Effective theory of lattice electrons strongly coupled to quantum electromagnetic fields

Abstract

Recent experiments have revealed the tantalizing possibility of fabricating lattice electronic systems strongly coupled to quantum fluctuations of electromagnetic fields, e.g., by means of geometry confinement from a cavity or artificial gauge fields in quantum simulators. In this work, we develop a high-frequency expansion to construct the effective models for lattice electrons strongly coupled to a continuum of off-resonant photon modes with arbitrary dispersion. The theory is nonperturbative in the light-matter coupling strength and is therefore particularly suitable for the ultrastrong light-matter coupling regime. Using the effective models, we demonstrate how the dispersion and topology of the electronic energy bands can be tuned by the cavity. In particular, quasi-one-dimensional physics can emerge in a two-dimensional square lattice due to a spatially anisotropic band renormalization, and a topologically nontrivial anomalous quantum Hall state can be induced in a honeycomb lattice when the cavity setup breaks time-reversal symmetry. We also demonstrate that the photon-mediated interaction induces an unconventional superconducting paired phase distinct from the pair-density-wave state discussed in models with truncated light-matter coupling. Finally, we study a realistic setup of a Fabry-Pérot cavity. Our work provides a systematic framework to explore the emergent phenomena due to strong light-matter coupling and points out alternative directions of engineering orders and topological states in solids.

Electron-photon Chern number in cavity-embedded 2D moiré materials

“…3 and 88% for the bottom one. Therefore, in such configuration, one can describe the system using an effective electronic Hamiltonian, following the methods proposed in the literature [20][21][22][23]. Indeed, we verified that the diagrams of Fig.…”

“…Recent theoretical works have investigated how to exploit cavity QED to control topological properties of systems, such as 1D tight-binding chains described by the SSH model [21]. Concerning 2D systems, a recent work has studied 2D bulk materials in squared lattices [22] where the standard electron Chern number is computed by considering an effective electronic Hamiltonian ob-tained by adiabatic elimination of the photon degrees of freeedom. A letter exploring single-sheet graphene ribbons [23] has studied electron Chern numbers computed once the cavity field is approximated in a classical coherent state.…”

Collective theory for an interacting solid in a single-mode cavity

“…Before presenting this approach, let us emphasize that the single-mode cavity, with mesoscopic length scales, should be clearly distinguished from an extended cavity or a waveguide, such as a coplanar cavity which confines the light only in one direction [26]. In such cavities matter can easily be taken to the thermodynamic limit, in which case the single-mode coupling vanishes, but there is a continuum of modes with different in-plane momenta which can have a non-vanishing combined effect on matter [13,[27][28][29][30]. The challenge is to ensure that the coupling affects a broad momentum range, whereas in free space only photons with momenta much smaller than the extent of the Brillouin zone are relevant for the low energy physics.…”

Halide Perovskite Artificial Solids as a New Platform to Simulate Collective Phenomena in Doped Mott Insulators

“…The first element to realize Ĥ normalt normalo normalt is given by the electromagnetic field that drives the long-range interaction among excitons in different nanocubes, which can be expressed by − Ĥ int = prefix− ∑ r Λ E ⃗ ̂ ( r Λ ) · D ⃗ ̂ boldr normalΛ where E ⃗ ̂ ( r Λ ) is the electromagnetic field and D ⃗ ̂ bold-italicr normalΛ the dipole operator at the superlattice site r Λ . If the electromagnetic field is traced out, eq can be written as an effective dipole–dipole interaction term, whose strength is characterized by a long-range | r Λ, n – r Λ, m | –1 decay, | r Λ, n – r Λ, m | being the distance between the n th and m th dipoles.…”