  Enhancing interactions in many-body quantum systems, while protecting them
from environmental decoherence, is at the heart of many quantum technologies.
Waveguide quantum electrodynamics is a promising platform for achieving this,
as it hosts infinite-range interactions and decoherence-free subspaces of
quantum emitters. However, as coherent interactions between emitters are
typically washed out in the wavelength-spacing regime hosting decoherence-free
states, coherent control over the latter becomes limited, and many-body
Hamiltonians in this important regime remain out of reach. Here we show that by
incorporating emitter arrays with nonlinear waveguides hosting parametric gain,
we obtain a unique class of many-body interaction Hamiltonians with coupling
strengths that increase with emitter spacing, and persist even for
wavelength-spaced arrays. We then propose to use these Hamiltonians to
coherently generate decoherence-free states directly from the ground state,
using only global squeezing drives, without the need for local addressing of
individual emitters. Interestingly, we find that the dynamics approaches a
unitary evolution in the limit of weak intra-waveguide squeezing, and discuss
potential experimental realizations of this effect. Our results pave the way
towards coherent control protocols in waveguide quantum electrodynamics, with
applications including quantum computing, simulation, memory and nonclassical
light generation.
