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We discuss how multichannel Kondo physics can arise in the setting of alocalized level coupled to several bosonic Tomonaga-Luttinger liquid leads. Wepropose one physical realization involving ultracold bosonic atoms coupled toan atomic quantum dot, and a second, based on superconducting nanowires coupledto a Cooper-pair box. The corresponding zero-temperature phase diagram isdetermined via an interplay between Kondo-type phenomena arising from the dotand the consequences of direct inter-lead hopping, which can suppress the Kondoeffect. We demonstrate that the multichannel Kondo state is stable over a widerange of parameters. We establish the existence of two nontrivial phasetransitions, involving a competition between Kondo screening at the dot andstrong correlations either within or between the leads (which respectivelypromote local number- and phase-pinning). These transitions coalesce at aself-dual multicritical point.

Approaching multichannel Kondo physics using correlated bosons: Quantum phases and how to realize them