Cooling microwave fields into general multimode Gaussian states

We show that a collection of lossy multichromatic modulated qubits can be used to dissipatively engineer arbitrary Gaussian states of a set of bosonic modes. Our ideas are especially suited to superconducting-circuit architectures, where all the required ingredients are experimentally available. The generation of such multimode Gaussian states is necessary for many applications, most notably measurement-based quantum computation. We build upon some of our previous proposals, where we showed how to generate single-mode and two-mode squeezed states through cooling and lasing. Special care must be taken when extending these proposals to many bosonic modes, and we discuss here how to overcome all the limitations and hurdles that naturally appear. For the sake of illustration, we work out two examples of Gaussian-state families consisting of Greenberger-Horne-Zeilinger and cluster states, which allow us to show that it is possible to use a set of N lossy qubits to cool down a bosonic chain of N modes to any desired Gaussian state.