Lossless polariton solitons

• We compute by quadrature all soliton solutions of the unforced lossless 1D coupled exciton-polariton equations.
• Repulsive nonlinearity allows two bands of dark solitons, and attractive nonlinearity allows two bands of bright solitons.
• There are discontinuous solitons—one dark band and a band with dark photon field and bright exciton field.
• Bright solitons have stable far fields, whereas dark solitons have both stable (lower band) and unstable (upper band) far fields.

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 ππ. 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 00 to ∞∞; 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.