Optical excitations in compressible and incompressible two-dimensional electron liquids

Abstract

Optically generated electron-hole pairs can probe strongly correlated electronic matter, or, by forming exciton-polaritons within an optical cavity, give rise to photonic nonlinearities. The present paper theoretically studies the properties of electron-hole pairs in a two-dimensional electron liquid in the fractional quantum Hall regime. In particular, we quantify the effective interactions between optical excitations by numerically evaluating the system's energy spectrum under the assumption of full spin and Landau level polarization. Optically most active are those pair excitations which do not modify the correlations of the electron liquid, also known as multiplicative states. In the case of spatial separation of electrons and holes, these excitations interact repulsively with each other. However, when the electron liquid is compressible, other non-multiplicative configurations occur at lower energies. The interactions of such dark excitations strongly depend on the liquid, and can also become attractive. For the case of a single excitation, we also study the effect of Landau level mixing in the valence band which can dramatically change the effective mass of an exciton.

Strongly correlated electron–photon systems

“…5b). Specifically, it has been experimentally observed that at low carrier density, the polariton-polariton interaction strength depends on the nature of underlying many-body electronic state 9800 , while the numerical simulation suggests that for high-density of carriers such dependence could be washed out 114 . Therefore, the effect of strongly correlated electronic states on the quantum optical response and engineering strong effective photon-photon interactions remain open problems.…”

Polaron spectroscopy of interacting Fermi systems: Insights from exact diagonalization

“…Given the hardness of the many-body problem, polarons in strongly interacting many-body backgrounds have been theoretically considered in a few special settings only or under very rough approximations. We mention attempts in the context of fractional Chern insulators [27,28], Fermi superfluids along the BEC-BCS crossover [29,30], excitonic insulators [31], Mott and charge transfer insulators [32], kinetic magnetism [33,34], Holstein polarons in Luttinger liquids [35], together with a few related works on the dressing of optical excitations in Mott insulators [36,37] and fractional quantum Hall systems [38]. Diffusion Quantum Monte Carlo can be used to study Bose [39] and Fermi polarons [40] in the intermediate correlation regime, but does not allow for the determination of the full spectral information.…”