Matter wave coupling of spatially separated and unequally pumped polariton condensates

TL;DR

This paper investigates the quantum coherence and coupling mechanisms between spatially separated polariton condensates with unequal pumping, revealing the roles of symmetric and asymmetric interactions and their implications for complex quantum systems.

Contribution

It introduces a detailed analysis of matter wave coupling in unequally pumped polariton condensates, deriving analytic expressions for interactions and exploring their application in solving complex matrix problems.

Findings

Coherence regions depend on pumping imbalance and phase dynamics.

Coupling involves symmetric Heisenberg exchange and Dzyaloshinskii-Moriya interactions.

Unequal pumping extends the computational capabilities of polariton condensate networks.

Abstract

Spatial quantum coherence between two separated driven-dissipative polariton condensates created non-resonantly and with a different occupation is studied. We identify the regions where the condensates remain coherent with the phase difference continuously changing with the pumping imbalance and the regions where each condensate acquires its own chemical potential with phase differences exhibiting time-dependent oscillations. We show that in the mutual coherence limit the coupling consists of two competing contributions: a symmetric Heisenberg exchange and the Dzyloshinskii-Moriya asymmetric interactions that enable a continuous tuning of the phase relation across the dyad and derive analytic expressions for these types of interactions. The introduction of non-equal pumping increases the complexity of the type of the problems that can be solved by polariton condensates arranged in a graph configuration. If equally pumped polaritons condensates arrange their phases to solve the constrained quadratic minimisation problem with a real symmetric matrix, the non-equally pumped condensates solve that problem for a general Hermitian matrix.