  General solutions to the quantum Rabi model involve subspaces with unbounded
number of photons. However, for the multiqubit multimode case, we find special
solutions with at most one photon for arbitrary number of qubits and photon
modes. Unlike the Juddian solution, ours exists for arbitrary single
qubit-photon coupling strength with constant eigenenergy. This corresponds to a
horizontal line in the spectrum, while still being a qubit-photon entangled
state. As a possible application, we propose an adiabatic scheme for the fast
generation of arbitrary single-photon multimode W states with nonadiabatic
error less than 1%. Finally, we propose a superconducting circuit design,
showing the experimental feasibility of the multimode multiqubit Rabi model.
