The contact hyperfine interaction and the integer and fractional quantum Hall effects

The single particle and many body physics behind the the integer and fractional quantum Hall effects is reviewed. We explain how the composite Fermion picture of Jain describes the fractional quantum Hall effect in terms of an integer quantum Hall effect of non interacting composite fermions and provides an intuitive understanding of spin reversed fractions and competing ground states. The contact hyperfine interaction between the nuclear and electronic spins can be used to probe the electronic spin polarization of the quantum Hall system via the Knight shift of the resistively detected NMR. Finally, we describe how pulsed resistively detected NMR on gated samples can be used to probe quantum Hall states (filling factors) which have zero resistance or are not sensitive to the electronic Zeeman energy.