Feedback cooling a levitated nanoparticle's libration to below 100 phonons
Abstract: Macroscopic rotors are interesting model systems to test quantum theory and for quantum sensing. A promising approach for bringing these systems to the quantum regime is to combine sensitive detection with feedback cooling to reduce the thermal occupation of the mechanics. Here, we implement a backward-scattering scheme to efficiently detect all three libration modes of an optically levitated nanoparticle. We demonstrate parametric feedback cooling of all three libration degrees of freedom to below 16~mK, with one of the modes reaching the temperature of 1.3~mK, corresponding to a mean phonon number of 84. Finally, we characterize the backward-scattering scheme by determining its measurement efficiency to be 0.5\%.
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- We define our power spectral densities according to ⟨α2⟩=∫\ilimits@0∞S~αα(f)dfdelimited-⟨⟩superscript𝛼2superscriptsubscript\ilimits@0subscript~𝑆𝛼𝛼𝑓differential-d𝑓\langle\alpha^{2}\rangle=\intop\ilimits@_{0}^{\infty}\tilde{S}_{\alpha\alpha}(% f)\,\mathrm{d}f⟨ italic_α start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ⟩ = ∫ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ∞ end_POSTSUPERSCRIPT over~ start_ARG italic_S end_ARG start_POSTSUBSCRIPT italic_α italic_α end_POSTSUBSCRIPT ( italic_f ) roman_d italic_f.
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