Lossless Polariton Solitons

TL;DR

This paper analytically derives all non-traveling harmonic soliton solutions in a lossless one-dimensional exciton-polariton system, revealing multiple stable and unstable soliton bands with distinct phase and amplitude characteristics.

Contribution

It provides a comprehensive calculation of all non-traveling harmonic solitons in a lossless polariton system, including novel discontinuous and merged soliton bands.

Findings

Two frequency bands of bright solitons exist with attractive nonlinearity.

Two frequency bands of dark solitons exist with repulsive nonlinearity.

Certain soliton bands are linearly unstable, while others are stable.

Abstract

Photons and excitons in a semiconductor microcavity interact to form exciton-polariton condensates. These are governed by a nonlinear quantum-mechanical system involving exciton and photon wavefunctions. We calculate all non-traveling harmonic soliton solutions for the one-dimensional lossless system. There are two frequency bands of bright solitons when the inter-exciton interactions produce an attractive nonlinearity and two frequency bands of dark solitons when the nonlinearity is repulsive. In addition, there are two frequency bands for which the exciton wavefunction is discontinuous at its symmetry point, where it undergoes a phase jump of pi. A band of continuous dark solitons merges with a band of discontinuous dark solitons, forming a larger band over which the soliton far-field amplitude varies from zero to infinity; the discontinuity is initiated when the operating frequency exceeds the free exciton frequency. The far fields of the solitons in the lowest and highest frequency bands (one discontinuous and one continuous dark) are linearly unstable, whereas the other four bands have linearly stable far fields, including the merged band of dark solitons.