# Polariton condensation into vortex states in the synthetic magnetic field of a strained honeycomb lattice

### Submission summary

 As Contributors: Cristóbal Lledó Preprint link: scipost_202104_00031v3 Date submitted: 2022-01-06 22:01 Submitted by: Lledó, Cristóbal Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Computational Quantum Physics Approaches: Theoretical, Computational

### Abstract

Photonic materials are a rapidly growing platform for studying condensed matter physics with light, where the exquisite control capability is allowing us to learn about the relation between microscopic dynamics and macroscopic properties. One of the most interesting aspects of condensed matter is the interplay between interactions and the effect of an external magnetic field or rotation, responsible for a plethora of rich phenomena---Hall physics and quantized vortex arrays. At first sight, however, these effects for photons seem vetoed: they do not interact with each other and they are immune to magnetic fields and rotations. Yet in specially devised structures these effects can be engineered. Here, we propose the use of a synthetic magnetic field induced by strain in a honeycomb lattice of resonators to create a non-equilibrium Bose-Einstein condensate of light-matter particles (polaritons) in a rotating state, without the actual need for external rotation nor reciprocity-breaking elements. We show that thanks to the competition between interactions, dissipation and a suitably designed incoherent pump, the condensate spontaneously becomes chiral by selecting a single Dirac valley of the honeycomb lattice, occupying the lowest Landau level and forming a vortex array. Our results offer a new platform where to study the exciting physics of arrays of quantized vortices with light and pave the way to explore the transition from a vortex-dominated phase to the photonic analogue of the fractional quantum Hall regime.

###### Current status:
Editor-in-charge assigned

### List of changes

1) We added references 4-7 to the introduction.
2) Below Eq.(5), we added the following sentence:
"Polaritons in micropillars have an on-site interaction energy smaller than the linewidth, $U/\hbar\gamma < 1$; in our results below we use modest ratios perfectly within the reach of current experiments (see e.g. Ref. [52])."
3) We added the footnote in page 5 to explain the origin of the form of the pump and of the noise correlations.
4) We submitted to the UCL data repository the videos we had accompanying Figures 3a and 3b. Reference 53 points to them.