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arXiv:quant-ph/0402120 · Physical Review A

Large negative and positive delay of optical pulses in coherently prepared dense Rb vapor with buffer gas

Eugeniy E. Mikhailov, Vladimir A. Sautenkov, Irina V. Novikova, George R. Welch

Published Jun 14, 2004• 66 citations
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Abstract

We experimentally study the group time delay for a light pulse propagating through hot $^{87}\mathrm{Rb}$ vapor in the presence of a strong coupling field in a $\ensuremath{\Lambda}$ configuration. We demonstrate that the ultraslow pulse propagation is transformed into superluminal propagation as the one-photon detuning of the light increases due to the change in the transmission resonance line shape. Negative group velocity as low as $\ensuremath{-}c∕{10}^{6}=\ensuremath{-}80\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s}$ is recorded. We also find that the advance time in the regime of the superluminal propagation grows linearly with increasing laser field power.

DOI
10.1103/physreva.69.063808

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We experimentally study the group time delay for a light pulse propagating through hot 87Rb^{87}\mathrm{Rb}87Rb vapor in the presence of a strong coupling field in a \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ configuration. We demonstrate that the ultraslow pulse propagation is transformed into superluminal propagation as the one-photon detuning of the light increases due to the change in the transmission resonance line shape. Negative group velocity as low as \ensuremath−c∕106=\ensuremath−80m∕s\ensuremath{-}c∕{10}^{6}=\ensuremath{-}80\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s}\ensuremath−c∕106=\ensuremath−80m∕s is recorded. We also find that the advance time in the regime of the superluminal propagation grows linearly with increasing laser field power.
We observe a narrow, isolated, two-photon absorption resonance in 87Rb for large one-photon detuning in the presence of a buffer gas. In the absence of a buffer gas, a standard Λ configuration of two laser frequencies gives rise to electromagnetically induced transparency (EIT) for all values of one-photon detuning throughout the inhomogeneously (Doppler) broadened line. However, when a buffer gas is added and the one-photon detuning is comparable to or greater than the Doppler width, an absorption resonance appears instead of the usual EIT resonance. We also observe a large negative group delay (≈−300 μs for a Gaussian pulse that propagates through the media with respect to a reference pulse not affected by the media), corresponding to a superluminal group velocity vg=−c/(3.6×106)=−84 m/s.
We study the behavior of the group velocity of light under conditions of electromagnetically induced transparency (EIT) in a Doppler broadened medium. Specifically, we show how the group delay (or group velocity) of probe and generated Stokes fields depends on the one-photon detuning of drive and probe fields. We find that for atoms in a buffer gas the group velocity decreases with positive one-photon detuning of the drive fields, and increases when the fields are red detuned. This dependence is counter-intuitive to what would be expected if the one-photon detuning resulted in an interaction of the light with the resonant velocity subgroup.
We demonstrate experimentally that a dense cloud of cold atoms with a size comparable to the wavelength of light can induce large group delays on a laser pulse when the laser is tightly focused on it and is close to an atomic resonance. Delays as large as $\ensuremath{-}10\phantom{\rule{0.28em}{0ex}}\mathrm{ns}$ are observed, corresponding to ``superluminal'' propagation with negative group velocities as low as $\ensuremath{-}300\phantom{\rule{0.28em}{0ex}}\mathrm{m}/\mathrm{s}$. Strikingly, this large delay is associated with a moderate extinction owing to the very small size of the dense cloud. It implies that a large phase shift is imprinted on the continuous laser beam. Our system may thus be useful for applications to quantum technologies, such as variable delay line for individual photons or phase imprint between two beams at the single-photon level.
We were able to arbitrarily control the speed of a light pulse from subluminal to superluminal velocity by changing only the power of the laser for coupling coherently the single transition between 62S1/2F=46{}^{2}{S}_{1/2}F=462S1/2​F=4 and $6{}^{2}{P}_{3/2}{F}^{\ensuremath{'}}=5$ in the D2{D}_{2}D2​ line of a Cs atomic vapor system. With weak coupling power, a Gaussian light pulse was propagated superluminally with a negative group velocity ${v}_{g}=\ensuremath{-}c/14400,$ which is caused by a highly anomalous dispersion related to an electromagnetically induced absorption. By increasing the coupling power at the same laser frequency, the pulses were propagated with a vacuum speed at the middle power and a subluminal group velocity vg=c/3000{v}_{g}=c/3000vg​=c/3000 at high power, which is caused by a normal dispersion related to an electromagnetically induced transparency. It was also found that group velocities depend largely on polarization combinations.
Propagation of optical pulses in a resonantly absorbing medium is studied. Propagation time of nanosecond pulses was measured for the Rb D1{D}_{1}D1​ transition. At the center of two absorption lines, delay of the pulse peak which is about ten times as large as the pulse width was observed, where zero delay is defined for the propagation with the light velocity in vacuum. On the other hand, at the peak of an absorption line, negative delay was observed for large absorption, where the advance time is as large as 25% of the pulse width. Simulation including the effect of absorption and phase shift reproduced well the experimental results.