Introducing time-dependent drive into the Hamiltonian of quantised electric circuits

Question

Suppose I have the schematic of a superconducting electric circuit composed of (quasi) lossless linear inductances and capacitances and some non-linear inductances, eg. Josephson junctions. The Hamiltonian of the circuit is derived according to Devoret, 1997.

However this article considers the case only of a classical DC drive (so calles bias). Questions:

(1) Do you have any idea how to introduce a time-dependent drive into the system and how to consctruct the Hamiltonian of the given system? The driving may be considered classical and to begin with sinusoidal is enough.

(2) Do you have any idea how to treat the a non-classical drive, ie. the energy from the generators into the cicrcuit is coming in the form of single photons well separated in time?