External seminar archive:

# A polariton graph optimiser

7 February 2018

Professor Natalia Berloff, University Of Cambridge and Skolkovo Institute of Science and Technology, Russia

Recently we proposed polariton graphs as a novel platform for solving hard optimisation problems that can be mapped into the XY model [1, 2]. Polariton condensates can be imprinted into any two-dimensional graph by spatial modulation of the pumping laser as Figure 1 below illustrates.

By controlling the pumping intensity and profile, the graph geometry and the separation distance between the lattice sites one can control the couplings between the sites and realise various phase configurations that minimise the XY model. This gives rise to the use of the polariton graph as an analogue XY Hamiltonian simulator.

The search for the global minimum of the XY Hamiltonian is via a bottom-up approach which has an advantage over classical or quantum annealing techniques, where the global ground state is reached through either a transition over metastable excited states or via tunnelling between the states in time that depends on the size of the system.

In my talk I will discuss the range of optimisation problems that can be efficiently solved by polariton graph [3]. In particular, I will elucidate a relationship between the energy spectrum of the XY Hamiltonian and the total number of condensed polariton particles.

Using as a test-bed the hexagonal unit lattice I will show that the lower energy states of the XY Hamiltonian are faithfully reproduced by mean-field numerical simulations utilising the Ginzburg-Landau equation coupled to an exciton reservoir [3].

Polariton graphs can be used to explore novels states and to go beyond next neighbour interactions [5].

Figure 1. Schematics of the experiment: Creating polariton condensates in the vertices of a graph and reading out the phase differences that minimise the XY Hamiltonian.

## References

N. G.Berloff, M. Silva, K. Kalinin, A. Askitopoulos, J D. Töpfer, P. Cilibrizzi, W. Langbein and P. G. Lagoudakis, Realizing the classical XY Hamiltonian in polariton simulators, Nature Materials, 16, 1120-1126 (2017).

P. G. Lagoudakis and N. G. Berloff, A polariton graph simulator, New Journal of Physics, 19, 125008 (2017).

K. Kalinin, P. G. Lagoudakis and N. G. Berloff, Matter wave coupling of spatially separated and unequally pumped polariton condensates, arXiv:1712.06279 (2017).

K. Kalinin, P. G. Lagoudakis and N. G. Berloff, Simulating the spectral gap with polariton graphs, arXiv:1709.04683 (2017).

K. Kalinin, P. G. Lagoudakis and N. G. Berloff, Exotic states of matter with polariton chains, arXiv:1710.02304 (2017).