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Formation of Andreev molecules at long distance using an embedding circuit
Phys. Rev. B 112, 214523 – Published 31 December, 2025
DOI: https://doi.org/10.1103/hbtb-8hds
Abstract
Andreev molecule states arise from hybridization of Andreev bound states in different Josephson junctions. Extensive theoretical and experimental research concentrates on direct coherent electron coupling between the junctions: this implies the distance between the junctions is of the order of the superconducting coherence length, that is, short. We propose and discuss the possibility to create Andreev molecules at long (in principle, arbitrary long) distance between the junctions. In this case, the hybridized states are excited quasiparticle singlets and the coupling is provided by an embedding electric circuit. To achieve a strong hybridization, one aligns the energies of the Andreev bound states by tuning the associated phase drops. In fact, a recent experiment realizes such setup. With circuit theory we derive the hybridization level splitting and estimate the scale of the effect. Since the phenomenon encompasses excited states, we derive and solve the associated Lindblad equation under condition of persistent resonant excitation. By analyzing the resulting dissipative dynamics, we identify relevant regimes where the hybridization and resonant excitation peaks are most pronounced. The low-frequency mutual inductance of the Josephson junctions is an important signature of the molecular state and the associated nonlocal Josephson effect. We demonstrate the peak structures for both mutual and self-inductance, and compute them in various frequency regimes. In an interesting common case, the embedding circuit includes an oscillator, which can be used both to enhance hybridization and to read out the quantum states with two-tone spectroscopy. We derive and solve the Lindblad equation for the two-tone spectroscopy setup to demonstrate the readout of the molecular states. If the readout and enhancement of the hybridization are provided by different oscillators, we demonstrate that the states can be immediately identified from the oscillator response. However, in a more restricted setup where the same oscillator is used, the oscillator response manifests more resonant peaks, indicating all transitions between states with different photon numbers.
