Pure nanodiamonds for levitated optomechanics in vacuum

Abstract

Optical trapping at high vacuum of a nanodiamond containing a nitrogen vacancy centre would provide a test bed for several new phenomena in fundamental physics. However, the nanodiamonds used so far have absorbed too much of the trapping light, heating them to destruction (above 800 K) except at pressures above ∼10 mbar where air molecules dissipate the excess heat. Here we show that milling diamond of 1000 times greater purity creates nanodiamonds that do not heat up even when the optical intensity is raised above 700 GW m −2 below 5 mbar of pressure.

Optimal control for feedback cooling in cavityless levitated optomechanics

“…on the modulation depth: if the modulation depth is too strong one risks losing track of the particle, or worse, losing the particle from the trap. In order to obtain the explicit expressions for the two control functions, one needs to solve the two coupled sets of equations (17)- (18). This is in general a hard task because, while the state equations (18) have initial boundary conditions and propagate forward in time, the co-state equations (17) have final boundary conditions (at the measurement time Δt) and propagate backward in time [59].…”

“…Levitated nanoparticles are extremely well isolated from their environment, opening up the possibility for very long decoherence times and ground state cooling in room temperature conditions. Indeed, optically levitated silica particles have had their centerof-mass motion cooled to millikelvin [11][12][13][14] and sub-millikelvin [15,16] temperatures, whereas nanodiamonds [17,18] have been used for spin coupling experiments [19,20]. Other levitation mechanisms, such as Paul traps [21], hybrid electro-optical traps [22], and magnetic traps [23][24][25] have also been proposed as candidates for preparing macroscopic quantum states [26][27][28] and testing spontaneous collapse models [29,30].…”

Measurement and feedback for cooling heavy levitated particles in low-frequency traps

“…All of the methods discussed are applicable to submicron sized Rayleigh scatterers that can be effectively treated as point dipoles. High quality nano-diamonds of this size have been produced for exactly the purpose of trapping and cooling [27]. Microscopic particles on the other hand would not usually be suitable for the subwavelength measurements suggested.…”

“…The applied feedback should limit this as much as possible, keeping the mean position and momentum values centred on zero. Using the equations for the mean position and momentum (27,28), and following the rules of Ito calculus, we can calculate the excess variances, which we have distinguished with a superscript 'E', The final state is always improved with stronger damping which effectively counteracts the measurement shot noise, as well as removing the initial thermal energy. The return for increasing Γ quickly drops off, and for moderate damping rates Γ > ω the steady state variances approach the ideal limits given by the measurement resolution.…”

“…To reach the lowest temperatures, k would ideally be kept as low as possible to avoid squeezing due to the measurement. There is a balance then between resolving the particle fast enough to outpace environmental Simulation of a damped levitated particle, using (27,28,18,19,20). The normalised measurement strength, κx 2 0 /ω = 1, with 10% quantum efficiency, and initial particle energy corresponding to a temperature of T = 1µK.…”