Completion of Phase I and Preparation for Phase II of the HAYSTAC Experiment

The HAYSTAC experiment utilizes a tunable resonant microwave cavity to search for dark matter axions. We report on the system and the results from Phase I of the experiment. This phase relied on a 9 T magnet, Josephson parametric amplifiers, and a dilution refrigerator for the operation of the experiment. Axion models with two photon coupling $\ g_{a\gamma\gamma}\gtrsim2\times 10^{-14}\ \mathrm{GeV}$ were excluded in the $\ 23.15<m_a<24.0\ \mathrm{\mu eV}$ mass range. Phase II of the experiment will include upgrades to the cryogenics system and a new squeezed-state receiver. Finally, we discuss work on multi-rod cavities and photonic band gap resonators for higher frequency operation.