Polaritonic network as a paradigm for dynamics of coupled oscillators

Abstract

Photonic and polaritonic lattices have been recently theoretically proposed and experimentally realised as many-body simulators due to the rich behaviors exhibited by such systems at the macroscale. We show that the networks of polariton condensates encapsulate a large variety of behaviours of systems of coupled oscillators. By eliminating spatial degrees of freedom in nonresonantly pumped polariton network, we establish that depending on the values of experimentally tunable parameters the networks of polariton condensates may represent Kuramoto, Sakaguchi-Kuramoto, Stuart-Landau, Lang-Kobayashi oscillators and beyond. The networks of polariton condensates are therefore capable of implementing various regimes acting as analogue spin Hamiltonian minimizers, producing complete and cluster synchronization, exotic spin glasses and large scale secondary synchronization of oscillations. We suggest that the recently implemented control of the system parameters for individual sites in polariton lattices allows addressing for the first time the interaction of sublattices that belong to different oscillatory classes.

Time-delay polaritonics

“…The two spatially separated antennas interfere and maximise their gain by adjusting both their common frequency and their relative phase difference ϕ ¼ argðc à i c j Þ. Similarities of the dynamics of coupled polariton condensates to equations of motion in the form of the Lang-Kobayashi equation was discussed in theoretical works recently for instantaneously coupled condensates with complexvalued couplings 51 . Unlike trapped ground state bosonic systems, such as cold atoms, the ballistically expanding polariton matterwave condensates necessarily experience time-delayed coupling since k c;0 d ) 1 similar to inter-cavity coupling of semiconductor lasers 33 .…”

Polaritonic XY-Ising machine

“…This time-delay effect is similar for both coupling schemes in simulating either spin Hamiltonian. Although for networks of condensates, the presence of a time-delay would result in a phase lag [41] in Eqs. 14- (12) which for significant τ can decrease the optimisation accuracy of the XY Hamiltonian, but not Ising.…”

“…The robustness of this technique has been demonstrated for a variety of lattice configurations and sizes [21,22,[38][39][40] proving the scalability of the polariton system for both trapped geometries and freely expanding condensates. The coupling between geometrically coupled condensates is generally of a complex nature [41] and consists of the dissipative (Heisenberg) and Josephson couplings. The latter prevents the system from achieving the minimum of a spin Hamiltonian as was previously elucidated [41].…”

“…The coupling between geometrically coupled condensates is generally of a complex nature [41] and consists of the dissipative (Heisenberg) and Josephson couplings. The latter prevents the system from achieving the minimum of a spin Hamiltonian as was previously elucidated [41]. Even when the Josephson coupling is negligible in comparison with the dissipative coupling, the geometric coupling barely allows one to control the interactions beyond the nearest neighbours.…”

“…This leads to a crucial and yet missing discussion of controlling the couplings beyond nearest neighbours for arbitrary graphs of polariton condensates. Moreover, spatially coupled polariton condensates are capable of representing different oscillator models [41] including the Kuramato, Sakaguchi-Kuramoto, Lang-Kobayashi, and Stuart-Landau models for different ranges of experimental parameters some of which are easier to adjust, e. g. exciton-polariton interactions, while others are harder, e. g. polariton lifetime. This apparent flexibility of a polariton system makes it harder to isolate a particular optimisation problem to address with polariton networks and, consequently, limits the optimisation accuracy of any objective function.…”