QTu3A.1.pdf Research in Optical Sciences © OSA 2014 Sending Quantum Correlations through Dispersive Media Paul D. Lett 1 , Jeremy Clark 1 , Ryan Glasser 1 , Tian Li 1 , Quentin Glorieux 2 , Ulrich Vogl 3 , Kevin Jones 4 1 Joint Quantum Institute, National Institute of Standards and Technology and the University of Maryland, Gaithersburg, Maryland 20899 USA 2 Laboratoire Kastler Brossel, Université Pierre et Marie Curie, 4 Place Jussieu, 75005 Paris, France 3 Institut of Optics, Information and Photonics University Erlangen-Nuremberg, 91058 Erlangen, Germany 4 Department of Physics, Williams College, Williamstown, Massachusetts 01267 USA paul.lett@nist.gov Abstract: We send one half of a bipartite entangled state through a dispersive medium and examine the effects of normal and anomalous dispersion on the quantum entanglement, correlations and arrival time of quantum mutual information. OCIS codes: (270.0270) Quantum Optics; (270.65700) Squeezed states 1. Introduction The propagation of classical information through dispersive media is well-understood. Normal dispersion leads to “slow light” effects, while anomalous dispersion leads to apparent superluminal propagation or “fast light” effects. These fast light effects are fully consistent with causality and even though the effects can be somewhat counterintuitive they logically and consistently obey the familiar laws of physics. It is easy to argue that, in keeping with causality, classical information cannot be advanced by sending it through an anomalously dispersive medium, even though it is rather difficult to prove the negative experimentally. On the other hand, there seems to be nothing to prevent quantum correlations, even in the form of quantum entanglement, from being advanced in an anomalously-dispersive medium, as no superluminal signaling is enabled in this way. Nonetheless, it seems natural to argue that quantum information, just like classical information, should not be able to be advanced. We explore the advancement of quantum correlations by sending one half of a bipartite entangled state through an anomalously dispersive medium. In this way we investigate the physical mechanisms that seem to act to constrain the system. Dispersion in an optical system, normal or anomalous, is generated in conjunction with gain or loss. Causal dispersion relationships, analogous to the familiar Kramers-Kronig relations for linear media, can be written for nonlinear optical interactions as well. In particular, we can take advantage of the dispersion near a four-wave- mixing (4WM) gain line in Rb vapor and the resulting rapid variation in the refractive index of the gas to create fast and slow light conditions. The gain or loss involved in the process results in noise being added to the optical signal. This noise affects our ability to discern an advance in any sort of signal sent through the medium. The region of linear dispersion near a gain or loss feature is typically rather small, and generating information whose spectrum fully fits within such a linearly-dispersive region is difficult. Classical analytic signals carry the information everywhere; the earliest leading edge carries all of the same information as in a peak that follows. Non- analytic points carry new information but also entail an infinitely broad spectrum, so that some frequency components always travel around the linear dispersive region, leading to precursors that travel precisely at the speed of light. We address these difficulties by explicitly looking only at narrowband signals, generated by quantum fluctuations, and measured by homodyne detection. Again taking advantage of a 4WM process in Rb vapor, we generate quantum-entangled “twin beams,” whose correlations are stronger than classically possible [1]. We then send one of these twin beams through either a fast or slow light medium and examine the effect on the intensity correlations, quantum entanglement, and quantum mutual information. While it is not surprising that we find that information, quantum or otherwise, cannot be advanced through a fast light medium, the manner in which these measures behave can tell us something about the mechanisms that prevent such advancements. Four-wave mixing (4WM) near atomic resonance lines in Rb vapor can generate strongly correlated twin beams of light [1]. The process can also be used to create a nearly quantum-noise-limited phase-insensitive amplifier, whose gain is associated with a rather sharp dispersive feature. The dispersion near a 4WM gain feature can be used to generate either slow- or fast- light conditions [2,3]. Dispersion is associated with gain or loss in the system, each of which will add noise to a signal. It is this added noise that seems to provide the physical means by which nature prevents the advance of information.