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

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 non-linearities 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 non-linearities observed in a recent experiment [M. Rehák et.al., Appl. Phys. Lett. 104, 162604], and we can evaluate the accomplishments of modified versions of the experimental circuit.

8 pages, 5 figures

References in corpus (13)

• Charge insensitive qubit design derived from the Cooper pair box
• Amplification and squeezing of quantum noise with a tunable Josephson metamaterial
• Photon-mediated interactions between distant artificial atoms
• Black-box superconducting circuit quantization
• Single artificial-atom lasing
• Ultrastrong coupling regime of cavity QED with phase-biased flux qubits
• Quantum limited amplification and entanglement in coupled nonlinear resonators
• Josephson junction-embedded transmission-line resonators: from Kerr medium to in-line transmon
• Four-qubit device with mixed couplings
• Blackbox Quantization of Superconducting Circuits using exact Impedance Synthesis
• Direct Josephson coupling between superconducting flux qubits
• Multi-frequency modes in superconducting resonators: Bridging frequency gaps in off-resonant couplings
• Two-photon lasing by a superconducting qubit