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 ℓ between SQUIDs and their Josephson energy E0 J . Moreover, the harmonic drive of the SQUIDs generating the DCE radiation can be tuned in terms of the drive frequency Ω, amplitude δEJ, n, and phase φn, where the latter two parameters can be modulated for each SQUID n in the periodic array individually, making our proposed lattice architecture quite versatile. We find a rich interplay between the band structure of the lattice, the harmonic drive of the SQUIDs, and the DCE photon-flux density, which thus allows us to control, guide, and manipulate DCE radiation. We develop a theoretical and computational model for our proposed system and calculate the DCE radiation for various experimental setups. In particular, we show that a harmonic drive that breaks the left-right symmetry results in quasi unidirectional DCE radiation. Possible applications of our results in quantum information technologies are discussed