Fractional quantum mechanics in polariton condensates with velocity dependent mass

TL;DR

This paper introduces a new mean-field model for polariton condensates with velocity-dependent effective mass, revealing fractional quantum mechanics behavior and significant effects at high velocities through numerical and analytical studies.

Contribution

The paper presents a novel mean-field model incorporating velocity-dependent mass, connecting polariton condensates to fractional quantum mechanics and analyzing its effects.

Findings

Mass dependence on wave vector affects condensate modes.

Fractional quantum mechanics behavior emerges at certain dispersion points.

Numerical studies show significant differences at high velocities.

Abstract

We introduce and analyze a novel mean-field model for polariton condensates with velocity dependence of the effective polariton mass due the photon and exciton components. The effective mass depends on the in-plane wave vector k, which at the inflection point of the lower polariton energy branch becomes infinite and above negative. The polariton condensate modes of the new mean-field theory are now sensitive to mass variations and for certain points of the energy dispersion the polariton condensate mode represents fractional quantum mechanics. The impact of the generalized kinetic energy term is elucidated by numerical studies in 1D and 2D showing significant differences for large velocities. Analytical expressions for plane wave solutions as well as a linear waves analysis show the significance of this new model.