High Fidelity Quantum Gates beyond spectral selection

Driving a certain transition without including undesired transitions is an ubiquitous problem in quantum control and the implementation of quantum information processing. This problem gets the more challenging the weaker the desired transition couples to the control field, and the denser the system's spectrum is. With the explicit example of a trapped ion we show how temporally shaped driving helps to increase the fidelity of a gate operation beyond the regular spectral selection of resonantly driven transitions. We chose the explicit example of side-band transitions, since those couple more weakly to a control field than carrier transitions. Driving a sideband transition without carrier excitation thus allows us to test the limits of frequently employed control tools, and we discuss their potential and limitations.