Exact State Evolution and Energy Spectrum in Solvable Bosonic Models

TL;DR

This paper presents an exact analytical solution for the state evolution and energy spectrum of a broad class of solvable bosonic models in quantum optics, aiding the understanding of light propagation in nonlinear media.

Contribution

It introduces a general analytic framework for solving the state evolution and energy spectrum in solvable bosonic models, applicable to arbitrary initial states.

Findings

Derived the characteristic equation for the energy spectrum.

Found eigenstates as continued fractions and principal minors of Jacobi matrices.

Provided a comprehensive analytical framework for solvable bosonic models.

Abstract

Solvable bosonic models provide a fundamental framework for describing light propagation in nonlinear media, including optical down-conversion processes that generate squeezed states of light and their higher-order generalizations. In quantum optics a central objective is to determine the time evolution of a given initial state. Exact analytic solution to the state-evolution problem is presented, applicable to a broad class of solvable bosonic models and arbitrary initial states. Moreover, the characteristic equation governing the energy spectrum is derived and the eigenstates are found in the form of continued fractions and as the principal minors of the associated Jacobi matrix. The results provide a solid analytical framework for discussion of exactly solvable bosonic models.