in resolved rotational states *

A precise deuteron-proton mass ratio enables precision laser and terahertz spectroscopy of HD⁺ to be used to test QED calculations and obtain an improved electron-proton mass ratio. Combined with a measurement of the atomic mass of the deuteron against carbon it also leads to a more precise value for the atomic mass of the proton. An advantageous approach to obtaining the deuteron-proton mass ratio is to measure the cyclotron frequency ratio of H₂⁺ to D⁺. This is because heavier ions are less subject to relativistic shifts to the cyclotron frequency, and higher precision can be obtained by measuring ions with similar mass-to-charge ratio and similar mass. Here we report measurements of the cyclotron frequency ratio of H₂⁺ to D⁺ with sufficient resolution that, in certain cases, will allow the identification of the rotational as well as the vibrational state of the H₂⁺ ion as it undergoes a sequence of ro-vibrational decays. This will enable us to precisely correct the measured H₂⁺ masses for rotational energy, which was a limitation in our previous measurement. The increased resolution is achieved by using the technique of simultaneous measurement of the cyclotron frequencies of two ions in a coupled cyclotron orbit.