Optical Fermi edge singularity of double-layer quantum Hall systems

We study the Fermi edge singularity in the absorption and emission spectra of quantum Hall states at filling fraction {ν}=1/k in double-layer systems. We found that power-law anomalies remain in these systems because of the neutral gapless mode. The exponents are calculated and we found that the ``orthogonality catastrophe'' exponent is positive. The ``excitonic'' exponent for optical recombination if the electron is located in a different layer has the opposite sign. So there exists two power-law anomalies for each localized core hole. We suggest that the Fermi edge singularity might be measurable in order to detect the neutral gapless modes.