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 DLCZ protocol, for which a single excitation is shared among thousands and millions atoms or ions. Another example is the possibility to create 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 for testing 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, e.g. the transition probability varies with the square of the pulse area. Here we propose a different method for generating a well-defined pre-selected very small transition probability -- of the order of $10^{-2}$ to $10^{-8}$ -- by using composite pulse sequences. The method features high fidelity and robustness to variations in the pulse area and the pulse duration.