  Asymmetry in the Josephson couplings between two superconductors through a
quantum dot is studied based on a single impurity Anderson model using the
numerical renormalization group (NRG). Specifically, we examine how the
difference between the couplings \Gamma_L and \Gamma_R affects the ground
state, which is known to show a quantum phase transition between a nonmagnetic
singlet and a magnetic doublet depending on the various parameters; the Coulomb
interaction U, onsite potential \epsilon_d, level width \Gamma_L, \Gamma_R,
caused by the hybridization, and superconducting gaps \Delta_L and \Delta_R for
the leads on the left and right. Our results show that whether the local moment
is fully screened or not depends substantially on the asymmetry in the
couplings \Gamma_L \neq \Gamma_R. It tends to make the singlet ground state
stable, while the size and phase difference of the two superconducting gaps
tend to suppress the screening. We also discuss some general symmetry
properties of the system and their relation to the current conservation.
