Open quantum systems and Dicke superradiance

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. * email: hichemeleuch@yahoo.fr † email: rotter@pks.mpg.de Recently, dynamical phase transitions (DPTs) are considered in different open quantum systems. They appear mostly at high level density and are observed experimentally as well as theoretically by using different approaches. Common to all of them is a very robust spectroscopic redistribution that takes place in the system in a critical region of a certain control parameter. As a result of the spectroscopic redistribution, short-lived states appear together with long-lived ones (called usually line width bifurcation) which all have lost their spectroscopic relation to the original states in the subcritical parameter region. Mathematically, the spectroscopic redistribution can be traced back to the existence of singular points in the continuum (called usually exceptional points (EPs)). For details see Appendix A. The DPTs observed in many-body open quantum systems show features which are similar to the Dicke superradiance known in optics [1]. This has been shown some years ago [2] : the DPT observed in a many-body open quantum system [3] is analogue to the formation of the superradiant Dicke state in optics. The simple model used in this study is based on statistical assumptions and can, of course, not explain the sensitive dependence of the system properties on the variation of external parameters. It shows however the meaning of the imaginary part of the coupling term between system and environment for the formation of the so-called superradiant (short-lived) and subradiant (long-lived) states in a many-body open quan...

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