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Turkish Journal of Physics

Abstract

We formulate a quantum-mechanical system consisting of a single discrete state coupled to an infinite ladder of equally spaced states, with the coupling described by a Lorentzian profile. Various limiting cases of this system correspond to well-known models in quantum optics: the narrow-resonance limit yields the Rabi model, the wide-resonance limit yields the Bixon--Jortner model, the wide-resonance true continuum limit yields the Wigner--Weisskopf model, and the fixed-resonance true continuum limit yields a system typically studied using methods developed by Fano. We obtain a semianalytical solution to the eigenvalue problem by reducing it to a transcendental equation and demonstrate the limiting behaviors described above. We then investigate numerically the dynamics of the initial discrete state and show that, in various limiting regimes, the system exhibits a wide range of behaviors predicted by the asymptotic theory, including exponential decay, revivals, Rabi oscillations, and damped oscillations. The ability of the system to interpolate between such a rich variety of behaviors and established model systems, together with the accessibility of a semianalytical solution, makes it a useful model in quantum optics and related fields.

Author ORCID Identifier

ENES İŞGÖRÜR: 0009-0000-8157-6201

OSMAN CEVHEROĞLU: 0009-0004-4572-5379

ARKADAŞ ÖZAKIN: 0000-0002-2318-9227

DOI

10.55730/1300-0101.2811

Keywords

Quantum mechanics, quantum optics, quantum revivals, Bixon-Jortner model, Wigner-Weisskopf approximation, Fano resonances

First Page

170

Last Page

191

Publisher

The Scientific and Technological Research Council of Türkiye (TÜBİTAK)

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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