Making ab initio QED functional(s): Nonperturbative and photon-free effective frameworks for strong light–matter coupling

Abstract

Strong light–matter coupling provides a promising path for the control of quantum matter where the latter is routinely described from first principles. However, combining the quantized nature of light with this ab initio tool set is challenging and merely developing as the coupled light–matter Hilbert space is conceptually different and computational cost quickly becomes overwhelming. In this work, we provide a nonperturbative photon-free formulation of quantum electrodynamics (QED) in the long-wavelength limit, which is formulated solely on the matter Hilbert space and can serve as an accurate starting point for such ab initio methods. The present formulation is an extension of quantum mechanics that recovers the exact results of QED for the zero- and infinite-coupling limit and the infinite-frequency as well as the homogeneous limit, and we can constructively increase its accuracy. We show how this formulation can be used to devise approximations for quantum-electrodynamical density-functional theory (QEDFT), which in turn also allows us to extend the ansatz to the full minimal-coupling problem and to nonadiabatic situations. Finally, we provide a simple local density–type functional that takes the strong coupling to the transverse photon degrees of freedom into account and includes the correct frequency and polarization dependence. This QEDFT functional accounts for the quantized nature of light while remaining computationally simple enough to allow its application to a large range of systems. All approximations allow the seamless application to periodic systems.

Molecular orbital theory in cavity QED environments

“…The electron-photon correlation basis is obtained diagonalizing the operator (d • ). Similar bases were also employed by Huo et al 25 as well as by Ashida et al 36 and Schäfer et al 39 . However, in our approach the ω p parameters are variationally optimized in this way dramatically improving the description of the system (See Supplementary Information).…”

Effective Hamiltonians in Nonrelativistic Quantum Electrodynamics

“…The effective Hamiltonian ( 26) is different from (15), and its physical interpretation is different. The response of the atom in the present case is not through the β ij (ω k ) function but through its dynamical polarizability, and the interaction of the k Fourier component of the induced dipole moment is with the total electric field and not with only its k component, as in the previous diagonal case (18).…”

“…All these possibilities have fostered the investigation of effective Hamiltonians containing an interaction term that is at least quadratic in the atom-field coupling, where the response of the atom is included in quantities such as, for example, its polarizability, thus allowing for a considerable reduction of the perturbative order required for calculating specific processes and of the number of relevant Feynman diagrams [6]. Very recently, resummation techniques, in which the polarizability is summed to any order, have been developed, and they could also be of great importance for the evaluation of radiative processes such as the Lamb shift and van der Waals interactions for nanostructured materials [16][17][18].…”

Pico-photonics: Anomalous Atomistic Waves in Silicon

“…This consideration is valid only in the long-wavelength limit, q → 0. Although there have been efforts to develop quantumelectrodynamic first-principles density-functional theory calculations [43,44], applications of such frameworks have been limited to artificial dielectric structures and cavities. These frameworks are also developed in the long-wavelength limit and the photon field is considered to be in vacuum.…”