Number-Resolved Detection of Dark Ions in Coulomb Crystals

While it is straightforward to count laser-cooled trapped ions by fluorescence imaging, detecting the number of dark ions embedded and sympathetically cooled in a mixed ion crystal is more challenging. We demonstrate a method to track the number of dark ions in real time with single-particle sensitivity. This is achieved by observing discrete steps in the amount of fluorescence emitted from the coolant ions while exciting secular motional resonances of dark ions. By counting the number of fluorescence steps, we can identify the number of dark ions without calibration and without relying on any physical model of the motional excitation. We demonstrate the scheme by detecting H$_2^+$ and H$_3^+$ ions embedded in a Be$^+$ ion Coulomb crystal in a linear radio frequency trap. Our method allows observing the generation and destruction of individual ions simultaneously for different types of ions. Besides high-resolution spectroscopy of dark ions, another application is the detection of chemical reactions in real time with single-particle sensitivity. This is demonstrated in this work.