Quantum Kerr-nonlinear oscillator is a paradigmatic model in cavity and circuit quantum electrodynamics, and quantum optomechanics. We theoretically study the echo phenomenon in a single impulsively excited (kicked) Kerr-nonlinear oscillator. We reveal two types of echoes, quantum and classical ones, emerging on the long and short time-scales, respectively. The mechanisms of the echoes are discussed, and their sensitivity to dissipation is considered. These echoes may be useful for studying decoherence processes in a number of systems related to quantum information processing.
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