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Interferometric position detection of levitated particles is crucial for the centre-of-mass (CM) motion cooling and manipulation of levitated particles. In combination with balanced detection and feedback cooling, this system has provided picometer scale position sensitivity, zeptonewton force detection, and sub-millikelvin CM temperatures. In this article, we develop an analytical model of this detection system and compare its performance with experimental results allowing us to explain the presence of spurious frequencies in the spectra.

A nitrogen-vacancy (NV(-)) centre in a nanodiamond, levitated in high vacuum, has recently been proposed as a probe for demonstrating mesoscopic centre-of-mass superpositions and for testing quantum gravity. Here, we study the behaviour of optically levitated nanodiamonds containing NV(-) centres at sub-atmospheric pressures and show that while they burn in air, this can be prevented by replacing the air with nitrogen. However, in nitrogen the nanodiamonds graphitize below ≈10 mB. Exploiting the Brownian motion of a levitated nanodiamond, we extract its internal temperature (T(i)) and find that it would be detrimental to the NV(-) centre's spin coherence time. These values of T(i) make it clear that the diamond is not melting, contradicting a recent suggestion. Additionally, using the measured damping rate of a levitated nanoparticle at a given pressure, we propose a new way of determining its size.