Coherent single-spin electron resonance spectroscopy manifested at an exceptional-point singularity in doped polyacetylene

Abstract

Spin-dependent charge-transfer decay in an alkali atom-doped polyacetylene is studied in terms of the complex spectral analysis, revealing the single-spin Zeeman splitting influenced by the spin-orbit interaction. A non-Hermitian effective Hamiltonian has been derived from the total system Hermitian Hamiltonian using the Brillouin-Wigner-Feshbach projection method where the microscopic spin-dependent dissipation effect is correctly incorporated in the energy-dependent self-energy. Since the present method maintains the dynamical and chiral symmetries of the total system, we discovered two types of exceptional point (EP) singularities: The EP surface and the EP ring are attributed to the dynamical and chiral symmetry breaking, respectively. We reveal that the coherent single-spin electron resonance (SSESR) spectrum reflects the complex eigenenergy spectrum of the system. We formulate the SSESR spectrum in terms of the non-linear-response function in the Liouville-space pathway approach where we have constructed the Liouville-space basis using the complex eigenstates of the total Hamiltonian. We calculate the one-dimensional Fourier transform (1DFT) and two-dimensional Fourier transform (2DFT) SSESR spectra reflecting the spin-relaxation dynamics at the donor site. Whereas the 1DFT SSESR spectrum reflects the complex eigenenergy spectrum, the 2DFT gives detailed information about the quantum coherence in the spin-relaxation dynamics as a cross correlation between the two frequencies. We reveal a giant response in the coherent SSESR around the EP ring singularity due to the vanishing normalization factors at the EP ring and the resonance effect. We show this giant response is even more heavily pronounced in the 2DFT spectrum than in the 1DFT spectrum, which illustrates that the 2DFT SSESR can become a useful tool to observe the single-spin response of a molecule.