Quantum electrodynamics and photon-assisted tunnelling in long Josephson junctions

We describe the interaction between an electromagnetic field and a long Josephson junction (JJ) driven by a dc current. We calculate the amplitudes of emission and absorption of light via the creation and annihilation of quantized Josephson plasma waves (JPWs). Both, the energies of JPW quanta and the amplitudes of light absorption and emission, strongly depend on the junction's length and can be tuned by an applied dc current. Moreover, photon-assisted macroscopic quantum tunnelling in long Josephson junctions show resonances when the frequency of the outside radiation coincides with the current-driven eigenfrequencies of the quantized JPWs.