Eur. Phys. J. D (2014) 68: 74
https://doi.org/10.1140/epjd/e2014-40780-8

Regular Article

Open quantum systems and Dicke superradiance

¹ Université de Montréal, C.P. 6128, Montréal ( QC), H3C 3J7, Canada
² Department of Physics, McGill University, Montreal, H3A 2T8, Canada
³ Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany

^a e-mail: rotter@pks.mpg.de

Received: 10 December 2013
Received in final form: 31 January 2014
Published online: 27 March 2014

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.