  Waveguide quantum electrodynamics, the study of atomic systems interacting
with propagating electromagnetic fields, is a powerful platform for
understanding the complex interplay between light and matter. Qubit control is
an indispensable tool in this field, and most experiments have so far focused
on narrowband electromagnetic waves that interact with qubits at specific
frequencies. This interaction, however, changes significantly with fast,
broadband pulses, as waveguide properties like dispersion affect the pulse
evolution and its impact on the qubit. Here, we use dispersion to achieve
spatial addressing of superconducting qubits separated by a sub-wavelength
distance within a microwave waveguide. This novel approach relies on a
self-focusing effect to create a position-dependent interaction between the
pulse and the qubits. This experiment emphasizes the importance of dispersion
in the design and analysis of quantum experiments, and offers new avenues for
the rapid control of quantum states.
