The detection of variations of fundamental constants of the Standard Model would provide us with compelling evidence of new physics, and could lift the veil on the nature of dark matter and dark energy. In this work, we discuss how a network of atomic and molecular clocks can be used to look for such variations with unprecedented sensitivity over a wide range of time scales. This is precisely the goal of the recently launched QSNET project: A network of clocks for measuring the stability of fundamental constants. QSNET will include state-of-the-art atomic clocks, but will also develop next-generation molecular and highly charged ion clocks with enhanced sensitivity to variations of fundamental constants. We describe the technological and scientific aims of QSNET and evaluate its expected performance. We show that in the range of parameters probed by QSNET, either we will discover new physics, or we will impose new constraints on violations of fundamental symmetries and a range of theories beyond the Standard Model, including dark matter and dark energy models.

Trapped molecular ions in pure rovibronic states are desirable in experiments ranging from cold chemistry to searches for physics beyond the Standard Model. Resonance-enhanced multiphoton ionisation (REMPI) can be used to prepare molecular ions in specific internal states with high fidelities. However, in the presence of electric fields, ionisation spectra exhibit frequency shifts and the ionisation thresholds are broadened. For this reason, REMPI studies are normally conducted in low and highly homogeneous electric fields, whereas the operating principle of rf ion traps requires electric fields that vary in space and time. In order to investigate the impact of this on the state-selectivity of REMPI in ion traps, we have simulated the expected broadening of the ionisation threshold under various operating conditions of a typical linear Paul trap. In many cases, the width of the ionisation threshold exceeds the separation between rotational energy levels, preventing state-selective ionisation. Careful choice of the trapping and laser parameters during loading can reduce this broadening, enabling state-selective ionisation in some instances. Where this strategy is not sufficient, the broadening can be reduced further by rapidly switching the trapping voltages off and on again during loading. This has been demonstrated experimentally for a Coulomb crystal of $$^{40}\hbox {Ca}^+$$ 40 Ca + ions without descrystallising it.