Simulating Trapped Ion Crystals as Potential Superradiant Emitters
L. Iqbal
Superradiant lasers have emerged as a promising platform for optical frequency references due to their potential to achieve exceptionally narrow linewidths with reduced sensitivity to cavity noise. Trapped ion Coulomb crystals provide an attractive emitting medium due to their long coherence times, great environmental isolation and precise control over their motional dynamics. However, scaling trapped ion systems to the large ion numbers required for strong collective emission introduces new challenges, including crystal stability and position-dependent decoherence mechanisms. This work presents a numerical framework for modelling large Coulomb crystals confined within a linear Paul trap and assessing their suitability for superradiant lasing. A numerical simulation was developed to generate equilibrium crystal configurations, followed by a normal mode analysis to verify crystal’s dynamical stability and characterise the collective motional spectrum. The dependence of the crystal properties on the trapping parameters was examined, while the damping coefficient and integration timestep used in the numerical relaxation procedure were systematically optimised to obtain equilibrium configurations. The decoherence mechanisms expected to influence superradiant operation, including RF micromotion and electric quadrupole shifts, were also investigated as functions of ion number and trapping conditions. The simulations can produce accurate models of mechanically stable Coulomb crystals with up to 10,000 ions under appropriate relaxation conditions. They also show how the collective motional spectrum evolves across the trapping parameter space where they were also compared with the theoretical lasing threshold to assess the suitability of the trapping conditions for superradiant operation. Although the largest micromotion amplitudes increase with crystal size, a significant fraction of the ions remain confined close to the RF null, suggesting that large ion numbers may still be compatible with superradiant operation. The developed framework also provides a means of quantifying the quadrupole shift, indicating that the resulting frequency shifts are relatively small for the trapping parameters considered here, although further optimisation of the operating conditions is required to fully assess their influence on superradiant perfomance. Overall, the computational suite developed here establishes a versatile platform for studies of large Coulomb ion crystals and provides the tools to determine whether superradiant lasing thresholds can be reached with trapped ion crystals.
•Jan 1, 2026•0 citations