  An amplifier combining noise performances as close as possible to the quantum
limit with large bandwidth and high saturation power is highly desirable for
many solid state quantum technologies such as high fidelity qubit readout or
high sensitivity electron spin resonance for example. Here we introduce a new
Traveling Wave Parametric Amplifier based on Superconducting QUantum
Interference Devices. It displays a 3 GHz bandwidth, a -102 dBm 1-dB
compression point and added noise near the quantum limit. Compared to previous
state-of-the-art, it is an order of magnitude more compact, its characteristic
impedance is in-situ tunable and its fabrication process requires only two
lithography steps. The key is the engineering of a gap in the dispersion
relation of the transmission line. This is obtained using a periodic modulation
of the SQUID size, similarly to what is done with photonic crystals. Moreover,
we provide a new theoretical treatment to describe the non-trivial interplay
between non-linearity and such periodicity. Our approach provides a path to
co-integration with other quantum devices such as qubits given the low
footprint and easy fabrication of our amplifier.
