Normal modes of a superconducting transmission-line resonator with embedded lumped element circuit components

Henrik Lund Mortensen; Klaus Mølmer; Christian Kraglund Andersen

doi:10.1103/PhysRevA.94.053817

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Normal modes of a superconducting transmission-line resonator with embedded lumped element circuit components

Henrik Lund Mortensen, Klaus Mølmer, Christian Kraglund Andersen

DOI 10.1103/PhysRevA.94.053817 · Physical Review A

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Abstract

We present a method to identify the coupled, normal modes of a superconducting transmission line with an embedded lumped element circuit. We evaluate the effective transmission-line nonlinearities in the case of Kerr-like Josephson interactions in the circuit and in the case where the embedded circuit constitutes a qubit degree of freedom, which is Rabi coupled to the field in the transmission line. Our theory quantitatively accounts for the very high and positive Kerr nonlinearities observed in a recent experiment [M. Rehák, P. Neilinger, M. Grajcar, G. Oelsner, U. Hübner, E. Il'ichev, and H.-G. Meyer, Appl. Phys. Lett. 104, 162604 (2014)], and we can evaluate the accomplishments of modified versions of the experimental circuit.