On global dynamics for damped driven Jaynes-Cummings equations

TL;DR

This paper studies the global behavior of damped driven Jaynes-Cummings equations, providing a mathematical framework for solutions with time-dependent pumping using operator theory and finite-dimensional approximations.

Contribution

It constructs global solutions for the equations with time-dependent pumping, extending the mathematical understanding of these quantum systems.

Findings

Established existence of global solutions in Hilbert space

Developed finite-dimensional approximation methods

Analyzed the structure of damping and pumping operators

Abstract

The article concerns damped driven Jaynes-Cummings equation which describes quantised one-mode Maxwell field coupled to a two-level molecule. We consider a broad class of damping and pumping which are polynomial in the creation and annihilation operators, and their structures correspond to the theory of completely positive and trace preserving generators (CPTP) of Lindblad and Kossakowski & al. Our main result is the construction of global generalised solutions with values in the Hilbert space of nonnegative Hermitian Hilbert-Schmidt operators in the case of time-dependent pumping. The proofs rely on finite-dimensional approximations of the annihilation and creation operators.