Squeezing and quantum state engineering with Josephson travelling wave amplifiers

We develop a quantum theory describing the input-output properties of Josephson traveling wave parametric amplifiers. This allows us to show how such a device can be used as a source of nonclassical radiation, and how dispersion engineering can be used to tailor gain profiles and squeezing spectra with attractive properties, ranging from genuinely broadband spectra to squeezing combs consisting of a number of discrete entangled quasimodes. The device's output field can furthermore be used to generate a multi-mode squeezed bath-a powerful resource for dissipative quantum state preparation. In particular, we show how it can be used to generate continuous variable cluster states that are universal for measurement based quantum computing. The favorable scaling properties of the preparation scheme makes this a promising path towards continuous variable quantum computing in the microwave regime.