Is there a minimum requirement to how long a justice is expected to serve on the supreme court?

Not in the Constitution. Justices "hold their Offices during good Behaviour".

In the tradition and convention that governs the actual function of the US government, Justices can resign their office. There is no notice period and a Judge could resign as their first and only act in the office. It has never happened, neither in the supreme court nor in any inferior court.