Selective pumping of a nonlinear quantum oscillator

Selective pumping of a quantum system under the influence of unmodulated short-range pulses of large amplitude is studied using the example of a weakly nonlinear Josephson oscillator. An exact solution is obtained in the case of small parameter anharmonicity for changes in the system energy and population of levels after impact. It is shown that due to the interference of state amplitudes, it is possible to stabilize the system and prevent undesirable excitations (energy growth). When anharmonicity is taken into account, the system stability conditions are studied numerically. The obtained results are important when analyzing leakage to high-lying levels in a transmon-qubit under the influence of short unipolar control pulses. (paper)