Multiple perfectly-transmitting states of a single-level at strong coupling

TL;DR

This paper investigates how strong coupling between a single-level system and reservoirs with band-structure can generate multiple perfectly-transmitting states, including bound states and additional transmission channels, altering transport properties.

Contribution

It reveals that strong coupling can create multiple perfectly-transmitting states, even outside the reservoirs' bands, and provides exact solutions for the nonlinear Lamb shift in such systems.

Findings

Strong coupling can produce multiple perfectly-transmitting states.

Additional states can appear inside the band when the coupling exceeds a critical value.

The results are applicable to microwave cavities and quantum dot conductance experiments.

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's 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.