Why a magnetized quantum wire can act as an optical amplifier: A short survey

TL;DR

This survey explores how magnetoplasmon excitations in a quantum wire with a magnetic field can exhibit negative group velocity and population inversion, enabling the wire to function as an optical amplifier.

Contribution

It provides a comprehensive review of magnetoroton excitations in quantum wires and their potential application as optical amplifiers based on negative group velocity phenomena.

Findings

Negative group velocity observed between maxon and roton

Existence of population inversion due to magnetic field

Magnetoroton modes can serve as optical amplifiers

Abstract

This article reviews the fundamental issues associated with the magnetoplasmon excitations investigated in a semiconducting quantum wire characterized by a harmonic confining potential and subjected to an applied (perpendicular) magnetic field. We embark on the charge-density excitations in a two-subband model within the framework of Bohm-Pines's random-phase approximation. The problem involves two length scales: ${\it l}_0=\sqrt{\hbar/m^*\omega_0}$ and ${\it l}_c=\sqrt{\hbar/m^*\omega_c}$, which characterize the strengths of the confinement and the magnetic field ($B$). Essentially, we focus on the device aspects of the intersubband collective (magnetoroton) excitation, which observes a negative group velocity between maxon and roton. Consequently, it leads to tachyon-like (superluminal) behavior without one's having to introduce the negative energies. Existence of the negative group velocity is a clear manifestation of a medium with population inversion brought about due to a metastable state caused by the magnetic field that satisfies the condition $B> B_{th}$; $B_{th}$ being the threshold value below which the magnetoroton does not exist. The interest in negative group velocity is based on anomalous dispersion in a medium with inverted population, so that gain instead of absorption occurs at the frequencies of interest. A medium with an inverted population has the remarkable ability of amplifying a small optical signal of definite wavelength, i.e., it can serve as an {\em active} laser medium. An extensive scrutiny of the gain coefficient suggests an interesting and important application: the electronic device designed on the basis of such magnetoroton modes can act as an optical amplifier. Examining the magnetic-field dependence of the life-time of magnetorotons leads us to infer that relatively smaller magnetic fields are optimal.