Nuclear magnetic resonance in ultra-small samples of superfluid ³He

By using small inclusions of liquid ³He trapped in a solid ⁴He matrix, it may be possible to study a sample of the superfluid A phase in the regime where quantum fluctuations of the relative phase of the "up" and "down" Cooper pairs are no longer negligible. Under these conditions there is little doubt that a standard quantum-mechanical (QM) calculation of the NMR dynamics should correctly describe the behavior of the total magnetization of a large ensemble of independent inclusions. However, it is less obvious that it should describe the behavior of a single inclusion on a single run of the experiment, and indeed it is tempting to argue that a "spontaneous breaking of the symmetry" corresponding to the relative phase should occur, analogously to what (allegedly) happens in the interference of two independent Bose condensates. Here I argue that the prima facie analogy is misleading, and that the QM calculation indeed describes the behavior of a single inclusion.