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arXiv:1812.01230 · Physical Review A

Electric feedback cooling of single charged nanoparticles in an optical trap

M. Iwasaki, T. Yotsuya, Naruki Tsubasa, Yasuyoshi Matsuda, Mitsuyoshi Yoneda, K. Aikawa

Published May 16, 2019• 31 citations
arXivHTMLPDF

Abstract

We demonstrate feedback cooling of the center-of-mass motion of single charged nanoparticles to millikelvin temperatures in three dimensions via applying oscillating electric fields synchronized to their optically observed motion. The observed motional temperatures at weak feedback agree with a simple model and allow us to estimate the charge number of trapped nanoparticles. The agreement between our model and experiments is confirmed by independent measurements of the charge numbers based on a shift in the oscillation frequency induced by a constant electric field. The demonstrated temperature of less than $10\phantom{\rule{0.16em}{0ex}}\mathrm{mK}$ at $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{0.16em}{0ex}}\mathrm{Pa}$ is lower than that with the conventional optical cooling approach at this pressure by one to two orders of magnitude. Our results form the basis of manipulating cold charged nanoparticles and pave the way to quantum mechanical studies with trapped nanoparticles near their ground state.

DOI
10.1103/physreva.99.051401

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We demonstrate feedback cooling of the center-of-mass motion of single charged nanoparticles to millikelvin temperatures in three dimensions via applying oscillating electric fields synchronized to their optically observed motion. The observed motional temperatures at weak feedback agree with a simple model and allow us to estimate the charge number of trapped nanoparticles. The agreement between our model and experiments is confirmed by independent measurements of the charge numbers based on a shift in the oscillation frequency induced by a constant electric field. The demonstrated temperature of less than 10mK10\phantom{\rule{0.16em}{0ex}}\mathrm{mK}10mK at 4\ifmmode×\else\texttimes\fi10\ensuremath−3Pa4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\phantom{\rule{0.16em}{0ex}}\mathrm{Pa}4\ifmmode×\else\texttimes\fi10\ensuremath−3Pa is lower than that with the conventional optical cooling approach at this pressure by one to two orders of magnitude. Our results form the basis of manipulating cold charged nanoparticles and pave the way to quantum mechanical studies with trapped nanoparticles near their ground state.
We report on direct feedback cooling of single nanoparticles in an optical lattice to near their motional ground state. We find that the laser phase noise triggers severe heating of nanoparticles' motion along the optical lattice. When the laser phase noise is decreased by orders of magnitude, the heating rate is reduced and accordingly the occupation number is lowered to about 3. We establish a model directly connecting the heating rate and the measured laser phase noise and elucidate that the occupation number under the lowest laser phase noise in our system is limited only by photon recoil heating. Our results show that the reduction of the laser phase noise near the oscillation frequency of nanoparticles is crucial for bringing them near the ground state and pave the way to sensitive accelerometers and quantum mechanical experiments with ultracold nanoparticles in an optical lattice.
We demonstrate a simple and robust geometry for optical trapping in vacuum of a single nanoparticle based on a parabolic mirror and the optical gradient force, and we demonstrate rapid parametric feedback cooling of all three motional degrees of freedom from room temperature to a few mK. A single laser at 1550nm, and a single photodiode, are used for trapping, position detection, and cooling for all three dimensions. Particles with diameters from 26nm to 160nm are trapped without feedback to 10−5^{-5}−5mbar and with feedback engaged the pressure is reduced to 10−6^{-6}−6mbar. Modifications to the harmonic motion in the presence of noise and feedback are studied, and an experimental mechanical quality factor >4×107>4\times 10^7>4×107 is estimated.
We propose and demonstrate purely optical feedback cooling of neutral nanoparticles in an optical lattice to an occupation number of 0.85 ± 0.20. The cooling force is derived from the optical gradients of displaced optical lattices produced with two sidebands on the trapping laser. To achieve highly accurate position observations required for cooling near the ground state, we reduce the laser intensity noise to a relative power noise of 6×10−8/Hz in a frequency band of 30 kHz to 600 kHz. We establish a reproducible method for neutralizing nanoparticles at high vacuum via a combination of discharging and irradiating an ultraviolet light. Our results form an important basis for the investigation of quantum mechanical properties of ultracold nanoparticles and are also useful for precision measurements with neutral nanoparticles.
We develop the theory describing the quantum coupled dynamics of the center-of-mass motion of a nanoparticle and an ensemble of ions co-trapped in a dual-frequency linear Paul trap. We first derive analytical expressions for the motional frequencies and classical trajectories of both nanoparticle and ions. We then derive a quantum master equation for the ion-nanoparticle system and quantify the sympathetic cooling of the nanoparticle motion enabled by its Coulomb coupling to a continuously Doppler-cooled ion. We predict that motional cooling down to sub-kelvin temperatures is achievable in state-of-the-art experiments even in the absence of motional feedback and in the presence of micromotion. We then extend our analysis to an ensemble of NNN ions, predicting a linear increase of the cooling rate as a function of NNN and motional cooling of the nanoparticle down to tenths of millikelvin in current experimental platforms. Our work establishes the theoretical toolbox needed to explore the ion-assisted preparation of non-Gaussian motional states of levitated nanoparticles.