OPTICAL FERMI-EDGE SINGULARITY OF DOUBLE-LAYER QUANTUM HALL SYSTEMS

We study the Fermi edge singularity in the absorption and emission spe ctra of quantum Hall states at filling fraction nu = 1/k in double-lay er systems. We found that two power-law anomalies remain in these syst ems because of the neutral gapless mode. The exponents axe calculated and we found that the ''orthogonality catastrophe'' exponent is positi ve. The ''excitonic'' exponent for optical recombination if the electr on is located in a different layer has the opposite sign. So there exi st two power-law anomalies for each localized core hole. We suggest th at the Fermi edge singularity might be measurable in order to detect t he neutral gapless modes.