Polariton entering a continuum: Giant diffuse polaritonic resonance

Polaritons arise due to a light-matter interaction and have been amply investigated for atoms and molecules in a quantum field. By increasing the coupling between the atom/molecule and the cavity, the upper polariton penetrates into the continuum (i.e., ionization continuum of atoms or molecules or dissociation continuum of molecules) within the standard two-level approach. We investigate what happens to the polaritons in reality. We first show that the upper polariton cannot enter the continuum if the atomic or molecular system itself does not support metastable states, often called resonances, and instead becomes a giant diffuse bound polariton which can be extended in space to any size one wishes. Then, we show how external perturbations can enable such a diffuse polariton to penetrate into the continuum and turn it into a metastable polariton, i.e., into a polaritonic resonance. In order to achieve these results the coupling of the bound states to the continuum induced by the quantum light has to be taken into account. We discuss how such giant diffuse bound polaritons as well as polaritonic resonances including their finite lifetime can be calculated and present explicit numerical examples. The results provide a complete picture of what happens to the upper polariton in the vicinity of the continuum and may be utilized to enhance ionization or dissociation inside the cavity.

Figure 1

The energies of the polaritons plotted as a function of the system-cavity coupling parameter ${\epsilon }_{\mathrm{cav}}^{}$ [see the Hamiltonian (3)]. Our calculations employ the Rosen-Morse potential [27, 28] as defined in the text. The energies of the TLS polaritons are presented in red color, and their counterparts computed including the continuum states are depicted in black color. As a reference, the threshold energy is marked by a dashed blue color. Atomic units are used throughout.

Figure 2

The energies of the TLS polaritons and the numerically exact eigenvalues of ${\widehat{H}}_{\mathrm{S}}+\text{perturbation}$. Here, ${\widehat{H}}_{\mathrm{S}}$ corresponds to Fig. 1, and the perturbation consists of two tiny potential barriers which generate shape-type resonances of the atomic/molecular system. The exact UP remains still lower in energy than the TLS UP, much as in Fig. 1. On the other hand, contrary to Fig. 1, the exact UP penetrates into the continuum, giving rise to a giant polaritonic resonance, manifested here by a series of avoided crossings. Atomic units are used throughout.

Figure 3

The UP resonance calculated by means of the complex scaling method [26] for ${\epsilon }_{\mathrm{cav}}=0.15$ for the same potential ${\widehat{H}}_{\mathrm{S}}+\text{perturbation}$ as in the calculation shown in Fig. 2. In this method, the bound states stay on the real energy axis, the continuum states rotate into the complex energy plane and align along a straight line in this plane depending on the scaling, and the resonances are uncovered as isolated points in this plane. The value of energy along the real axis provides the energetic position of the resonance and the imaginary part is half the width of the resonance. The plot shows the bound LP, the rotated continuum states, and the uncovered UP resonance as black dots. The red lines are drawn to guide the eye. Atomic units are used throughout.