Kirill Kalinin

Realizing the classical XY Hamiltonian in polariton simulators

The vast majority of real-life optimization problems with a large number of degrees of freedom are intractable by classical computers, since their complexity grows exponentially fast with the number of variables. Many of these problems can be mapped into classical spin models, such as the Ising, the XY or the Heisenberg models, so that optimization problems are reduced to finding the global minimum of spin models. Here, we propose and investigate the potential of polariton graphs as an efficient analogue simulator for finding the global minimum of the XY model. By imprinting polariton condensate lattices of bespoke geometries we show that we can engineer various coupling strengths between the lattice sites and read out the result of the global minimization through the relative phases. Besides solving optimization problems, polariton graphs can simulate a large variety of systems undergoing the U(1) symmetry-breaking transition. We realize various magnetic phases, such as ferromagnetic, anti-ferromagnetic, and frustrated spin configurations on a linear chain, the unit cells of square and triangular lattices, a disordered graph, and demonstrate the potential for size scalability on an extended square lattice of 45 coherently coupled polariton condensates. Our results provide a route to study unconventional superfluids, spin liquids, Berezinskii-Kosterlitz-Thouless phase transition, and classical magnetism, among the many systems that are described by the XY Hamiltonian.

Networks of non-equilibrium condensates for global optimization

Recently several gain-dissipative platforms based on the networks of optical parametric oscillators, lasers, and various non-equilibrium Bose-Einstein condensates have been proposed and realised as analogue Hamiltonian simulators for solving large-scale hard optimisation problems. However, in these realisations the parameters of the problem depend on the node occupancies that are not known a priori, which limits the applicability of the gain-dissipative simulators to the classes of problems easily solvable by classical computations. We show how to overcome this difficulty and formulate the principles of operation of such simulators for solving the NP-hard large-scale optimisation problems such as constant modulus continuous quadratic optimisation and quadratic binary optimisation for any general matrix. To solve such problems any gain-dissipative simulator has to implement a feedback mechanism for the dynamical adjustment of the gain and coupling strengths.

Measure the heisenberg interaction in a polariton dyad

Solving large optimization problems lies at heart of modem science and technology from social sciences to technological applications, i.e. protein design [1]. Recently, we proposed a new platform for an analog Hamiltonian simulator based on polariton graphs [2], which benefit from continuous read-out and single site control. Ability to control and engineer a wide range of strengths of coupling interactions between two sites is crucial for mapping a desired optimization problem into a polariton graph. We study the phase coupling mechanism (see also [3]) between two condensates (a dyad) at different separation distances (Fig. 1a) and measure the coupling strength, |J|, observing an oscillatory decay (Fig. 1b). We interpret the interaction as a shift of the balance among polariton and exciton populations, which leads to an increase of the emission energy as the dyad separation increases. Therefore, we defined the coupling as |J|= E(∞) − E(kcd) where kc is the condensation wavevector, d is the dyad distance and E(∞) is the saturation energy for a dyad at infinite distance. The characterisation of the coupling represents a crucial step to build up a “Look-Up-Table” to engineering interactions in a polariton graph, an essential tool to realise a polariton simulator.

Dataset for Realizing the classical XY Hamiltonian in polariton simulators

Dataset in support to Realising the classical XY Hamiltonian in polariton simulators accepted in Nature Materials.

Dataset for Non-resonant optical control of a spinor polariton condensate

Dataset supports:nAskitopoulos, Alexis et al (2016) Non-resonant optical control of a spinor polariton condensate. Physical Review B.We investigate the spin dynamics of polariton condensates spatially separated from and effectively confined by the pumping exciton reservoir. We obtain a strong correlation between the ellipticity of the non-resonant optical pump and the degree of circular polarisation (DCP) of the condensate at the onset of condensation. With increasing excitation density we observe a reversal of the DCP. The spin dynamics of the trapped condensate are described within the framework of the spinor complex Ginzburg-Landau equations in the Josephson regime, where the dynamics of the system are reduced to a current-driven Josephson junction. We show that the observed spin reversal is due to the interplay between an internal Josephson coupling effect and the detuning of the two projections of the spinor condensate via transition from a synchronised to a desynchronised regime. These results suggest that spinor polariton condensates can be controlled by tuning the non-resonant excitation density offering applications in electrically pumped polariton spin switches.