidium in a high-intensity beam including the hyperfine structure of the relevant atomic levels. Decay from these states to the 6P manifolds is ruled out as a cause of experimentally observed fluorescence due to the amount of power broadening associated with intensities necessary to provide any significant level of population in these highly excited states. We combine the nonlinear effects of optical solitons and EIT to explain experimentally observed steepened pulses in a V-type system in a micron-length cell. We explain the behaviour as the early formation of a simulton pulse drawn from a CW probe field by a strong coupling pulse, due to coherent population trapping. We predict that in a longer cell it may be possible to facilitate propagation of matched pulses, even when the transitions in the system have different propagation coefficients, as long as decoherence from collision broadening can be controlled. The fact that weak pulses can propagate with this scheme suggests an approach to achieving transparent propagation of single or few photon pulses distinct from, but related to, both SIT and EIT.

•Jan 1, 2016•0 citations
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 vp=d\ensuremathωdk{v}_{p}=\frac{d\ensuremath{\omega}}{\mathrm{dk}}vp​=dkd\ensuremathω​ 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.
The narrow-line output of a dye laser on the low-frequency side of the 2P12^{2}P_{\frac{1}{2}}2P21​​ resonance line (7948 \AA{}) of rubidium was self-defocused by passage through dilute rubidium vapor. The defocusing was caused by the electronic nonlinearity associated with "adiabatic following" of the laser field by the pseudomoment of the resonant atoms. By using the corresponding nonlinear dielectric constant, the wave equation was solved numerically and gave excellent quantitative agreement with experiment.
We experimentally studied Zeeman electromagnetically induced transparency (EIT) resonances and slow light propagation in hot Rb vapor. Propagation of weak σ− polarized light pulses in the presence of stronger σ+ polarized background through Rb vapor was realized using a single laser beam and the Pockels cell. The dependences of slow light group velocity and fractional pulse delay on the overall laser beam intensity and temporal pulse length showed that lower optical power and longer light pulses lead to improved EIT and slow light features. The connection between EIT and slow light was also investigated showing that narrower and more contrasted EIT resonances are necessary for further decreasing a group velocity.
Self-induced transparency has been studied in detail experimentally for a simple two-level atomic absorption. A Hg II laser pulse is used at resonance with the D1{D}_{1}D1​ line of Rb. This system eliminates many previous experimental problems such as nonuniform wave fronts and degenerate off-resonant absorbers. Nonlinear transmission, pulse delays, pulse breakup, peak amplification, incoherent-decay effects, off-resonance effects, and focusing effects have been observed. Quantitative comparison with theory is obtained by computer solutions which include the incoherent decay and optical-pulse shapes of the Hg-Rb system. Good agreement is obtained with the theory of McCall and Hahn. Pulse compression by an order of magnitude is obtained by focusing in the resonant absorber. The theory predicting preferred pulse widths and velocities proposed by Davidovich and Eberly is discussed and found inappropriate for the Hg-Rb and other similar systems.
We investigate the propagation of ultrashort laser pulses in atomic rubidium vapor. The pulses are intensive enough to ionize the atoms and are directly resonant with the 780-nm D2{D}_{2}D2​ line. We derive a relatively simple theory for computing the nonlinear optical response of atoms and investigate the competing effects of strong resonant nonlinearity and ionization in the medium using computer simulations. A nonlinear self-channeling of pulse energy is found to produce a continuous plasma channel with complete ionization. We evaluate the length, width, and homogeneity of the resulting plasma channel for various values of pulse energy and initial focusing to identify regimes optimal for applications in plasma-wave accelerator devices such as that being built by the AWAKE collaboration at CERN. Similarities and differences with laser pulse filamentation in atmospheric gases are discussed.
This thesis presents theoretical models and results of numerical simulations describing the propagation of optical pulses through dense, thermal atomic vapours. In particular we investigate the nonlinear effects of optical solitons due to self-induced transparency (SIT) in two-level systems, optical simultons in V-type three-level systems and electromagnetically induced transparency (EIT) in Λ-type systems, including the storage and retrieval of dark-state polaritons. An investigation is made into two-photon excitation of the 5D states of rubidium in a high-intensity beam including the hyperfine structure of the relevant atomic levels. Decay from these states to the 6P manifolds is ruled out as a cause of experimentally observed fluorescence due to the amount of power broadening associated with intensities necessary to provide any significant level of population in these highly excited states. We combine the nonlinear effects of optical solitons and EIT to explain experimentally observed steepened pulses in a V-type system in a micron-length cell. We explain the behaviour as the early formation of a simulton pulse drawn from a CW probe field by a strong coupling pulse, due to coherent population trapping. We predict that in a longer cell it may be possible to facilitate propagation of matched pulses, even when the transitions in the system have different propagation coefficients, as long as decoherence from collision broadening can be controlled. The fact that weak pulses can propagate with this scheme suggests an approach to achieving transparent propagation of single or few photon pulses distinct from, but related to, both SIT and EIT.