Eur. Phys. J. B (2013) 86: 368
https://doi.org/10.1140/epjb/e2013-40190-4

Regular Article

Quantum signal transmission through a single-qubit chain

¹ Department of Physics and TechniquesNovosibirsk State Technical University, 630092 Novosibirsk, Russia
² William Jewell College, Liberty, 64068 Missouri, USA
³ Department of Electrical and Computer Engineering, College of Engineering, Michigan State University, East Lansing, 48824 Michigan, USA
⁴ Department of Physics and Astronomy, Michigan State University, East Lansing, 48824 Michigan, USA
⁵ National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, 48824 Michigan, USA

^a e-mail: greenbergy@online.nsk.su

Received: 9 March 2013
Received in final form: 30 June 2013
Published online: 2 September 2013

Abstract

A system of a two-level atom of an impurity (qubit) inserted into a periodic chain coupled to the continuum is studied with the use of the effective non-Hermitian Hamiltonian. Exact solutions are derived for the quasistationary eigenstates, their complex energies, and transport properties. Due to the presence of the qubit, two long-lived states corresponding to the ground and excited states of the qubit emerge outside the Bloch energy band. These states remain essentially localized at the qubit even in the limit of sufficiently strong coupling between the chain and the environment when the super-radiant states are formed. The transmission through the chain is studied as a function of the continuum coupling strength and the chain-qubit coupling; the perfect resonance transmission takes place through isolated resonances at weak and strong continuum coupling, while the transmission is lowered in the intermediate regime.