Topological interfaces of two-dimensional conformal field theories contain information about symmetries of the theory and exhibit striking spectral and entanglement characteristics. While lattice realizations of these interfaces have been proposed for unitary minimal models, the same has remained elusive for the paradigmatic Luttinger liquid, i.e., the free, compact boson model. Here, we show that a topological interface of two Luttinger liquids can be realized by coupling special one-dimensional superconductors. The gapless excitations in the latter carry charges that are specific integer multiples of the charge of Cooper pairs. The aforementioned integers are determined by the windings in the target space of the bosonic fields — a crucial element required to give rise to nontrivial topological interfaces. The latter occur due to the perfect transmission of certain number of Cooper pairs across the interface. The topological interfaces arise naturally in Josephson junction arrays with the simplest case being realized by an array of experimentally demonstrated $0-\pi$ qubits, capacitors and ordinary Josephson junctions. Signatures of the topological interface are obtained through entanglement entropy computations. In particular, the subleading contribution to the so-called interface entropy is shown to differ from existing field theory predictions. The proposed lattice model provides an experimentally realizable alternative to spin and anyon chains for the analysis of several conjectured conformal fixed points which have so far eluded ab initio investigation.

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• Conformal field theory
• Defects
• Entanglement in field theory
• Quantum field theory (low energy)
• Quantum simulation
• Strings & branes
• Topological materials
• XY model