Phase Diagrams of Systems of 2 and 3 levels in the presence of a Radiation Field

TL;DR

This paper investigates the phase diagrams of 2- and 3-level atomic systems interacting with a single electromagnetic mode, using exact quantum methods and variational states to accurately identify phase transitions and critical phenomena.

Contribution

It introduces an exact quantum-mechanical approach with variational states that respect Hamiltonian symmetries, avoiding divergences in phase transition analysis.

Findings

Identifies phase transition loci and their order for various configurations.

Provides analytic expressions for phase boundaries and critical exponents.

Studies the phase structure at the triple point in the {\

Abstract

We study the structure of the phase diagram for systems consisting of 2- and 3- level particles dipolarly interacting with a 1-mode electromagnetic field, inside a cavity, paying particular attention to the case of a finite number of particles, and showing that the divergences that appear in other treatments are a consequence of the mathematical approximations employed and can be avoided by studying the system in an exact manner quantum-mechanically or via a catastrophe formalism with variational trial states that satisfy the symmetries of the appropriate Hamiltonians. These variational states give an excellent approximation not only to the exact quantum phase space, but also to the energy spectrum and the expectation values of the atomic and field operators. Furthermore, they allow for analytic expressions in many of the cases studied. We find the loci of the transitions in phase space from one phase to the other, and the order of the quantum phase transitions are determined explicitly for each of the configurations, with and without detuning. We also derive the critical exponents for the various systems, and the phase structure at the triple point present in the {\Xi}-configuration of 3-level systems is studied.