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Driven-dissipative quantum fluids can differ substantially from their equilibrium counterparts. The long-wavelength phase dynamics of a polariton/photon condensate has been shown to obey Kardar-Parisi-Zhang (KPZ) equation. Since the phase is a compact variable, vortices in 2D and phase slips in 1D can proliferate destroying the KPZ scaling. The interplay between KPZ physics and topological defects is currently subject of great interest, especially in polariton context. In this talk, I will review our work on the topic [1,2,3].

In particular, we demonstrate [1,3] that in the optical parametric oscillator regime of a polariton condensate, simply changing the strength of the pumping mechanism can substantially alter the level of effective spatial anisotropy and move the system into distinct scaling regimes. These include (i) the classic algebraically ordered superfluid below the Berezinskii-Kosterlitz-Thouless (BKT) transition, as in equilibrium; (ii) the nonequilibrium, long-wavelengthfluctuation-dominated Kardar-Parisi-Zhang (KPZ) phase; and the two associated topological-defect-dominated disordered phases caused by proliferation of (iii) entropic BKT vortex-antivortex pairs or (iv) repelling vortices in the KPZ phase. We then study the dynamics of vortices in the compact Kardar-Parisi-Zhang equation [2], after a sudden quench across the critical region. Our exact numerical solution of the phase-ordering kinetics shows that the unique interplay between nonequilibrium and the variable degree of spatial anisotropy leads to different critical regimes. We provide an analytical expression for the vortex evolution, based on scaling arguments, which agrees with the numerical results, and confirms the form of the interaction potential between vortices in this system. Finally, we consider multicomponent system relevant to polariton condensate with different polarisations. The effective theory for Z2 degenerate coupled condensates with U(1)xU(1) symmetries maps onto coupled multicomponent KPZ equations. We perform dynamical renormalisation group analysis as well as exact numerical simulations to place polariton condensates in the subspace of a generally rich flow diagram.

[1] A. Ferrier, A. Zamora, G. Dagvadorj, and M.H. Szymańska Phys. Rev. B 105, 205301 (2022);

[2] A. Zamora, N. Lad, and M. H. Szymanska Phys. Rev. Lett. 125, 265701 (2020);

[3] A. Zamora, L. M. Sieberer, K. Dunnett, S. Diehl, and M. H. Szymańska Phys. Rev. X 7, 041006 (2017).

Bio: Professor Marzena Szymańska is the lead investigator of the Quantum Collective Dynamics in Light-Matter systems group at University College London. She achieved her PhD in Physics from Cambridge University in 2002, where she was then awarded a Research Fellowship. After this, her impressive resume has includes positions at the University of Oxford and University of Warwick before she joined UCL in 2014. Her research focuses on collective phenomena in light-matter systems, particularly exciton-polaritons and cold atoms and cQED (circuit quantum electrodynamics).