Cavity-assisted superconductivity in low-dimensional systems*

Coupling to vacuum fluctuations of an electromagnetic cavity mode can significantly enhance the electron-electron pairing. The enhancement is due to significant compression of the cavity field far below the free-space diffraction limit. We consider low-dimensional systems, such as helical one-dimensional edge modes on a topological material or discrete energy levels in quantum dots coupled via a cavity mode with proper polarization. Applying an Eliashberg-type self-consistent approximation, we investigate the resulting superconducting pairing in various unconventional channels, including both a finite center-of-mass momentum, as well as dynamical superconducting pairing. We explore signatures in the single-particle excitation spectrum, spin response, as well as polariton collective excitation. The platform enables exploration of optical control of superconducting states, enhanced charge transport, polariton superconductivity, and cavity BEC transition.