On the paradoxical evolution of the number of photons in a new model of interpolating Hamiltonians

TL;DR

This paper introduces a new Hamiltonian model with two interpolation parameters that smoothly transitions between different Jaynes-Cummings-like models, addressing a paradox in photon evolution and analyzing photon statistics.

Contribution

It presents a novel two-parameter interpolating Hamiltonian model enabling continuous transition between various models, expanding the analytical framework for photon dynamics.

Findings

Demonstrates continuous interpolation between Hamiltonians

Analyzes photon statistics evolution in different models

Highlights the impact of average excitation on photon behavior

Abstract

We introduce a new Hamiltonian model which interpolates between the Jaynes-Cummings model and other types of such Hamiltonians. It works with two interpolating parameters, rather than one as traditional. Taking advantage of this greater degree of freedom, we can perform continuous interpolation between the various types of these Hamiltonians. As applications we discuss a paradox raised in literature and compare the time evolution of photon statistics obtained in the various interpolating models. The role played by the average excitation in these comparisons is also highlighted.