Haloscope At Yale Sensitive To Axion CDM (HAYSTAC) is looking for dark matter in the form of Axions which are very low mass particles that are predicted in the context of the standard model of electroweak interactions (quark, gluon, W, Z, Higgs, etc. are all part of this model). If they do indeed exist and form dark matter, they will convert to radiofrequency photons in the presence of a strong magnetic field. The photon energy, hence frequency, is essentially determined by the axion mass, and is expected to be in the 1-20 GHz region. The heart of our experiment is a tunable radiofrequency (microwave) cavity resonator, which serves to build up the axion signal, and a quantum limited amplifier based on the Josephson effect which occurs when Cooper pairs tunnel though an insulating layer separating two superconductors.