Toward Arbitrary Control of Lattice Interactions in Nonequilibrium Condensates

There is a growing interest in investigating new states of matter using out-of-equilibrium lattice spin models in two dimensions. However, a control of pairwise interactions in such systems has been elusive as due to their nonequilibrium nature they maintain nontrivial particle fluxes even at the steady state. Here it is suggested how to overcome this problem and formulate a method for engineering reconfigurable networks of nonequilibrium condensates with control of individual pairwise interactions. Representing spin by condensate phase, the effective two spin interactions are created with nonresonant pumping, are directed with dissipative channels, and are further controlled with dissipative gates. The dissipative barriers are used to block unwanted interactions between condensates. Together, spatial anisotropy of dissipation and pump profiles allow an effective control of sign and intensity of the coupling strength between any two neighbouring sites independent of the rest of the spins, which is demonstrated with a 2D square lattice of polariton condensates. Experimental realization of such fully controllable networks offers great potential for reservoir computing, modelling of the systems of coupled oscillators, simulation of the new state of matters, studying the phase transitions in large-scale systems, and optimization.