# Spinor polariton condensates under nonresonant pumping: Steady states and elementary excitations

## TL;DR

This paper provides a theoretical analysis of spinor polariton condensates under nonresonant pumping, exploring their steady states, elementary excitations, and how polarization and reservoir parameters influence their spectral properties.

## Contribution

It introduces a comprehensive model for spinor polariton condensates, analyzing phase transitions, excitation spectra, and the visibility of ghost branches in photoluminescence.

## Key findings

- Homogeneous condensate transitions from unpolarized to polarized phase depending on interactions.
- Elementary excitations include diffusive or gapped modes influenced by reservoir decay rates.
- Ghost branch of the relative-phase mode can be observed in photoluminescence.

## Abstract

We theoretically investigate a spinor polariton condensate under nonresonant pumping, based on driven-dissipative Gross-Pitaevskii equations coupled to the rate equation of a spin-unpolarized reservoir. We find the homogeneous polariton condensate can transit from the spin-unpolarized phase, where it is linearly polarized, to the spin-polarized phase, where it is elliptically polarized, depending on the cross-spin versus same-spin interactions and the linear polarization splitting. In both phases, we study elementary excitations using Bogoliubov approach, in a regime where the decay rate of total exciton density in reservoir crosses over from the slow to the fast limit. Depending on reservoir parameters, the global-phase mode can be either diffusive or gapped. By contrast, the relative-phase mode always possesses a gapped energy, undamped in the spin-unpolarized phase but weakly damped in the spin-polarized phase. In the spin-unpolarized phase, both modes are linearly polarized despite pumping and decay. However, in the spin-polarized phase, the mode polarization can be significantly affected by the reservoir and depends strongly on the circular polarization degree of the condensate. Interestingly, we demonstrate that the `ghost' branch of the Bogoliubov spectrum of the relative-phase mode can be visualized in the photoluminescence emission, distinguishable from that of the global-phase mode and thus allowing for experimental observation, when the spinor polariton condensate is elliptically polarized.