Molecular Interactions Induced by a Static Electric Field in Quantum Mechanics and Quantum Electrodynamics

Abstract

We study the interaction between two neutral atoms or molecules subject to a uniform static electric field, using quantum mechanics (QM) and quantum electrodynamics (QED) applied to coupled harmonic Drude oscillators. Our focus is to understand the interplay between dispersion interactions and field-induced electrostatics and polarization in both retarded and non-retarded regimes. We present an exact solution for two coupled oscillators using QM and Rayleigh-Schrödinger perturbation theory, demonstrating that the external field controls the strength of different intermolecular interactions and relative orientations of the molecules. In the retarded regime described by QED and rationalized by stochastic electrodynamics, our analysis shows that field-induced electrostatics and polarization terms remain unchanged (in isotropic and homogeneous vacuum) compared to the non-retarded QM description, in contrast to a recent work. Our framework combining four complementary theoretical approaches paves the way to a systematic description and enhanced understanding of molecular interactions under the combined action of external and vacuum fields.

Controlling the atom-sphere interaction with an external electric field

“…[48] for a simple argument). Hence, we may comfortably neglect any effect of E 0 in the dispersive interaction [50,51].…”

“…It was recently shown that an electrostatic field could generate a repulsive interaction between atoms [47]. The interpretation of their result was disputed [48,49], and subsequently, a thorough and rigorous study was carried out to settle the issue [50,51]. However, regardless of the interpretation, Ref.…”