Rabi oscillations in systems with small anharmonicity

When a two-level quantum system is irradiated with a microwave signal in resonance with the energy difference between the levels, it starts Rabi oscillations between those states. If there are other states close, in energy, to the first two, the microwave signal will also induce transitions to those. Here we study the probability of transition to the third state, in a three-level system, while Rabi oscillations between the first two states are performed. We investigate the effect of pulse shaping on the probability and suggest methods for optimizing the pulse shapes to reduce the transition probability.