On the ubiquity of Beutler-Fano profiles: from scattering to dissipative processes

Abstract

Fano models - consisting of a Hamiltonian with discrete-continuous spectrum - are one of the basic toy models in spectroscopy. They have been succesfull in explaining the lineshape of experiments in atomic physics and condensed matter. These models however have largely been out of the scope of dissipative dynamics, with ony a handful of works considering the effect of a thermal bath. Yet in nanostructures and condensed matter systems, dissipation strongly modulates the dynamics. In this article, we present an overview of the theoretical works dealing with Fano interferences coupled to a thermal bath and compare them to the scattering formalism. We provide the solution to any discrete-continuous Hamiltonian structure within the wideband approximation coupled to a Markovian bath. In doing so, we update the toy models that have been available for unitary evolution since the 1960s. We find that the Fano lineshape is preserved as long as we allow a rescaling of the parameters, and an additional Lorentzian contribution that reflects the destruction of the interference by dephasings. We discuss the pertinence of each approach - dissipative and unitary - to different experimental setups: scattering, transport and spectroscopy of dissipative systems. We finish by discussing the current limitations of the theories due to the wideband approximation and the memory effects of the bath.

Expanded bibliography, minor typos corrected

References in corpus (10)

• Semiconductor-metal nanoparticle molecules: hybrid excitons and non-linear Fano effect
• Non-Markovian quantum jumps
• Giant In-Particle Field Concentration and Fano Resonances at Light Scattering by High-Refractive Index Particles
• Probing decoherence through Fano resonances
• Exact quantum jump approach to open systems in Bosonic and spin baths
• Efimov states and their Fano resonances in a neutron-rich nucleus
• From Majorana theory of atomic autoionization to Feshbach resonances in high temperature superconductors
• Fano-Liouville Spectral Signatures in Open Quantum Systems
• Non-linear Fano Interferences in Open Quantum Systems: an Exactly Solvable Model
• Detecting weak coupling in mesoscopic systems with a nonequilibrium Fano resonance

Cited by in corpus (9)

• Adiabatic Elimination and Sub-space Evolution of Open Quantum Systems
• Probing electronic decoherence with high-resolution attosecond photoelectron interferometry
• The quantum and classical Fano parameter $q$
• Non-Hermitian Hamiltonians for Linear and Nonlinear Optical Response: a Model for Plexcitons
• Two-dimensional Fano lineshapes: Excited-state absorption contributions
• Fano Resonance between Stokes and Anti-Stokes Brillouin Scattering
• Suppressing deleterious effects of spontaneous emission in creating bound states in cold atom continuum
• Floquet-Engineering of Feshbach Resonances in Ultracold Gases
• Fano resonance in XUV generated by helium with few-cycle intense laser pulses and its classical analogy