Polarization dependence of spin-electric transitions in molecular exchange qubits

TL;DR

The paper develops a polarization-based framework to discriminate spin-electric and magnetic-dipole transitions in molecular spin triangles, addressing quasi-optical probing where both couplings contribute. By constructing explicit dipole operators for magnetic and electric channels and analyzing several spin-qubit families (chirality, spin-sum, generalized exchange) across parallel and tilted magnetic fields, the authors show that circular, linear, and elliptical polarizations selectively address different transition channels, thereby revealing the physical origin of zero-field splitting and the underlying spin-Hamiltonian terms. The work extends to higher spins ($s_i>\tfrac12$) and to Faraday and Voigt geometries, providing detailed polarization rules and, in many cases, quantitative intensity and ellipticity descriptions to guide experiments. Overall, the results offer a practical, geometry-aware method to identify spin-electric couplings and to tailor spin-qubit control in molecular magnets, with implications for coherence properties and quantum information processing in exchange-coupled spin triangles.

Abstract

Quasi-optical experiments are emerging as a powerful technique to probe magnetic transitions in molecular spin systems. However, the simultaneous presence of the electric- and magnetic-dipole induced transitions poses the challenge of discriminating between these two contributions. Besides, the identification of the spin-electric transitions can hardly rely on the peak intensity, because of the current uncertainties on the value of the spin-electric coupling in most molecular compounds. Here, we compute the polarizations required for electric- and magnetic-dipole induced transitions through spin-Hamiltonian models of molecular spin triangles. We show that the polarization allows a clear discrimination between the two kinds of transitions. In addition, it allows one to identify the physical origin of the zero-field splitting in the ground multiplet, a debated issue with significant implications on the coherence properties of the spin qubit implemented in molecular spin triangles.

Figures (4)

• Figure 1: Schematic view of a spin triangle interacting with a freely propagating beam. The scheme indicates the convention used in the calculations for the molecular reference frame (gray) and the interspin in-plane unit vectors ${\bf n}_{ij}^\perp$ (blue), perpendicular to the sides of the triangle.
• Figure 2: Level scheme of the spin triangle with Dzyaloshinskii-Moriya interaction (chirality qubit), for magnetic field (a) oriented along the $z$ axis ($\theta=0$) or (b) tilted away from such axis ($\theta\neq 0$). Red and blue arrows correspond to magnetic- and electric-field induced transitions, respectively. The letter "C" denotes circular polarization.
• Figure 3: Level scheme of the spin triangle with inhomogeneous Heisenberg couplings (spin-sum qubit), for arbitrary orientations of the magnetic field. Red and blue arrows correspond to magnetic- and electric-field induced transitions, respectively. The letter "C" ("L") denotes circular (linear) polarization.
• Figure 4: Level scheme of the spin triangle with Dzyaloshinskii-Moriya interaction and inhomogeneous Heisenberg exchange (generalized exchange qubit), for magnetic field (a) oriented along the main molecule ($\theta=0$) or (b) tilted away from such axis ($\theta\neq 0$). Red (blue) arrows correspond to magnetic-field (electric-field) induced transitions. The letters "C", "L", and "E" denote circular, linear, and elliptical polarizations, respectively.