Unstable quantum systems coupled via continuum and super-radiance

Excited states of a quantum system are unstable and decay into the continuum. The dynamics of the transmission quantum signal through a two-dimensional lattice with open decay channels coupled to the continuum is treated by means of a discretized effective non-Hermitian Hamiltonian. The energies and widths are treated as real and imaginary parts of complex eingenvalues for the effective Hamiltonian. This coupling through the continuum reorganizes the dynamics of the system, as a result the energy widths of the intrinsic states are redistributed and very broad states are formed absorbing a significant part of all the summed energy width. As a result these broad, super-radiant states become highly unstable, with short lifetimes, while the remaining states become trapped and long-lived. This notion of super-radiance was suggested by Dicke, over fifty years ago, for systems pertaining to coherent states in quantum optics. A sharp, sort of phase transition, between weak and strong coupling to the continuum is considered for a two-dimensional open periodic lattice. Due to this continuum coupling a sharp redistribution of energy widths occurs. The weak coupling limit corresponds to isolated sharp resonances, whereas strong coupling corresponds to the collectivization of widths and the formation of the short-lived Dicke state. Introduction All excited states in a quantum system are unstable and the notion of a closed physical system is an idealization. Through interactions with the outside world, Heisenberg’s uncertainty principle says that excited states acquire a finite lifetime τ and an energy uncertainty (decay width) of τ h ≅ Γ . The standard treatment of quantum mechanics of unstable states introduces their complex energies