Ultrafast adiabatic passages in ultrastrongly coupled light-matter systems

We have obtained the solutions of the multimode quantum Rabi model when all modes have identical frequencies $\omega$, including dark states $|\phi_K\rangle$ with at least $K$ $(K=1,2,3,\ldots)$ photons. Extended to the multiqubit case, they lie close to another dark state $\vert \psi\rangle$ with at most one photon in the spectrum. Taking advantages of such solutions, we find a linear and symmetry-protected adiabatic passage through $\vert \psi\rangle$ to fast generate arbitrary single-photon $M$-mode $W$ states $\vert W_M\rangle$ with exactly the same speed. The effective minimum energy gap during the adiabatic evolution is further enlarged to $0.63\omega$ when Stark shifts are included, such that arbitrary $\vert W_M\rangle$ can be ultrafast generated in $1.55\times 2\pi\omega^{-1}$ with fidelity $99\%$, indepedent of $M$. This work reveals the existence of linear ultrafast adiabatic passages in light-matter systems.