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arXiv:1709.09244 · Optics Express

Causality and information transfer in simultaneously slow- and fast-light media

Jon D. Swaim, Ryan T. Glasser

Published Sep 26, 2017• 7 citations
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Abstract

We demonstrate the simultaneous propagation of slow- and fast-light optical pulses in a four-wave mixing scheme using warm potassium vapor. We show that when the system is tuned such that the input probe pulses exhibit slow-light group velocities and the generated pulses propagate with negative group velocities, the information velocity in the medium is nonetheless constrained to propagate at, or less than, c. These results demonstrate that the transfer and copying of information on optical pulses to those with negative group velocities obeys information causality, in a manner that is reminiscent of a classical version of the no-cloning theorem. Additionally, these results support the fundamental concept that points of non-analyticity on optical pulses correspond to carriers of new information.

DOI
10.1364/oe.25.024376

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We demonstrate the simultaneous propagation of slow- and fast-light optical pulses in a four-wave mixing scheme using warm potassium vapor. We show that when the system is tuned such that the input probe pulses exhibit slow-light group velocities and the generated pulses propagate with negative group velocities, the information velocity in the medium is nonetheless constrained to propagate at, or less than, c. These results demonstrate that the transfer and copying of information on optical pulses to those with negative group velocities obeys information causality, in a manner that is reminiscent of a classical version of the no-cloning theorem. Additionally, these results support the fundamental concept that points of non-analyticity on optical pulses correspond to carriers of new information.
We recently demonstrated optical pulses with large negative group velocities using a scheme based on four-wave-mixing in rubidium vapor. Both the probe and the generated conjugate pulses can experience anomalous dispersion, and we have demonstrated a maximum group advancement of 64% relative to the input pulse width. The four-wave-mixing scheme allows us to send whole images through a fast light medium, and we have analyzed the arrival of spatially-encoded information in the system. We are currently investigating the transport of quantum correlations that are shared by the probe and conjugate modes when sent through fast light media.
It is widely believed that the velocity of information ${\ensuremath{\upsilon}}_{i}$ encoded on an optical pulse is equal to the group velocity ${\ensuremath{\upsilon}}_{g}$, at least when ${\ensuremath{\upsilon}}_{g}$ is less than the speed of light in vacuum ccc. On the other hand, several authors suggest that ${\ensuremath{\upsilon}}_{i}=c$, although the size of the signal traveling at this velocity may be small, thereby making it difficult to measure. Here, we measure ${\ensuremath{\upsilon}}_{i}$ for pulses propagating through a resonant ``slow-light'' medium where ${\ensuremath{\upsilon}}_{g}\ensuremath{\approx}0.006c$. We find ${\ensuremath{\upsilon}}_{i}=1.03{c}_{\ensuremath{-}0.25c}^{+0.49c}$, or that ${\ensuremath{\upsilon}}_{i}\ensuremath{\approx}168{\ensuremath{\upsilon}}_{g}$, clearly demonstrating that the speed of information cannot be generally described by ${\ensuremath{\upsilon}}_{g}$, but is characterized by its own velocity.
We examined the propagation of information encoded as nonanalytical points on temporally Gaussian-shaped optical pulses in fast- and slow-light systems. The bandwidth of the input pulses determined the sharpness of the nonanalytical points. A sharp bending nonanalytical point propagated with luminal velocity in both fast- and slow-light systems, in good agreement with relativistic causality. As the bandwidth was reduced, the bending point became broad and propagated with the relevant group velocities. This transition was, however, qualitatively different in the fast- and slow-light systems. We also examined the predictability of the future pulse shape beyond the practical nonanalytical point on the basis of the expansion. When the bandwidth was reduced below a critical value, the expansion well predicted the future pulse shape.
We examined the propagation of nonanalytical points encoded on temporally Gaussian-shaped optical pulses in fast and slow light in an optical ring resonator at $\ensuremath{\lambda}$ = 1.5 \ensuremath{\mu}m. The temporal peak of the Gaussian pulse was either advanced or delayed, reflecting anomalous or normal dispersions in the ring resonator, relevant to under- or overcoupling conditions, respectively. The nonanalytical points were neither advanced nor delayed but appeared as they entered the ring resonator. The nonanalytical points could be interpreted as information; therefore, the experimental results suggested that information velocity is equal to the light velocity in vacuum or the background medium, independent of the group velocity. The transient behaviors at the leading and trailing edges of the nonanalytical points are discussed in terms of optical precursors.
\n Using pulses based on functions with compact support and perfectly smooth infinitely differentiable zero-intensity nonanalytical points, a new approach to model information propagating through an anomalous dispersive medium is demonstrated. Information can be unambiguously associated to the nonanalytical point in the pulse's leading edge, and its velocity investigated numerically and experimentally in fast-light media. We have clearly observed that the velocity of this nonanalytical point is bounded by Einstein causality and it is exactly equal to the light speed in vacuum c when the pulse's group velocity is superluminal. Moreover, we observed that causality can also cause steepening and a pulse shock-like effect.\n
We investigate the propagation of a weak probe laser field in a medium of warm Rb atoms, controlled with two strong resonant pump fields tuned to the D1 and D2 optical transitions to form an N-scheme arrangement. We have shown theoretically that four-wave mixing has a profound effect on the probe-field group velocity and absorption, allowing the probe-field propagation to be continuously tuned from superluminal to slow-light regimes with amplification. We have also identified the experimental conditions for observation of such tunable slow-to-fast light regime (continuously through the point of zero group index) with positive probe-field gain, and demonstrated that the spectral range corresponding to the zero group index can be tuned by controlling the power of one of the pump laser.