Phase transitions and dark-state physics in two-color superradiance

TL;DR

This paper extends the Dicke model to a three-level Lambda system, revealing multiple phase transitions, including a dark state analogous to stimulated Raman adiabatic passage, with implications for quantum optics.

Contribution

It introduces a generalized model with three energy levels, analyzes phase transitions, and identifies a dark state similar to STIRAP in a many-body quantum system.

Findings

Identifies normal and two superradiant phases with first and second order transitions.

Discovers a stable dark state in the degenerate ground state limit.

Provides a theoretical framework for multi-level superradiance phenomena.

Abstract

We theoretically study an extension of the Dicke model, where the single-particle Hamiltonian has three energy levels in Lambda-configuration, i.e. the excited state is coupled to two non-degenerate ground states via two independent quantized light fields. The corresponding many-body Hamiltonian can be diagonalized in the thermodynamic limit with the help of a generalized Holstein--Primakoff transformation. Analyzing the ground-state energy and the excitation energies, we identify one normal and two superradiant phases, separated by phase transitions of both first and second order. A phase with both superradiant states coexisting is not stable. In addition, in the limit of two degenerate ground states a dark state emerges, which seems to be analogous to the dark state appearing in the well known stimulated Raman adiabatic passage scheme.