Analogue physics is an interesting direction in modern Physics, based on the similarities of the mathematical models describing different systems. Such similarities were known for a very long time, the most famous example being the ubiquitous harmonic oscillator. However, the idea to use these similarities to study inaccessible systems and regimes in the lab has appeared relatively recently. The directions of research in analogue physics and associated effects include analogue gravity (Hawking emission ), early Universe (Kibble-Zurek mechanism ), high-energy physics (Klein tunnelling , Zitterbewegung ), quantum simulations (Heisenberg model ), and others.
Different model systems can be used to build a representation of the original ones. Quantum fluids, such as a Bose-Einstein condensate of exciton-polaritons, offer numerous advantages for the studies in all directions cited above. Exciton-polaritons are half-light half-matter particles that can be formed in microcavities in the strong coupling regime . Their photonic part allows using the well-developed optical techniques to control the configuration of the system and to measure all parameters of the quantum fluid: density, velocity, phase. A particular feature of a quantum fluid is the existence of a single-particle wavefunction (the order parameter), making possible the topological defects  such as solitons in 1D and quantum vortices in 2D. Such defects can be considered as analogues of elementary particles.
In this talk, I will discuss several examples of analogue physics with topological defects in a condensate of exciton-polaritons. Starting from solitons which exhibit relativistic behaviour  and allow simulating magnetic monopoles  or the formation of domain walls in the early Universe , we will then turn to vortices, which can also be considered as charged relativistic particles  obeying to the equations of analogue electrodynamics or allowing to simulate the quantum spin Hall effect . The last part of the talk will be devoted to the analogue of a Kerr black hole in a condensate of exciton-polaritons  and the possibility to use the vortices as the analogues of massive particles in order to study the time-like geodesics and to reproduce the Penrose effect, making a step towards fully dynamic analogue metric.
1 W. G. Unruh, Phys. Rev. Lett. 46, 1351 (1981).
2 W. Zurek, Nature 317, 505 (1985).
3 M. I. Katsnelson et al, Nature Physics 2, 620 (2006).
4 J. Schliemann et al, Phys. Rev. Lett. 94, 206801 (2005).
5 C. Gross, I. Bloch, Science 357, 995 (2017). 6 A. Kavokin, J. J. Baumberg, G. Malpuech, F.P. Laussy, Microcavities (Oxford University Press, 2011).
7 D. J. Thouless, Topological quantum numbers in nonrelativistic physics (World Scientific, London, 1998).
8 L. Pitaevskii, S. Stringari, Bose-Einstein Condensation (Clarendon Press, Oxford, 2003). 9 R. Hivet et al, Nat. Phys. 8, 724 (2012).
10 D. Solnyshkov et al, Phys. Rev. Lett. 116, 046402 (2016).
11 D. Solnyshkov et al, Phys. Rev. B 85, 073105 (2012).
12 O. Bleu et al, Nat. Comm. 9, 3991 (2018).
13 D. Solnyshkov et al, arXiv :1809.05386 (2018).