Andreev levels as a quantum dissipative environment

In this talk I will address the problem of supercurrent instability in highly transparent weak links. I will demonstrate that at subgap energies quantum behavior of superconducting weak links can be exactly accounted for by an effective Hamiltonian for a Josephson particle in a quantum dissipative environment formed by Andreev levels. I will identify several macroscopic quantum tunneling (MQT) regimes and predict a non-trivial non-monotonous dependence of the switching current distribution on temperature which can be observed in MQT experiments with transparent superconducting weak links. I will also argue that intrinsic dissipation in such weak links can be studied by means of qubit spectroscopy. Varying either the bias current or magnetic flux through a superconducting ring in the rf-SQUID setup, one can tune the level splitting value close to the bottom of the Josephson potential well. Monitoring the qubit energy relaxation time one can probe the spectral density of the effective dissipative bath and unambiguously identify the contribution emerging from Andreev levels.