Creation of a squeezed photon distribution using artificial atoms with broken inversion symmetry

We consider a two level system with both a transversal and a longitudinal coupling to the electromagnetic field of a resonator. Using a polaron transformation, this Hamiltonian can be mapped onto a Jaynes-Cummings Hamiltonian with generalized field operators acting on the electromagnetic field in the resonator. In contrast to the usual ladder operators $a$ and $a^{†}$, these operators exhibit a non-monotous coupling strength with respect to the number $n$ of photons in the resonator. Especially, there are roots of the coupling between qubit and resonator at certain photon numbers $n_0$. We show, that this effect can be exploited to generate photon-number squeezed light, characterized by a Fano factor $F\ll 1$, with a large number of photons (e.g. of the order of ${10}^4$).