Deterministic generation of arbitrary ultrasmall excitation of quantum systems by composite pulse sequences

In some applications of quantum control, it is necessary to produce very weak excitation of a quantum system. Such an example is presented by the concept of single-photon generation in cold atomic ensembles or doped solids, e.g., by the Duan-Lukin-Cirac-Zoller (DLCZ) protocol, for which a single excitation is shared among thousands and millions of atoms or ions. Another example is the possibility to create a huge Dicke state of N qubits sharing a single or a few excitations. Other examples are using tiny rotations to tune high-fidelity quantum gates, or using these tiny rotations to test high-fidelity quantum process tomography protocols. Ultrasmall excitation of a quantum transition can be generated by either a very weak or far-detuned driving field. However, these two approaches are sensitive to variations in the experimental parameters. Here we propose a different method for generating a well-defined arbitrary preselected very small transition probability-in the range from 10(-2) to 10(-8)-by using composite pulse sequences. Contrary to other methods, it features both high fidelity and robustness to variations in the pulse area and the pulse duration.