A Fock state lattice approach to quantum optics

TL;DR

This paper introduces a Fock state lattice approach to analyze quantum optical models, revealing connections to condensed matter lattice models and uncovering phenomena like fractal spectra, chiral evolution, and topological states.

Contribution

It develops a method to map quantum optical Hamiltonians onto Fock-state lattices, providing new insights into their spectral and topological properties.

Findings

Demonstrates fractal spectrum in three-mode boson model

Shows chiral evolution with localized distributions in Fock-state lattices

Identifies topological edge states analogous to SSH model

Abstract

We analyze a set of models frequently appearing in quantum optical settings by expressing their Hamiltonians in terms of Fock-state lattices. The few degrees-of-freedom of such models, together with the system symmetries, make the emerging Fock-state lattices rather simple such that they can be linked to known lattice models from the condensed matter community. This sheds new light on known quantum optical systems. While we provide a rather long list of models and their corresponding Fock-state lattices, we pick a few ones in order to demonstrate the strength of the method. The three-mode boson model, for example, is shown to display a fractal spectrum, and chiral evolution in the Fock-state lattice characterized by localized distributions traversing along symmetric trajectories. In a second example we consider the central spin model which generates a Fock-state lattice reminiscent of the SSH-model hosting topological edge states. We further demonstrate how the phenomena of flat bands in lattice models can manifest in related Fock-state lattices, which can be linked to so called dark states.