Spinful double-dot-cavity system as a nonlocal Kondo phase transition simulator

Double quantum dot devices are well-established quantum simulation platforms. The dots emulate localised magnetic impurities that showcase Kondo-like hybridisations with their respective environment while competing with direct dot-dot coupling mediated by Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions. Here, we consider a double-dot device in which whispering gallery modes in a 2DEG form an all-electronic dot-cavity-dot system [Phys. Rev. Lett. 120, 236801 (2018)]. In this dot-cavity-dot system, we theoretically describe and predict (i) the experimentally observed coherent coupling between the two distant dots, where the cavity meditates their hybridisation, (ii) conventional Kondo effects, where the dots separately form a singlet with their coupled reservoir, (iii) a nonlocal Kondo effect, where the dot-cavity-dot impurity forms a magnetic state that spans over the full device, which in turn is screened by the reservoir. We furthermore study the robustness of the effects in the presence of spin decoherence and temperature scaling. Thus, we fully characterise the crossover between the (i)-(iii) phases. Our results pave the way for the experimental observation of nonlocal Kondo-like phase transitions and the realisation of exotic nonlocal magnetic impurities in mesoscopic devices.