Capacity estimates for optical transmission based on the nonlinear Fourier transform

What is the maximum rate at which information can be transmitted error-free in fibre-optic communication systems? For linear channels, this was established in classic works of Nyquist and Shannon. However, despite the immense practical importance of fibre-optic communications providing for >99% of global data traffic, the channel capacity of optical links remains unknown due to the complexity introduced by fibre nonlinearity. Recently, there has been a flurry of studies examining an expected cap that nonlinearity puts on the information-carrying capacity of fibre-optic systems. Mastering the nonlinear channels requires paradigm shift from current modulation, coding and transmission techniques originally developed for linear communication systems. Here we demonstrate that using the integrability of the master model and the nonlinear Fourier transform, the lower bound on the capacity per symbol can be estimated as 10.7 bits per symbol with 500 GHz bandwidth over 2,000 km

Mapping Dirac quasiparticles near a single Coulomb impurity on graphene

The response of Dirac fermions to a Coulomb potential is predicted to differ significantly from how non-relativistic electrons behave in traditional atomic and impurity systems. Surprisingly, many key theoretical predictions for this ultra-relativistic regime have not been tested. Graphene, a two-dimensional material in which electrons behave like massless Dirac fermions, provides a unique opportunity to test such predictions. Graphene’s response to a Coulomb potential also offers insight into important material characteristics, including graphene’s intrinsic dielectric constant, which is the primary factor determining the strength of electron–electron interactions in graphene. Here we present a direct measurement of the nanoscale response of Dirac fermions to a single Coulomb potential placed on a gated graphene device. Scanning tunnelling microscopy was used to fabricate tunable charge impurities on graphene, and to image electronic screening around them for a Q = +1|e| charge state. Electron-like and hole-like Dirac fermions were observed to respond differently to a Coulomb potential. Comparing the observed electron–hole asymmetry to theoretical simulations has allowed us to test predictions for how Dirac fermions behave near a Coulomb potential, as well as extract graphene’s intrinsic dielectric constant: ε[subscript g] = 3.0±1.0. This small value of ε[subscript g] indicates that electron–electron interactions can contribute significantly to graphene properties.United States. Office of Naval Research. Multidisciplinary University Research Initiative (Award N00014-09-1-1066)United States. Dept. of Energy. Office of Science (Contract DE-AC02-05CH11231)National Science Foundation (U.S.) (Award DMR-0906539

Higher-order renormalization of graphene many-body theory

We study the many-body theory of graphene Dirac quasiparticles interacting via the long-range Coulomb potential, taking as a starting point the ladder approximation to different vertex functions. We test in this way the low-energy behavior of the electron system beyond the simple logarithmic dependence of electronic correlators on the high-energy cutoff, which is characteristic of the large-N approximation. We show that the graphene many-body theory is perfectly renormalizable in the ladder approximation, as all higher powers in the cutoff dependence can be absorbed into the redefinition of a finite number of parameters (namely, the Fermi velocity and the weight of the fields) that remain free of infrared divergences even at the charge neutrality point. We illustrate this fact in the case of the vertex for the current density, where a complete cancellation between the cutoff dependences of vertex and electron self-energy corrections becomes crucial for the preservation of the gauge invariance of the theory. The other potentially divergent vertex corresponds to the staggered (sublattice odd) charge density, which is made cutoff independent by a redefinition in the scale of the density operator. This allows to compute a well-defined, scale invariant anomalous dimension to all orders in the ladder series, which becomes singular at a value of the interaction strength marking the onset of chiral symmetry breaking (and gap opening) in the Dirac field theory. The critical coupling we obtain in this way matches with great accuracy the value found with a quite different method, based on the resolution of the gap equation, thus reassuring the predictability of our renormalization approach.Comment: 27 pages, 7 figures, references adde