We study the Josephson current 0-π transition of a quantum dot tuned to
the Kondo regime. The physics can be quantitatively captured by the numerically
exact continuous time quantum Monte Carlo method applied to the single-impurity
Anderson model with BCS superconducting leads. For a comparison to an
experiment the tunnel couplings are determined by fitting the normal-state
linear conductance. Excellent agreement for the dependence of the critical
Josephson current on the level energy is achieved. For increased tunnel
couplings the Kondo scale becomes comparable to the superconducting gap and the
regime of the strongest competition between superconductivity and Kondo
correlations is reached; we predict the gate voltage dependence of the critical
current in this regime.Comment: 5 pages, 3 figure
