This book provides an introduction to the general principles of nuclear magnetic resonance and relaxation, concentrating on simple models and their application. The concepts of relaxation and the time domain are particularly emphasised. Some relatively advanced topics are treated, but the approach is graduated and all points of potential difficulty are carefully explained. An introductory classical discussion of relaxation is followed by a quantum-mechanical treatment. Only when the the principles of relaxation are firmly established is the density operator approach introduced; and then its power becomes apparent. A selection of case studies is considered in depth, providing applications of the ideas developed in the text. There are a number of appendices, including one on random functions. This treatment of one of the most important experimental techniques in modern science will be of great value to final-year undergraduates, graduate students and researchers using nuclear magnetic resonance, particularly physicists, and especially those involved in the study of condensed matter physics.

Two-dimensional helium-3 (3He) provides a simple model for the experimental investigation of the emergence of quantum complexity in a strongly correlated Fermi system. We have observed two-dimensional, two-band heavy-fermion behavior in bilayer films of 3He atoms when adsorbed on the surface of graphite preplated by a solid bilayer of 4He. Thermodynamic measurements on this system showed that the relevant control parameter is the total density of the 3He film. The 3He bilayer system can be driven toward a quantum critical point at which the effective mass appears to diverge, interband coupling vanishes, and a local-moment state appears. It opens a new testing ground for theories of quantum criticality in heavy-fermion materials.

The superfluid phases of helium-3 ((3)He) are predicted to be strongly influenced by mesoscopic confinement. However, mapping out the phase diagram in a confined geometry has been experimentally challenging. We confined a sample of (3)He within a nanofluidic cavity of precisely defined geometry, cooled it, and fingerprinted the order parameter using a sensitive nuclear magnetic resonance spectrometer. The measured suppression of the p-wave order parameter arising from surface scattering was consistent with the predictions of quasi-classical theory. Controlled confinement of nanofluidic samples provides a new laboratory for the study of topological superfluids and their surface- and edge-bound excitations.

The heat capacity and magnetization of a fluid 3He monolayer adsorbed on graphite plated with a bilayer of HD have been measured in the temperature range 1-60 mK. Approaching the density at which the monolayer solidifies into a sqrt[7]xsqrt[7] commensurate solid, we observe an apparent divergence of the effective mass and magnetization corresponding to a T=0 Mott-Hubbard transition between a 2D Fermi liquid and a magnetically disordered solid. The observations are consistent with the Brinkman-Rice-Anderson-Vollhardt scenario for a metal-insulator transition. We observe a leading order T2 correction to the linear term in heat capacity.

Superfluidity is a manifestation of the operation of the laws of quantum mechanics on a macroscopic scale. The conditions under which superfluidity becomes manifest have been extensively explored experimentally in both quantum liquids (liquid 4 He being the canonical example) and ultra-cold atomic gases ( 1, 2), including as a function of dimensionality ( 3,4). Of particular interest is the hitherto unresolved question whether a solid can be superfluid ( 5,6). Here we report the identification of a new state of quantum matter with intertwined superfluid and density wave order in a system of twodimensional bosons subject to a triangular lattice potential. Using a torsional oscillator we have measured the superfluid response of the second atomic layer of 4 He adsorbed on the surface of graphite, over a wide temperature range down to 2 mK. Superfluidity is observed over a narrow range of film densities, emerging suddenly and subsequently collapsing towards a quantum critical point. The unusual temperature dependence of the superfluid density in the limit of zero temperature and the absence of a clear superfluid onset temperature are explained, self-consistently, by an ansatz for the excitation spectrum, reflecting density wave order, and a quasi-condensate wavefunction breaking both gauge and translational symmetry.2 Superfluid 4 He is described by a condensate wavefunction, with long-range coherence of the global phase ()  r , determining the quantum hydrodynamic and nonclassical rotation properties ( 1,2). In two dimensions (2D) the superfluid state has power law correlations of the local phase ( 4,7,8). While in bulk the destruction of superfluidity at finite transition temperature arises from the creation of thermal excitations (phonons and rotons), in two dimensions topological excitations (vortices) play a crucial role. In this case the quasicondensate is suddenly destroyed at the Berezinskii-Kosterlitz-Thouless (BKT) phase transition by the unbinding of vortex-antivortex pairs, accompanied by a universal jump in superfluid density ( 3, 7). On the other hand superfluidity may be destroyed at a T = 0 quantum phase transition by increasing correlations or disorder. Here the classic example is the superfluid -Mott insulator transition ( 9), which has been observed in cold bosonic atoms in optical lattices ( 10, 11), by tuning the periodic potential.The novelty of the putative supersolid is that it manifests both superfluid and density wave order ( 12). Unambiguous detection has proved elusive in bulk solid 4 He ( 6, 13) , where a variety of scenarios have been proposed to establish superfluidity coexisting with solid order. These involve mobile zero-point vacancies, frozen-in dislocations and disorder ( 14,15), and the defects determine the strength of the superfluid response. Supersolids have been predicted on model 2D quantum lattices, again arising from mobile vacancies and favoured by triangular lattice symmetry ( 16). Several schemes to realize supersolids in ultracold atoms have also been proposed ( 17, 1...