Quantum vortices in Josephson junction arrays

Alexander van Oudenaarden, S. J. K. Várdy, Johan E. Mooij

Andreas J. Wallraff, Alexander V. Lukashenko, Jürgen Lisenfeld +5 more

Samuel A. Wilkinson

Josephson junction arrays (JJAs) are engineered many-body quantum systems consisting of several superconducting islands connected by thin tunnel barriers - Josephson junctions (JJs). They are of interest both from a fundamental point of view (e.g. addressing questions of macroscopic quantum physics, providing model systems in which to study complex many-body phenomena) and from the prospect of technological applications (e.g. quantum computing, metrology, metamaterials). In this thesis we present various tools and techniques for the theoretical study of JJAs, and then put these tools to use in the modelling of two particular experiments on JJAs. In our presentation of the physics of JJAs, we emphasise phenomena unique to arrays (i.e. not seen in single junction devices such as qubits). We investigate charge transport through the the bilinear array, consisting of two linear chains of JJs, and show that it exhibits both Coulomb drag and depinning. We predict new phenomena arising from the interplay between Coulomb drag and depinning at voltages higher than have so far been experimentally reported. We then turn our attention to recent experiments in which planar JJAs were placed in 3-D microwave cavities, with vortices being injected via an externally applied magnetic eld. We calculate the impedance spectrum using linear response theory, which enables us to see when new vortices enter the system in the form of sharp changes in the resonance frequency.

Samuel A. Wilkinson, Jared H. Cole

Recent experiments on Josephson junction arrays (JJAs) in microwave cavities have opened up a new avenue for investigating the properties of these devices while minimizing the amount of external noise coming from the measurement apparatus itself. These experiments have already shown promise for probing many-body quantum effects in JJAs. In this work, we develop a general theoretical description of such experiments by deriving a quantum phase model for planar JJAs containing quantized vortices. The dynamical susceptibility of this model is calculated for some simple circuits, and signatures of the injection of additional vortices are identified. The effects of decoherence are considered via a Lindblad master equation.

Caspar H. van der Wal, P Kuiper, Johan E. Mooij

Alexander van Oudenaarden, B. van Leeuwen, M. P. M. Robbens +1 more

The quantum transport of vortices in very long and narrow arrays of small Josephson junctions is studied experimentally. We investigate the forming of a Mott insulator in periodic arrays. When the vortex density is commensurate with the one-dimensional periodic potential, the vortices localize due to the strong repulsive vortex-vortex interaction. We explore the influence of interaction strength, bandwidth, sample geometry, and temperature on the stability of the Mott states.