Classical Fano oscillator

Abstract

Starting from the quantum-mechanical Fano-Anderson Hamiltonian, we derive classical equations of motion for coordinates associated with the discrete and continuum states. The frequency-dependent absorption spectrum associated with this classical system exhibits the same Fano line shape as the quantum-mechanical system when appropriate correspondences between classical and quantum variables are made. In the time domain, the response of this classical Fano oscillator depends upon the asymmetry parameter $q$ that appears in the expression for the Fano line shape. In particular, under the influence of impulsive driving of the system, the discrete oscillator's phase changes by $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$ as $q$ increases from zero (maximum asymmetry in the frequency domain) to $\ensuremath{\mp}\ensuremath{\infty}$ (minimum asymmetry). Previously published ultrafast-laser-pulse-driven coherent-phonon oscillations in degenerate $p$-type Si [K. Kato et al., Jpn. J. Appl. Phys. 48, 100205 (2009)] are discussed in light of these theoretical results.