Fluorescence calorimetry of an ion crystal

Motivated by the challenge of identifying intruder ions in a cold ion crystal, we investigate calorimetry from emitted fluorescence light. Under continuous Doppler cooling, the ion crystal reaches a temperature equilibrium with a fixed level of fluorescence intensity and any change in the motional energy of the crystal results in a modification of this intensity. We theoretically determine the fluorescence rate of an ion crystal as a function of the temperature, assuming that laser light is scattered along a two-level electronic transition, which couples to the crystal's vibrations via the mechanical effects of light. We analyze how the heat dissipated by collisions of an incoming intruder ion alters the scattering rate. We argue that an energy change by an incoming $^{229}$Th$^{10+}$ ion can be unambiguously detected within 100 $\mu$s via illuminating a fraction of a 10$^{3}$ ion crystal. This method enables applications including capture and spectroscopy of charged states of thorium isotopes and investigation of highly charged ions.