Nuclear magnetic resonance in two-dimensional superfluidHe3

We study the continuous-wave (cw) NMR spectrum of a two-dimensional p-wave superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ film. Two thickness regimes are considered: thickness comparable to the interparticle separation, and thickness much larger than the interparticle separation but smaller than the superfluid coherence length. We find that the form of the dipole Hamiltonian is similar for both regimes, but numerical differences in the coefficients of various terms in some cases lead to qualitatively different results. We find remarkable differences in the NMR spectrum of the two superfluid phases of interest (Anderson-Brinkman-Morel and Balian-Werthamer types of states) and two thickness regimes. From our results it follows that cw NMR is an excellent diagnostic tool for the pairing state in films, as it is in the bulk. We emphasize the qualitative features of our results which are most likely to prove useful to experimentalists.