# Purification Hamiltonians

## TL;DR

This paper introduces a method to analyze the Jaynes-Cummings interaction with mixed states by purifying the field and atom states, enabling entropy calculations and the creation of artificial Hamiltonians that mimic entropy dynamics.

## Contribution

It presents a novel purification approach for mixed states in the Jaynes-Cummings model and constructs artificial Hamiltonians to replicate entropy evolution.

## Key findings

- Purified the mixed field state to a wavefunction for analysis.
- Derived artificial Hamiltonians that reproduce entropy dynamics.
- Extended the approach to more realistic models with entangled atoms.

## Abstract

We study the Jaynes-Cummings interaction when initial mixed states, for the atom or the field, are considered. The evolved mixed field density matrix is purified to a wavefunction that describes the interaction between a quantised field and an artificial four-level atom. This allows us to use the Araki-Lieb inequality to calculate the field entropy from the atomic entropy. We then generate {\it artificial} Hamiltonians that reproduce the field entropy dynamics. We finally show that more realistic Hamiltonians may be considered by using two entangled two-level atoms.