  The rapid progress in quantum information processing leads to a rising demand
for devices to control the propagation of electromagnetic wave pulses and to
ultimately realize a universal and efficient quantum memory. While in recent
years significant progress has been made to realize slow light and quantum
memories with atoms at optical frequencies, superconducting circuits in the
microwave domain still lack such devices. Here, we demonstrate slowing down
electromagnetic waves in a superconducting metamaterial composed of eight
qubits coupled to a common waveguide, forming a waveguide quantum
electrodynamics system. We analyze two complementary approaches, one relying on
dressed states of the Autler-Townes splitting, and the other based on a
tailored dispersion profile using the qubits tunability. Our time-resolved
experiments show reduced group velocities of down to a factor of about 1500
smaller than in vacuum. Depending on the method used, the speed of light can be
controlled with an additional microwave tone or an effective qubit detuning.
Our findings demonstrate high flexibility of superconducting circuits to
realize custom band structures and open the door to microwave dispersion
engineering in the quantum regime.
