Spatial quantum coherence between two separated driven-dissipative polariton condensates created nonresonantly 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 nonequal pumping increases the complexity of the type of 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 nonequally pumped condensates solve that problem for a general Hermitian matrix.

中文翻译：

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空间分离和不均匀泵浦极化子冷凝物的物质波耦合

研究了非谐振且具有不同职业的两个分离的驱动耗散极化子冷凝物之间的空间量子相干性。我们确定了冷凝物保持相干的区域，相差随泵送不平衡的变化而不断变化，以及每个冷凝物获得其自身化学势且相差表现出随时间变化的振荡的区域。我们证明，在相互相干极限中，耦合包括两个相互竞争的贡献：对称的Heisenberg交换和Dzyloshinskii-Moriya不对称的相互作用，使得能够连续调整整个dyad的相位关系，并为这些类型的相互作用得出解析表达式。不均等泵浦的引入增加了可以通过以图形配置方式排列的极化子冷凝物解决的问题类型的复杂性。如果同等泵浦的极化子冷凝物排列其相以解决带有实对称矩阵的约束二次最小化问题，那么非等泵浦的冷凝物对于一般的Hermitian矩阵可以解决该问题。