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arXiv:2106.07342

On the question of the classical analogue of the Fano problem

M.B. Lebedev, O. V. Misochko

Published May 24, 2021• 0 citations
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Abstract

A system of interacting classical oscillators is discussed, similar to a quantum mechanical system of a discrete energy level, interacting with the energy quasi-continuum of states considered Fano. The limit of a continuous spectrum is analyzed together with the possible connection of the problem under study with the generation of coherent phonons.

DOI
10.48550/arxiv.2106.07342

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A system of interacting classical oscillators is discussed, similar to a quantum mechanical system of a discrete energy level, interacting with the energy quasi-continuum of states considered Fano. The limit of a continuous spectrum is analyzed together with the possible connection of the problem under study with the generation of coherent phonons.
In a multi-level quantum system Fano coherences stand for the formation of quantum coherences due to the interaction with the continuum of modes characterizing an incoherent process. In this paper we propose a V-type three-level quantum system on which we certify the presence of genuinely quantum traits underlying the generation of Fano coherences. We do this by determining work conditions that allows for the loss of positivity of the Kirkwood-Dirac quasiprobability distribution of the stochastic energy changes within the discrete system. We also show the existence of nonequilibrium regimes where the generation of Fano coherences leads to a non-negligible excess energy given by the amount of energy that is left over with respect to the energy of the system at the beginning of the transformation. Excess energy is attained provided the initial state of the discrete system is in a superposition of the energy eigenbasis. We conclude the paper by studying the thermodynamic efficiency of the whole process.
We seek to illustrate Fano interference in a classical coupled oscillator by using classical analogues of the atom–laser interaction. We present an analogy between the dressed state picture of coherent atom–laser interaction and a classical coupled oscillator. The Autler–Townes splitting due to the atom–laser interaction is analogous to the splitting of normal-mode frequencies of a coupled oscillator. Using this analogy, we simulate and experimentally demonstrate Fano interference and the associated phenomena in three-level atoms in a coupled electrical resonator circuit. This work aims to highlight analogies between classical and quantum systems for students at the postgraduate and graduate levels. Also, the reported technique can be easily realized in undergraduate laboratories.
Abstract The Fano resonance has been a familiar and important feature in atomic and molecular physics for more than half a century. Typically, the combination of a discrete state with one or more continua results in an asymmetric peak in the ionization spectrum. The peak-shape, called the Fano profile, can be expressed by a simple formula derived by Fano in 1935. However, the interpretation of its characteristic parameter q , which represents the asymmetry of the peak in the formula, is not necessarily intuitively transparent. The Fano resonance is not necessarily a quantum effect, but it is a manifestation of a certain physical mechanism in various systems, both quantum and classical. Through the derivation of q from the known classical pictures with the classical coupled oscillator, we interpret the q value with a geometrical view. And further, we introduce a complex valued q parameter for the description of the resonance with a damped oscillator.
In the present contribution we discuss the role of experimental limitations in the classical limit problem. We studied some simple models and found that Quantum Mechanics does not re-produce classical mechanical predictions, unless we consider the experimental limitations ruled by uncertainty principle. We have shown that the discrete nature of energy levels of integrable systems can be accessed by classical measurements. We have defined a precise limit for this procedure. It may be used as a tool to define the classical limit as far as the discrete spectra of integrable systems are concerned. If a diffusive environment is considered, we conclude that the "lifetime" of discreteness is approximately 1/κ1/κ1/κ (κκκ is the diffusion constant), thus it was possible to relate the classical limit of a spectra with the action of an environment and experimental resolution.
In the present contribution we discuss the role of experimental limitations in the classical limit problem. We studied some simple models and found that Quantum Mechanics does not re-produce classical mechanical predictions, unless we consider the experimental limitations ruled by uncertainty principle. We have shown that the discrete nature of energy levels of integrable systems can be accessed by classical measurements. We have defined a precise limit for this procedure. It may be used as a tool to define the classical limit as far as the discrete spectra of integrable systems are concerned.