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(k c d) where k c 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.