Multiple perfectly transmitting states of a single level at strong coupling

¹ Department of Physics and Astronomy, University of Rochester - Rochester, NY 14627, USA
² Laboratoire de Physique et Modélisation des Milieux Condensés, Université Grenoble Alpes and CNRS 25 Avenue des Martyrs, BP 166, 38042 Grenoble, France

^(a) ejussiau@UR.Rochester.edu
^(b) robert.whitney@grenoble.cnrs.fr

Received: 27 January 2020
Accepted: 24 February 2020

Abstract

We study transport through a single-level system placed between two reservoirs with band-structure, taking strong level-reservoir coupling of the order of the energy scales of these band-structures. An exact solution in the absence of interactions gives the nonlinear Lamb shift. As expected, this moves the perfectly transmitting state (the reservoir state that flows through the single level without reflection), and can even turn it into a bound state. However, here we show that it can also create additional pairs of perfectly transmitting states at other energies, when the coupling exceeds critical values. Then the single-level transmission function resembles that of a multi-level system. Even when the discrete level is outside the reservoirs' bands, additional perfectly transmitting states can appear inside the band when the coupling exceeds a critical value. We propose observing the bosonic version of this in microwave cavities, and the fermionic version in the conductance of a quantum dot coupled to 1D or 2D reservoirs.