We discuss phase-locking phenomena at low-level of quanta for parametrically
driven nonlinear Kerr resonator (PDNR) in strong quantum regime. Oscillatory
mode of PDNR is created in the process of a degenerate down-conversion of
photons under interaction with a train of external Gaussian pulses. We
calculate the Wigner functions of cavity mode showing two-fold symmetry in
phase space and analyse formation of phase-locked states in the regular as well
as the quantum chaotic regime.Comment: 6 pages, 4 figure
