Josephson coupling energy ($U_J=-E_J\cos \varphi ,E_J=\hslash I_c/(2e)$)

The ideal Josephson junction has a phase-dependent energyDifferentiating and using the voltage–phase relation yieldsThus the ideal pair element stores and returns energy. At $V=0$ it carries a static electric current without electrical power loss. Under a nonzero periodic drive its instantaneous power need not vanish, but its energy returns after a full phase cycle. Real junctions also have a capacitance, quasiparticle transport and an external circuit; their total losses cannot be inferred from this conservative pair term alone.