Open quantum systems and Dicke superradiance

TL;DR

This paper explores the universal features of open quantum systems, revealing a dynamical phase transition characterized by width bifurcation and exceptional points, with implications for quantum control and optical phenomena.

Contribution

It introduces a comprehensive analysis of dynamical phase transitions in open quantum systems, highlighting the role of complex coupling and exceptional points, and connects these phenomena to optical effects like EIT.

Findings

Identification of a dynamical phase transition at high level density.

Existence of exceptional points when coupling is imaginary.

Qualitative similarity to optical phenomena such as EIT.

Abstract

We study generic features of open quantum systems embedded into a continuum of scattering wavefunctions and compare them with results discussed in optics. A dynamical phase transition may appear at high level density in a many-level system and also in a two-level system if the coupling $W$ to the environment is complex and sufficiently large. Here nonlinearities occur. When $W_{ij}$ is imaginary, two singular (exceptional) points may exist. In the parameter range between these two points, width bifurcation occurs as function of a certain external parameter. A unitary representation of the S-matrix allows to calculate the cross section for a two-level system, including at the exceptional point (double pole of the S-matrix). The results obtained for the transition of level repulsion at small (real) $W_{ij}$ to width bifurcation at large (imaginary) $W_{ij}$ show qualitatively the same features that are observed experimentally in the transition from Autler-Townes splitting to electromagnetically induced transparency in optics. Fermi's golden rule holds only below the dynamical phase transition while it passes into an anti-golden rule beyond this transition. The results are generic and can be applied to the response of a complex open quantum system to the action of an external field (environment). They may be considered as a guideline for engineering and manipulating quantum systems in such a way that they can be used for applications with special requirements.