Dynamical Casimir effect in a superconducting circuit periodic lattice

The dynamical Casimir effect (DCE) is the generation of real photons out of the quantum vacuum due to a rapid modulation of boundary conditions for the electromagnetic field, such as a mirror oscillating at speeds comparable to the speed of light. Previous work demonstrated experimentally that DCE radiation can be generated in electrical circuits based on superconducting microfabricated waveguides, where a rapid modulation of boundary conditions corresponding to semi-transparent mirrors is realized by tuning the applied magnetic flux through superconducting quantum-interference devices (SQUIDs) that are embedded in the waveguide circuits. We propose a novel SQUID periodic lattice architecture, in which SQUIDs embedded in a coplanar waveguide (CPW) form the sites of a one-dimensional periodic lattice, resulting in a band structure and band gaps for the DCE radiation akin to classical photonic crystals. The band structure in our "quantum photonic crystals" can be tuned by the spatial distance between SQUIDs in the lattice and their Josephson energy. Moreover, the harmonic drive of the SQUIDs generating the DCE radiation can be tuned in terms of the drive frequency, amplitude, and phase. We find a rich interplay between the band structure of the lattice, the harmonic drive of the SQUIDs, and the DCE photon-flux density. We develop a theoretical and computational model for our proposed system and calculate the DCE radiation for various experimental setups.