Controlled dephasing of Andreev states in superconducting quantum point contacts

We have studied the relaxation and dephasing processes in a superconducting quantum point contact induced by the interaction with an electromagnetic environment. Based on a density matrix approach we obtain the rates for the dissipative dynamics as function of the transmission, the phase difference on the contact, and the external impedance. Our calculation allows us to determine the appropriate range of parameters for the observation of coherent oscillations in the current through the contact.