An oxygen pump can produce high-purity high-pressure oxygen. Oxygen ions (O2−) are electrochemically pumped through a multi-stage electrolysis stack of cells. Each cell includes an oxygen-ion conducting solid-state electrolyte between cathode and anode sides. Oxygen dissociates into the ions at the cathode side. The ions migrate across the electrolyte and recombine at the anode side. An insulator is between adjacent cells to electrically isolate each individual cell. Each cell receives a similar volt potential. Recombined oxygen from a previous stage can diffuse through the insulator to reach the cathode side of the next stage. Each successive stage similarly incrementally pressurizes the oxygen to produce a final elevated pressure.