Cavity engineering of Hubbard $U$ via phonon polaritons

TL;DR

This paper explores how phonon polaritons in optical cavities can be used to control electronic interactions, revealing regimes where interactions decrease or increase, and identifying spectral features observable by photoemission.

Contribution

It introduces a microscopic model for nonlinear electron-phonon interactions in cavities and analyzes their impact on electronic correlations and spectral features.

Findings

Electronic interactions increase inside a dark cavity.

Driving the cavity decreases electronic interactions.

Spectral splitting into three bands could be observed experimentally.

Abstract

Pump-probe experiments have suggested the possibility to control electronic correlations by driving infrared-active phonons with resonant midinfrared laser pulses. In this work we study two possible microscopic nonlinear electron-phonon interactions behind these observations, namely coupling of the squared lattice displacement either to the electronic density or to the double occupancy. We investigate whether photon-phonon coupling to quantized light in an optical cavity enables similar control over electronic correlations. We first show that inside a dark cavity electronic interactions increase, ruling out the possibility that $T_c$ in superconductors can be enhanced via effectively decreased electron-electron repulsion through nonlinear electron-phonon coupling in a cavity. We further find that upon driving the cavity, electronic interactions decrease. Two different regimes emerge: (i) a strong coupling regime where the phonons show a delayed response at a time proportional to the inverse coupling strength, and (ii) an ultra-strong coupling regime where the response is immediate when driving the phonon polaritons resonantly. We further identify a distinctive feature in the electronic spectral function when electrons couple to phonon polaritons involving an infrared-active phonon mode, namely the splitting of the shake-off band into three bands. This could potentially be observed by angle-resolved photoemission spectroscopy.