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Theory of microwave spectroscopy of Andreev bound states with a Josephson junction

L Bretheau 1 C Girit 1 M Houzet 2 H Pothier 1 D Esteve 1 C Urbina 1
1 QUANTRONICS - Quantronics Group
SPEC - UMR3680 - Service de physique de l'état condensé, IRAMIS - Institut Rayonnement Matière de Saclay
2 GT - Laboratory of Quantum Theory
PHELIQS - PHotonique, ELectronique et Ingénierie QuantiqueS : DRF/IRIG/PHELIQS
Abstract : We present a microscopic theory for the current through a tunnel Josephson junction coupled to a non-linear environment, which consists of an Andreev two-level system coupled to a harmonic oscillator. It models a recent experiment [Bretheau, Girit, Pothier, Esteve, and Urbina, Nature 499, 312 (2013)] on photon spectroscopy of Andreev bound states in a superconducting atomic-size contact. We find the eigenenergies and eigenstates of the environment and derive the current through the junction due to inelastic Cooper pair tunneling. The current-voltage characteristic reveals the transitions between the Andreev bound states, the excitation of the harmonic mode that hybridizes with the Andreev bound states, as well as multi-photon processes. The calculated spectra are in fair agreement with the experimental data.
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L Bretheau, C Girit, M Houzet, H Pothier, D Esteve, et al.. Theory of microwave spectroscopy of Andreev bound states with a Josephson junction. Physical Review B: Condensed Matter and Materials Physics, American Physical Society, 2014, 90 (13), pp.134506. ⟨10.1103/PhysRevB.90.134506⟩. ⟨cea-01384746⟩