ADHM and the 4d quantum Hall effect

Yang-Mills instantons are solitonic particles in d=4+1 dimensional gauge theories. We construct and analyse the quantum Hall states that arise when these particles are restricted to the lowest Landau level. We describe the ground state wavefunctions for both Abelian and non-Abelian quantum Hall states. Although our model is purely bosonic, we show that the excitations of this 4d quantum Hall state are governed by the Nekrasov partition function of a certain five dimensional supersymmetric gauge theory with Chern-Simons term. The partition function can also be interpreted as a variant of the Hilbert series of the instanton moduli space, counting holomorphic sections rather than holomorphic functions. It is known that the Hilbert series of the instanton moduli space can be rewritten using mirror symmetry of 3d gauge theories in terms of Coulomb branch variables. We generalise this approach to include the effect of a five dimensional Chern-Simons term. We demonstrate that the resulting Coulomb branch formula coincides with the corresponding Higgs branch Molien integral which, in turn, reproduces the standard formula for the Nekrasov partition function

On the generation of ultra-broad bandwidth light in air at atmospheric pressure

We predict that ultra-broadband light consisting of over 150 distinct frequencies of comparable energy can be generated in air at atmospheric pressure by stimulated Raman scattering using resonant symmetric pumping. Nanosecond input pulses and the highest available intensities are found to be optimal. Gain suppression analysis, incorporating a finite Stokes shift, gives a qualitative explanation of the pumping requirements

Nonlinear competing processes in multifrequency Raman generation

We investigate the extent to which the Raman generation of ultrabroad-band light will be affected by nonlinear competing processes. The model equations are generalized to incorporate an off-axis competing signal and a quantitative study is undertaken of its affect on the primary process. An effective gain-length product for the parasitic process is introduced and its characteristics examined. A simple analytical model has been developed for the case of a competing process generated from background noise or amplified spontaneous emission. Predictions of this model are found to be in good agreement with numerical simulations. We find that the efficiency and character of ultrabroad-band multifrequency Raman generation, with resonant and symmetric pumping, effectively drives such nonlinear competing processes below threshold. The roles played by dispersion, transiency and the initial intensity of the competing process are all systematically investigated. Multifrequency conversion is also found to be robust when the competing signal grows from a strong seed, as could arise from scattering of a pump beam