Waveguides with exceptional points of degeneracy for circuit QED

The dispersion relation of a superconducting waveguide can be engineered by periodically modulating parameters along its length. Previous experiments have coupled superconducting qubits to the approximately quadratic band edges of microwave photonic crystals [1] [2]. However, higher-order polynomial dispersion is also possible, when multiple waveguides are side-coupled such that the resulting system has an exceptional point of degeneracy (EPD) [3]. EPDs of orders 3 (a cubic stationary inflection point), 4 (a quartic degenerate band edge), and higher have been realized with centimeter-scale copper waveguides [4]. In this talk I present experimental and theoretical progress towards realizing (greater than quadratic) exceptional points of degeneracy in a circuit QED architecture that consists of multiple superconducting coplanar waveguides periodically coupled in parallel. I also discuss how superconducting qubits can be coupled to these waveguides, with applications in slow light and multimode strong coupling.

[1] Y. Liu and A. A. Houck, Nat. Phys. 13, 48 (2017).

[2] N. M. Sundaresan, R. Lundgren, G. Zhu, A. V. Gorshkov, and A. A. Houck, Phys. Rev. X 9, 011021 (2019).

[3] A. Figotin and I. Vitebskiy, Laser Photonics Rev. 5, 201 (2011).

[4] T. Mealy, A. Nikzamir, A. F. Abdelshafy, M. Y. Nada and F. Capolino, 2021 International Applied Computational Electromagnetics Society Symposium (ACES), 2021, pp. 1-3, doi: 10.1109/ACES53325.2021.00133.