Waveguide Bandgap Engineering with an Array of Superconducting Qubits

The interaction of qubits with free space instead of a cavity gives rise to several effects, which could play an important role for the implementation of a quantum computer. One of the most intriguing features is that in one-dimensional free space the interaction between qubits is of infinite range and can be tuned by varying the qubit separation [1]. In this work, we experimentally study an array of eight superconducting transmon qubits with local frequency control, which are all coupled to the mode continuum of a superconducting waveguide. The spacing between adjacent qubits is substantially smaller than the wavelength corresponding to their excitation frequency, eliminating almost completely the coherent exchange type interaction between qubits. By consecutively tuning the qubits to a common resonance frequency we observe the formation of super- and subradiant states as well as the emergence of a bandgap. Making use of the anharmonic level structure of the transmon qubit we study the nonlinear saturation of the collective modes with increasing photon number and electromagnetically induce a transparency window in the bandgap region of the ensemble.

[1] van Loo et al.,Science 342,1494 (2013)