Superradiance in a Two-Channel Quantum Wire

TL;DR

This paper investigates superradiance phenomena in a two-channel quantum wire using an effective non-Hermitian Hamiltonian, revealing how coupling strength affects state widths and transport, with a focus on the super-radiance transition.

Contribution

It provides analytical expressions for the band structure and demonstrates the impact of super-radiance on transport properties in a two-channel quantum wire.

Findings

At weak coupling, eigenenergies have small, uniform widths.

Strong coupling causes some states to become super-radiant and broadened.

Maximum transmission occurs at the super-radiance transition.

Abstract

A one-dimensional, two-channel quantum wire is studied in the effective non-Hermitian Hamiltonian framework. Analytical expressions are derived for the band structure of the isolated wire. Quantum states and transport properties of the wire coupled to two ideal leads at the edges are studied in detail. The width distribution of the quasistationary states varies as a function of the coupling strength to the environment. At weak coupling, all the eigenenergies uniformly acquire small widths. The picture changes entirely at strong coupling, a certain number of states ("super-radiant") are greatly broadened, while the rest remain long-lived states, a pure quantum mechanical effect as a consequence of quantum interference. The transition between the two regimes greatly influences the transport properties of the system. The maximum transmission through the wire occurs at the super-radiance transition. We consider also a realistic situation with energy-dependent coupling to the continuum due to the existence of decay threshold where super-radiance still plays a significant role in transport properties of the system.