Real-time Kalman filter: Cooling of an optically levitated nanoparticle

Abstract

We demonstrate that a Kalman filter applied to estimate the position of an optically levitated nanoparticle, and operated in real-time within a Field Programmable Gate Array (FPGA), is sufficient to perform closed-loop parametric feedback cooling of the centre of mass motion to sub-Kelvin temperatures. The translational centre of mass motion along the optical axis of the trapped nanoparticle has been cooled by three orders of magnitude, from a temperature of 300K to a temperature of 162 ± 15mK.

Optimal control for feedback cooling in cavityless levitated optomechanics

“…It is thus reasonable to consider larger timesteps, Δt=M Δt E and D = D t C t N , for the measurement and tracking/control respectively, with  Î N M , . To simulate the current experimental capabilities presented in [13] we set N=5, M=2000 and Δt E =0.5 ns. We have verified numerically that such a value of Δt E provides with enough temporal resolution to simulate sufficiently well the evolution of the system.…”

“…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].…”

“…The Kalman filter, a filtering technique used in engineering applications [32][33][34][35], can be implemented in real-time to accurately estimate the state of the particle's position and velocity. This state information is then used to apply the modulating feedback signal [13,36]. Such schemes are very effective for estimating the particle motion for small laser modulation, but above a certain (low) threshold loses track of the particle.…”

Quantum State Smoothing for Linear Gaussian Systems

“…For filtering (ρ C = ρ F ), the PDF of unobserved records is In this Letter we present the theory of quantum state smoothing for Linear Gaussian Quantum (LGQ) systems. This can be applied to a large number of physical systems, e.g., multimodal light fields [23,24], optical and optomechanical systems [13,20,21,[25][26][27][28][29][30][31][32][33][34][35], atomic ensembles [36][37][38], and Bose-Einstein condensates [39]. Due to the nice properties of LGQ systems, we are able to obtain closed-form solutions for the smoothed LGQ state.…”

Static force characterization with Fano anti-resonance in levitated optomechanics

“…1). To stabilize the motion at low pressure p the nanoparticle is cooled using parametric feedback cooling [41][42][43] . The strong cooling confines the motion of the nanoparticle to small oscillations, δr = (δx, δy, δz) , around an equilibrium position, r eq.…”