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.

Change of the title, addition of two appendices with details on dynamical phase transitions and open quantum systems, resp. The final publication is available at link.springer.com

References in corpus (12)

• Dissipative Phase Transition in Central Spin Systems
• Self-organization of a Bose-Einstein condensate in an optical cavity
• Photon localization and Dicke superradiance in atomic gases
• Cooperative Spontaneous Emission as a Many Body Eigenvalue Problem
• Environmentally induced Quantum Dynamical Phase Transition in the spin swapping operation
• Cooperativity in light scattering by cold atoms
• Experimental Investigation of the Transition between Autler-Townes Splitting and Electromagnetically-Induced Transparency
• Revisiting the Fermi Golden Rule: Quantum Dynamical Phase Transition as a Paradigm Shift
• Phase rigidity and avoided level crossings in the complex energy plane
• Correlated behavior of conductance and phase rigidity in the transition from the weak-coupling to the strong-coupling regime
• Avoided level crossings in open quantum systems
• Dynamical stabilization and time in open quantum systems

Cited by in corpus (23)

• The emergence, coalescence and topological properties of multiple exceptional points and their experimental realization
• A review of progress in the physics of open quantum systems: theory and experiment
• Experimental demonstration of an anisotropic exceptional point
• Capturing Vacuum Fluctuations and Photon Correlations in Cavity Quantum Electrodynamics with Multi-Trajectory Ehrenfest Dynamics
• Nearby states in non-Hermitian quantum systems
• Anisotropic exceptional points of arbitrary order
• Quantum Zeno effect and nonclassicality in a PT symmetric system of coupled cavities
• Nuclear Spin Dynamics in Double Quantum Dots: Multi-Stability, Dynamical Polarization, Criticality and Entanglement
• Linear Quantum Entropy and Non-Hermitian Hamiltonians
• Fano-Feshbach resonances in two-channel scattering around exceptional points
• Damping of quasiparticles in a Bose-Einstein condensate coupled to an optical cavity
• Photon blockade with a trapped $\Lambda$-type three-level atom in asymmetrical cavity
• Collective bosonic effects in an array of transmon devices
• Open quantum systems with loss and gain
• The von Neumann Entropy for Mixed States
• Exceptional points treatment of cavity spectroscopies
• Superradiance in dynamically modulated Tavis-Cumming model with spectral disorder
• Van Hove bound states in the continuum: Localised subradiant states in finite open lattices
• A Vision for the Science of Rare Isotopes
• Superradiance in finite quantum systems randomly coupled to continuum
• Entanglement control of two-level atoms in dissipative cavities
• Topological Switching via Exceptional Point Pairs in an Optical Microcavity Laser
• Exact Regions of Superradiant Instability of Kerr-Newman Black Holes and Massive Scalar Fields