Raman scattering and excitations in fractional quantum Hall systems*

Raman scattering provides an important probe of the fractional quantum Hall effect. In addition to the enegy spectrum of magnetoroton exciitations, polarized Raman scattering can also measure the spin of the magnetoroton. The problem of Raman scattering involves physics at two vastly different scales: the scale of the energy of the photons and the energy scale of the FQHE. In a certain regime, one can "factor out" the calculable physics at the photon energy scale, reducing the problem to the calculation of the spectral density of a pair of spin-2 operators on a single Landau level. Thus Raman scattering does not measure the density response but a certain "stress response." This is reminiscent of Haldane's proposal that the long-wavelength magnetoroton is a kind of "emergent graviton." We will argue that the single mode approximation does not work for Jain states near  ν=1/4. In the simplest scenario these states contain two magnetoroton modes, which have different chirality for ν=n/(4n-1) and the same chirality for ν=n/(4n+1), measureable in polarized Raman scattering. Polarized Raman scattering, in principle, can also help the determination of the nature of the ν=5/2 plateau.