Diamonds levitating in a Paul trap under vacuum: measurements of laser-induced heating via NV center thermometry

We present measurements of the Electronic Spin Resonance (ESR) of Nitrogen Vacancy (NV) centers in diamonds that are levitating in a ring Paul trap under vacuum. We observe ESR spectra of NV centers embedded in micron-sized diamonds at vacuum pressures down to $2\times 10^{-1}$ mbar, limited by the green laser heating of the diamond. We also observe the NV photoluminescence at vacuum pressures down to $10^{-2}$ mbar and discuss the steps required to control the NV spin under ultra-high vacuum.