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We consider the propagation of a classical electromagnetic wave through a transmission line, formed by identical superconducting charge qubits inside a superconducting resonator. Since the qubits can be in a coherent superposition of quantum states, we show that such a system demonstrates interesting new effects, such as a "breathing" photonic crystal with an oscillating bandgap, and a "quantum Archimedean screw" that transports, at an arbitrary controlled velocity, Josephson plasma waves through the transmission line. The key ingredient of these effects is that the optical properties of the Josephson transmission line are controlled by the quantum coherent state of the qubits.

The recent growing interest in terahertz (THz) and sub-THz science and technology is due to its many important applications in physics, astronomy, chemistry, biology, and medicine, including THz imaging, spectroscopy, tomography, medical diagnosis, health monitoring, environmental control, as well as chemical and biological identification. We review the problem of linear and nonlinear THz and sub-THz Josephson plasma waves in layered superconductors and their excitations produced by moving Josephson vortices. We start by discussing the coupled sine-Gordon equations for the gauge-invariant phase difference of the order parameter in the junctions, taking into account the effect of breaking the charge neutrality, and deriving the spectrum of Josephson plasma waves.We also review surface and waveguide Josephson plasma waves. The spectrum of these waves is presented, and their excitation is discussed. We review the propagation of weakly nonlinear Josephson plasma waves below the plasma frequency, ω J , which is very unusual for plasma-like excitations.In close analogy to nonlinear optics, these waves exhibit numerous remarkable features, including a self-focusing effect, and the pumping of weaker waves by a stronger one. In addition, an unusual stop-light phenomenon, when ∂ω/∂k ≈ 0, caused by both nonlinearity and dissipation, can be observed in the Josephson plasma waves. At frequencies above ω J , the current-phase nonlinearity can be used for transforming continuous sub-THz radiation into short, strongly amplified, pulses.We also present quantum effects in layered superconductors, specifically, the problem of quantum MQT -macroscopic quantum tunnelling.z-axis is directed across the layers; y-axis is directed along the magnetic field.4