Testing fundamental physics with charged particle nano-oscillators

I will describe experiments that use nanoparticle oscillators formed by trapping a single or two charged silica nanoparticles in a Paul trap. The oscillators operate in high vacuum, and at room temperature, with microhertz mechanical linewidths. We characterise the important noise sources for this oscillator and outline a means to achieve even lower linewidths and higher mechanical quality factors for future experiments that aim to test the macroscopic limits of quantum mechanics. The stability of this oscillator, and our measurement of this ultra-narrow linewidth as a function of residual gas pressure, allows us to put experimental bounds for the first time on both the dissipative continuous spontaneous localisation and Diosi-Penrose models. Lastly, we demonstrate and compare different feedback cooling methods for a single oscillator and show how feedback cooling of a single co-trapped nanoparticle can be used to sympathetically cool the motion of the other oscillator. We show that this strong coupling can also be used for sympathetic squeezing and describe important future applications.